Survival Lung Cancer Event (0,1) Modeling With Python & R
- Images, Radiomics and Clinical data Exploration.
- xgboost modeling with Masks slides
- xgboost modeling with Masks + Features (Radiomics & Clinical data)
- RF Survival Model (Ranger package) and GBM with Features
- xgboost modeling with Masks slides
- xgboost modeling with Masks + Features (Radiomics & Clinical data)
- RF Survival Model (Ranger package) and GBM with Features
Karim Mezhoud
2020-02-13
- 1 Description
- 2 Tumor Arrays Slides Exploration
- 3 R xgboost with best masks
- 4 Python xgboost with best masks
- 5 Exploratory Data Analysis of radiomics and clinical data
- 6 Preprocessing of Train and Test dataset
- 7 Pull Radiomics, Clinical data and the best Masks
- 8 R Xgboost modeling with Radiomics, Clinical and Masks
- 8.1 Scaling Train and Test dataset
- 8.2 Split Train dataset into Train & Valid sets
- 8.3 Format train and test to DMatrix
- 8.4 Optimize features with Cross validation
- 8.5 Train the model
- 8.6 Predict valid_2 dataset
- 8.7 Transform propability to binary classification
- 8.8 Confusion matrix for Tree model and performances
- 8.9 Extract the most important features from tree xgboost model
- 8.10 Test Xgboost Prediction
- 8.11 submission
- 9 Python xgboost Prediction (Python, Radiomics, Clinical, Masks datasets)
- 10 Random Forest Survival model (ranger package)
In pdf format, some plots are crowded. Please follow this link to html format.
Source of the datasets
1 Description
This report is subset into 3 parts:
Exploratory of tumor arrays slides using python code
Exploratory radiomics, and clinical data (train) using R code
Prediction Event by: xgboost, RF, GBM
1.1 Clinical Context
Computed Tomography scanner (CT scan) is a widely spread and popular exam in oncology: it reflects the density of the tissues of the human body. It is, then, adapted to the study of lung cancer because lungs are mostly filled with air (low density) while tumors are made of dense tissues.
1.2 Clinical context
Small Cell Lung Cancer can itself be split into four major subtypes based on histology observations: squamous cell carcinoma, large cell carcinoma, adenocarcinoma and a mixture of all
1.3 Goal
Predict the survival time of a patient (remaining days to live) from one three-dimensional CT scan (grayscale image) and a set of pre-extracted quantitative imaging features, as well as clinical data.
1.4 dataset
To each patient corresponds one CT scan, and one binary segmentation mask. The segmentation mask is a binary volume of the same size as the CT scan, except that it is composed of zeroes everywhere there is no tumour, and 1 otherwise. The CT scans and the associated segmentation masks are subsets of two public datasets:
- NSCLC Radiomics (subset of 285 patients)
- NSCLC RadioGenomics(subset of 141 patients)
Both training and validation contain for each patient, the time to event (days), as well as the censorship. Censorship indicates whether the event (death) was observed or whether the patient escaped the study: this can happen when the patient’s track was lost, or if the patient died of causes not related to the disease.
2 Tumor Arrays Slides Exploration
2.1 Setting python version and anaconda environment for R :-)
reticulate::use_python("/Library/Frameworks/Python.framework/Versions/3.7/bin/python3", required = TRUE)
#reticulate::use_python("/Users/Mezhoud/anaconda3/bin/python3", required = TRUE)
reticulate::py_config()## python: /Library/Frameworks/Python.framework/Versions/3.7/bin/python3
## libpython: /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/config-3.7m-darwin/libpython3.7.dylib
## pythonhome: /Library/Frameworks/Python.framework/Versions/3.7:/Library/Frameworks/Python.framework/Versions/3.7
## version: 3.7.3 (v3.7.3:ef4ec6ed12, Mar 25 2019, 16:52:21) [Clang 6.0 (clang-600.0.57)]
## numpy: /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/numpy
## numpy_version: 1.18.1
##
## NOTE: Python version was forced by use_python functionknitr::opts_chunk$set(engine.path = list(
python = '/Library/Frameworks/Python.framework/Versions/3.7/bin/python3'
))
# check xgboost module
reticulate::py_module_available("seaborn")## [1] TRUE2.2 Load scans and masks of Tumor lung cancer
import numpy as np
from matplotlib import pyplot as plt
#from matplotlib import pyplot
from PIL import Image
img_array = np.load('train/images/patient_002.npz')
scan = img_array['scan']
mask = img_array['mask']
print("the dimension of scan array is: ", str(scan.shape))## the dimension of scan array is: (92, 92, 92)## the dimension of mask array is: (92, 92, 92)## plot some images from patient 002:f, axarr = plt.subplots(2,3)
axarr[0,0].imshow(scan[1:92, 1:92, 0])
axarr[1,0].imshow(mask[1:92, 1:92, 0])
axarr[0,1].imshow(scan[:, :, 3])
axarr[1,1].imshow(mask[:, :, 3])
axarr[0,2].imshow(scan[:, :, 80])
axarr[1,2].imshow(mask[:, :, 80])
2.2.1 Function to plot multiple image from array
def plot_figures(figures, nrows = 1, ncols=1):
"""Plot a dictionary of figures.
Parameters
----------
figures : <title, figure> dictionary
ncols : number of columns of subplots wanted in the display
nrows : number of rows of subplots wanted in the figure
"""
fig, axeslist = plt.subplots(ncols=ncols, nrows=nrows)
for ind,title in zip(range(len(figures)), figures):
axeslist.ravel()[ind].imshow(figures[title], cmap=plt.jet())
axeslist.ravel()[ind].set_title(title)
axeslist.ravel()[ind].set_axis_off()
plt.tight_layout()
img_array = np.load('train/images/patient_002.npz')
scan = img_array['scan']
mask = img_array['mask']
# generation of a dictionary of (title, images)
number_of_im = 6
scan = {'scan'+str(i): scan[1:92, 1:92, i] for i in range(number_of_im)}
# plot of the images in a figure, with 5 rows and 4 columns
plot_figures(scan, 2, 3)
plt.show()
The plot shows colored images scan of 6 slides. At this step it is not easy to distinguish the tumor.
The dataset has aslo the masks for each scan slide which locate the position of the tumor in the scan.
mask = {'mask'+str(i): mask[1:92, 1:92, i] for i in range(number_of_im)}
# plot of the images in a figure, with 5 rows and 4 columns
plot_figures(mask, 2, 3)
plt.show()
The first 3 slides do not have tumor streak, however the next 3 ones indicate the position of the tumor in red color.
If we plot more slides, we can observe the increase of the size of the tumor during plotting slides.
At the end the size the Tumor is decreasing.
We can note that the crop is adjusted to the size of the tumor
img_array = np.load('train/images/patient_002.npz')
scan = img_array['scan']
mask = img_array['mask']
mask = {'mask'+str(i): mask[1:92, 1:92, i] for i in range(90)}
# plot of the images in a figure, with 5 rows and 4 columns
plot_figures(mask, 9, 10)
plt.show()
- We can select the representative mask per patient by the sum of pixels (0,1). The matrix with higher value can be selected to represent owner patient.
If we compare with the scan slides, we obtain:
scan = {'scan'+str(i): scan[1:92, 1:92, i] for i in range(90)}
# plot of the images in a figure, with 5 rows and 4 columns
plot_figures(scan, 9, 10)
plt.show()
It is always not easy to delimit the tumor in scan images
Comparing to masks, we can note that, between scan 34 and scan 65, the slides have more yellow stain or less blue color.
2.2.2 Superimposing Scan and Mask images
import numpy as np
from matplotlib import pyplot as plt
from PIL import Image
img_array = np.load('train/images/patient_002.npz')
scan = img_array['scan']
mask = img_array['mask']
background = mask[1:92, 1:92, 56]
overlay = scan[1:92, 1:92, 56]
plt.title("Scan/Mask: 56")
plt.imshow(background, cmap='gray')
plt.imshow(overlay, cmap='jet', alpha=0.9)
- It is now clear that masks seems to be more useful that scans because the tumor in not visible in scan slides.
2.3 Load images from test dataset
img_array = np.load('test/images/patient_001.npz')
scan = img_array['scan']
mask = img_array['mask']
# generation of a dictionary of (title, images)
number_of_im = 90
scan = {'scan'+str(i): scan[1:92, 1:92, i] for i in range(number_of_im)}
# plot of the images in a figure, with 5 rows and 4 columns
plot_figures(scan, 9, 10)
plt.show()
- Plot mask slides from test dataset
mask = {'mask'+str(i): mask[1:92, 1:92, i] for i in range(number_of_im)}
# plot of the images in a figure, with 5 rows and 4 columns
plot_figures(mask, 9, 10)
plt.show()
- Superimpose mask and scan slide from test dataset
img_array = np.load('test/images/patient_001.npz')
scan = img_array['scan']
mask = img_array['mask']
background = mask[1:92, 1:92, 35]
overlay = scan[1:92, 1:92, 35]
plt.title("Scan/Mask: 35")
plt.imshow(background, cmap='gray')
plt.imshow(overlay, cmap='jet', alpha=0.9)
In the test images, we can also observe tumor slides like in train dataset.
For training step, it maybe better to use masks slides than scan. But we need to explore variables in clinical data and radiomics and think how to associate images with numeric variables.
One think we can do is the convert slides to dataframe (each slide in one row) and then we can obtain one matrix for each patient tumor.
At this step I will switch from python to R :-)
2.4 Import image from python environment to R
The goal of this step is to convert image matrices as a vector. So, each image can be ranged in one row. Finally, we can obtain one dataframe with 92 rows (images) for each sample (patient).
2.4.1 Import useful R packages
2.4.1.1 Useful python function
2.4.1.2 Understanding the structure of the array of images
patient_002 <- reticulate::py$load_img_array('train/images/patient_002.npz')
paste0("One image is a: ", class(patient_002[[1]][,,1]))## [1] "One image is a: matrix"## [1] "Two images are an: array"## [1] "Print the first 10 pixels of Scan N°1: "## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] -777 -759 -707 -697 -749 -796 -826 -837 -858 -860
## [2,] -783 -791 -774 -768 -787 -808 -827 -826 -829 -829
## [3,] -804 -841 -827 -812 -820 -840 -831 -801 -792 -794
## [4,] -830 -857 -839 -816 -805 -818 -801 -764 -734 -722
## [5,] -844 -854 -843 -823 -799 -787 -771 -743 -704 -670
## [6,] -844 -849 -844 -831 -821 -810 -809 -791 -760 -719
## [7,] -848 -847 -848 -844 -847 -841 -849 -841 -829 -806
## [8,] -847 -856 -854 -846 -840 -813 -826 -849 -848 -836
## [9,] -840 -851 -836 -823 -835 -796 -803 -853 -857 -833
## [10,] -847 -841 -829 -817 -860 -832 -799 -842 -865 -838## [1] "Print the first 10 pixels of Mask N°1: "## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [4,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [5,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [6,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [7,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE2.4.1.3 Convert the array of matrices to a list of matrices
ls_scan_patient_002 <- lapply(seq(dim(patient_002[[1]])[3]), function(x) patient_002[[1]][ , , x])
ls_mask_patient_002 <- lapply(seq(dim(patient_002[[2]])[3]), function(x) patient_002[[2]][ , , x])
paste0("The dimension of the scan images is: ", length(ls_scan_patient_002))## [1] "The dimension of the scan images is: 92"## [1] "The dimension of the mask images is: 92"2.4.1.4 Convert image matrix to vector
mat2vec <- function(path, target = 'mask'){
# Load patient CT scan
patient <- py$load_img_array(path)
#### For scans
if('scan' %in% target){
# list scans
scan <- lapply(seq(dim(patient[[1]])[3]), function(x) patient[[1]][ , , x])
# vectorize each matrix (image) into vector
vec_scan <- lapply(scan, function(x) as.vector(x))
# bind vector into dataframe by row
df_scan <-as.data.frame( do.call(rbind, vec_scan))
# extract patient_id from path
scan_id <- paste0(tools::file_path_sans_ext(basename(path)), "_scan")
}
#### For Masks
if('mask' %in% target){
# list masks
mask <- lapply(seq(dim(patient[[2]])[3]), function(x) patient[[2]][ , , x])
# vectorise each mask (image) to vector
vec_mask <- lapply(mask, function(x) as.vector(x))
# bind vector into dataframe by row
df_mask <-as.data.frame( do.call(rbind, vec_mask))
# extract patient_id from path
mask_id <- paste0(tools::file_path_sans_ext(basename(path)), "_mask")
}
if("scan" %in% target && "mask" %in% target){
# group in list the scan and the mask dataframes
ls <- list(df_scan, df_mask)
# Rename list
names(ls) <- c(scan_id, mask_id)
return(ls)
} else if(target == "scan"){
names(df_scan) <- scan_id
return(df_scan)
}else{
#ls <- list(df_mask)
#names(ls) <- mask_id
return(df_mask)
}
}
patient2 <- mat2vec('train/images/patient_002.npz', target = c("mask", "scan"))
paste0("The output is a: ", class(patient2))## [1] "The output is a: list"## [1] "With length of: 2"## [1] "The names of two elements are: "## [1] "patient_002_scan" "patient_002_mask"## [1] "which are: data.frame"## [1] "The dimension of each dataframe is: "## [1] 92 8464We think to use only masks for modeling
Potential method: keras, mxnet
The training dataset must contain 92 rows corresponding to 92 masks of each patient. The first column is the Event (target) of each patient. The remain columns are the pixel intensity or in our case (0,1) tags which delimit the tumor if exists.
2.4.1.5 Select only the best mask for each Patient
We consider that the mask that has more TRUE is the best representative slide for patient. The idea is to convert all matrices to vectors and count the value TRUE for each row.
masks2 <- mat2vec('train/images/patient_002.npz', target = c("mask"))
## display the sum of TRUE in each row for Patient002
paste("Number of TRUE in each slide for Patient_002:") ; rowSums(masks2)## [1] "Number of TRUE in each slide for Patient_002:"## [1] 0 0 0 55 60 60 195 209 209 504 548 548 1158 1256 1276
## [16] 1737 1809 1835 2353 2429 2474 2870 2920 2960 3225 3251 3280 3537 3567 3546
## [31] 3619 3619 3608 3558 3557 3557 3537 3534 3534 3664 3668 3671 3872 3911 3928
## [46] 3994 4025 4026 3818 3822 3806 3553 3492 3495 3552 3520 3503 2973 2913 2887
## [61] 2080 2024 1988 1479 1479 1460 1257 1293 1289 1175 1192 1199 663 679 674
## [76] 901 922 924 771 741 755 745 671 654 622 255 237 206 0 0
## [91] 0 0get_best_mask <- function(masks){
# Display the biggest row with TRUE value
Case <- masks[sort(rowSums(masks), index=TRUE, decreasing=TRUE)$ix, ][1,]
#d <- cbind(`Patients` = as.character(names(masks)),Case)
return(Case)
}
masks2[sort(rowSums(masks2), index=TRUE, decreasing=TRUE)$ix, ][1,][1:10]## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
## 48 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE2.4.1.6 Convert all images to matrices, each matrix corresponds to one patient
require(stringr)
require(data.table)
get_best_masks_img2mat <- function(path){
list_path <- as.list(list.files(path,full.names = TRUE))
list_matrices <- lapply(list_path, function(x) mat2vec(x, target = c("mask")))
best_masks <- lapply(list_matrices, function(x) get_best_mask(x))
nm <- lapply(list_path, function(x) str_remove(tools::file_path_sans_ext(basename(x)), "patient_"))
#names(best_masks) <- as.numeric(nm)
#img_df <- bind_rows(best_masks)
img_df <- data.table::rbindlist(best_masks)*1
row.names(img_df) <- nm
df_img <- tibble::rownames_to_column(img_df, "PatientID")
return(df_img)
}
img_tr <- get_best_masks_img2mat("train/images/")
img_ts <- get_best_masks_img2mat("test/images/")
output_train <- data.table::fread("output_train.csv")
output_test <- data.table::fread("output_test.csv")
train_img <- img_tr %>%
mutate(PatientID = as.numeric(PatientID)) %>%
left_join(output_train, by = "PatientID") %>%
select(PatientID, SurvivalTime, Event, everything()) #%>%
#setDT() # convert to data.table
test_img <- img_ts %>%
mutate(PatientID = as.numeric(PatientID)) %>%
left_join(output_test, by = "PatientID") %>%
select(PatientID, SurvivalTime, Event, everything())#%>%
#setDT() # convert to data.table
train_img[1:5,1:10]## PatientID SurvivalTime Event V1 V2 V3 V4 V5 V6 V7
## 1 2 638 0 0 0 0 0 0 0 0
## 2 3 421 0 0 0 0 0 0 0 0
## 3 4 465 1 0 0 0 0 0 0 0
## 4 5 1295 1 0 0 0 0 0 0 0
## 5 7 1393 0 0 0 0 0 0 0 03 R xgboost with best masks
3.1 Split Train dataset into Train & Valid sets
require(rsample)
train_img <- data.table::fread("train_img.csv")
test_img <- data.table::fread("test_img.csv")
# remove PatientID column
train_img[,PatientID:= NULL]
test_img[,Event :=NULL]
set.seed(100)
train_valid_split <- rsample::initial_split(train_img, prop = 0.8)
train_valid_split## <241/59/300>## SurvivalTime Event V1 V2 V3 V4 V5
## 1: 638 0 0 0 0 0 0
## 2: 421 0 0 0 0 0 0
## 3: 465 1 0 0 0 0 0
## 4: 1295 1 0 0 0 0 0
## 5: 1393 0 0 0 0 0 0
## ---
## 296: 528 1 0 0 0 0 0
## 297: 1503 0 0 0 0 0 0
## 298: 315 0 0 0 0 0 0
## 299: 360 1 0 0 0 0 0
## 300: 515 1 0 0 0 0 0- We can retrieve our training and testing sets using training() and testing() functions.
# Retrieve train and test sets
train_8 <- rsample::training(train_valid_split)
valid_2 <- rsample::testing(train_valid_split)
train_8[1:10, 1:10]## SurvivalTime Event V1 V2 V3 V4 V5 V6 V7 V8
## 1: 638 0 0 0 0 0 0 0 0 0
## 2: 421 0 0 0 0 0 0 0 0 0
## 3: 465 1 0 0 0 0 0 0 0 0
## 4: 1393 0 0 0 0 0 0 0 0 0
## 5: 1076 1 0 0 0 0 0 0 0 0
## 6: 87 1 0 0 0 0 0 0 0 0
## 7: 98 1 0 0 0 0 0 0 0 0
## 8: 316 0 0 0 0 0 0 0 0 0
## 9: 65 1 0 0 0 0 0 0 0 0
## 10: 476 1 0 0 0 0 0 0 0 03.2 Format train and test to DMatrix (R, Masks)
require(Matrix)
require(xgboost)
# the option na.pass avoids missing value in age column
options(na.action='na.pass')
train_8_sparse <- sparse.model.matrix(Event ~., data=train_8)
dtrain_8 <- xgb.DMatrix(data=train_8_sparse, label = train_8$Event)
options(na.action='na.pass')
valid_2_sparse <- sparse.model.matrix(Event ~., data=valid_2)
dvalid_2 <- xgb.DMatrix(data=valid_2_sparse, label = valid_2$Event)3.3 Optimize features with Cross validation
Here, we can see after how many rounds, we achieved the smallest test error.
params <- list(booster = "gbtree",
tree_method = "auto",
objective = "binary:logistic",
eval_metric = "auc", # for Binary classification error rate
max_depth = 2, # 6 makes training heavy, there is no correlation between features #1 is not better
eta = 0.03, # learning rate
subsample = 0.8, # prevent overfitting
colsample_bytree = 0.1 # specify the fraction of columns to be subsampled. # 0.5 is not better
)
tme <- Sys.time()
cv_model <- xgb.cv(params = params,
data = dtrain_8,
nthread = parallel::detectCores(all.tests = FALSE, logical = TRUE), #2,
nrounds = 25000,
verbose = TRUE,
nfold = 7,
print_every_n = 500,
early_stopping_rounds = 1000,
maximize = TRUE,
prediction = TRUE) # prediction of cv folds## [1] train-auc:0.682223+0.055012 test-auc:0.569252+0.097524
## Multiple eval metrics are present. Will use test_auc for early stopping.
## Will train until test_auc hasn't improved in 1000 rounds.
##
## [501] train-auc:0.995171+0.000974 test-auc:0.731163+0.052885
## [1001] train-auc:0.999758+0.000141 test-auc:0.734070+0.056987
## [1501] train-auc:0.999919+0.000033 test-auc:0.731769+0.050985
## Stopping. Best iteration:
## [607] train-auc:0.997563+0.000629 test-auc:0.738315+0.050803## Time difference of 2.06715 mins3.4 Train the model
watchlist <- list(train = dtrain_8, eval = dvalid_2)
tme <- Sys.time()
xgboost_tree_img <- xgb.train(data = dtrain_8,
params = params,
watchlist = watchlist,
nrounds = cv_model$best_iteration, # more than 12000 ~0.897
print_every_n = 500,
verbose = TRUE)## [1] train-auc:0.673327 eval-auc:0.594706
## [501] train-auc:0.992188 eval-auc:0.852941
## [607] train-auc:0.996197 eval-auc:0.851765## Time difference of 8.565483 secs## Predict valid_2 dataset
pred_valid_img <- predict(xgboost_tree_img, dvalid_2)
paste0('SUMMARY: '); summary(pred_valid_img)## [1] "SUMMARY: "## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1078 0.3356 0.6286 0.5908 0.8195 0.9572# We suppose that if Prob > 0.5 (Median), the Event is 1, else 0
pred_bin_img <- as.numeric(pred_valid_img >= 0.5)
paste("RATIO: "); table(pred_bin_img)## [1] "RATIO: "## pred_bin_img
## 0 1
## 21 38## Confusion matrix for Tree model
data.frame(prediction = as.numeric(pred_bin_img),
label = as.numeric(valid_2$Event)) %>%
count(prediction, label)## # A tibble: 4 x 3
## prediction label n
## <dbl> <dbl> <int>
## 1 0 0 16
## 2 0 1 5
## 3 1 0 9
## 4 1 1 293.5 Prediction with (R, Masks)
test_sparse <- sparse.model.matrix(PatientID ~., data=test_img)
dtest <- xgb.DMatrix(data=test_sparse, label = test_img$PatientID)
pred_tree_img <- predict(xgboost_tree_img, dtest)
pred_bin_xgboost_img <- as.numeric(pred_tree_img >= 0.5)
print("ratio of predicted Events in test datset: "); table(pred_bin_xgboost_img)## [1] "ratio of predicted Events in test datset: "## pred_bin_xgboost_img
## 0 1
## 54 71## [1] "ratio of Events in train datset: "##
## 0 1
## 138 162## submission
pred_img <- data.frame(
PatientID = test_img$PatientID,
Event = pred_tree_img
)
output_test <- fread("output_test.csv")
submission_img <- output_test %>%
select(PatientID, SurvivalTime) %>%
left_join(pred_img, by = "PatientID")
fwrite(submission_img, "submission_img.csv")
## Refresh memory
rm(list=ls())
invisible(gc())4 Python xgboost with best masks
import matplotlib
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import seaborn as sns
from sklearn.model_selection import train_test_split
import xgboost
test_img = pd.read_csv("test_img.csv")
train_img = pd.read_csv("train_img.csv")
# Set weed
SEED = 1423
#test_img.pop('PatientID')
#test_img.pop('Event')
#test_img.head()# split data into train and test portions and model
features = [feat for feat in list(train_img) if feat != 'Event']
X_train, X_valid, y_train, y_valid = train_test_split(train_img[features],
train_img[['Event']],
test_size=0.3,
random_state=SEED)
import xgboost as xgb
xgb_params = {
'max_depth':3,
'eta':0.01,
'silent':0,
'eval_metric':'auc',
'subsample': 0.8,
'colsample_bytree': 0.8,
'objective':'binary:logistic',
'seed' : 1423
}
dtrain = xgb.DMatrix(X_train, y_train, feature_names=X_train.columns.values)
dvalid = xgb.DMatrix(X_valid, y_valid, feature_names=X_valid.columns.values)
evals = [(dtrain,'train'),(dvalid,'eval')]
xgb_model_img = xgb.train ( params = xgb_params,
dtrain = dtrain,
num_boost_round = 5000,
verbose_eval=200,
early_stopping_rounds = 500,
evals=evals,
maximize = True)## [0] train-auc:0.847485 eval-auc:0.81475
## Multiple eval metrics have been passed: 'eval-auc' will be used for early stopping.
##
## Will train until eval-auc hasn't improved in 500 rounds.
## [200] train-auc:0.961917 eval-auc:0.85
## [400] train-auc:0.983145 eval-auc:0.8545
## [600] train-auc:0.995171 eval-auc:0.858
## [800] train-auc:0.998907 eval-auc:0.857
## [1000] train-auc:0.999818 eval-auc:0.8555
## Stopping. Best iteration:
## [615] train-auc:0.995809 eval-auc:0.8595# get dataframe version of important feature for model
xgb_img_imp = pd.DataFrame(list(xgb_model_img.get_fscore().items()),
columns = ['feature','importance']).sort_values('importance', ascending=False)
xgb_img_imp.head(10)## feature importance
## 0 SurvivalTime 899
## 14 PatientID 430
## 2 V4823 82
## 94 V4620 74
## 130 V6370 73
## 231 V3701 61
## 105 V3539 53
## 104 V4639 48
## 52 V5538 48
## 39 V6018 45# Confusion matrix
dval_predictions = xgb_model_img.predict(dvalid)
from sklearn.metrics import confusion_matrix
cm = confusion_matrix(y_valid, [1 if p > 0.5 else 0 for p in dval_predictions])
plt.figure(figsize = (6,4))
plt.ticklabel_format(style='plain', axis='y', useOffset=False)
sns.set(font_scale=1.4)
sns.heatmap(cm, annot=True, annot_kws={"size": 16})
plt.show()
# evaluate predictions
from sklearn.metrics import accuracy_score
predictions_img = [round(value) for value in dval_predictions]
accuracy = accuracy_score(y_valid, predictions_img)
print("Accuracy: %.2f%%" % (accuracy * 100.0))## Accuracy: 78.89%4.1 Prediction (Python,Masks)
dtest = xgb.DMatrix(test_img.drop('PatientID', axis=1), feature_names=X_train.columns.values)
dtest_predictions = xgb_model_img.predict(dtest)
dtest_predictions[dtest_predictions > 0.5] = 1
dtest_predictions[dtest_predictions <= 0.5] = 0
output_test = pd.read_csv("output_test.csv", index_col = False)
#submission_img_p['Event'] = np.where(submission_img_p['Event'] >0.5, 1, 0)
# Format predictions in DataFrame: prediction_df
#prediction_df = pd.DataFrame(PatientID = test_img['PatientID'] ,
# Event = predictions_img)
#output_test.join(submission_img.set_index('PatientID'), on='PatientID')
output_test['Event'] = dtest_predictions
output_test.to_csv("submission_img_p.csv", index=False)
## save predictions for an ensemble
#pickle.dump(Y_pred, open('xgb_train.pickle', 'wb'))
#pickle.dump(Y_test, open('xgb_test.pickle', 'wb'))5 Exploratory Data Analysis of radiomics and clinical data
#Load dataset
radiomics <- fread("train/features/radiomics.csv", quote = "")
clinical <- fread("train/features/clinical_data.csv")
# display only 8 columns and 5 rows
head(radiomics)[,1:8]## V1 V2 V3
## 1: shape shape
## 2: original_shape_Compactness1 original_shape_Compactness2
## 3: PatientID
## 4: 202 0.027815034 0.274891585
## 5: 371 0.02301549 0.188210005
## 6: 246 0.027348106 0.265739895
## V4 V5
## 1: shape shape
## 2: original_shape_Maximum3DDiameter original_shape_SphericalDisproportion
## 3:
## 4: 48.55924217 1.537964054
## 5: 75.70336849 1.744961158
## 6: 70.43436661 1.555420243
## V6 V7
## 1: shape shape
## 2: original_shape_Sphericity original_shape_SurfaceArea
## 3:
## 4: 0.650210255 5431.33321
## 5: 0.573078659 10369.56873
## 6: 0.642913068 10558.81869
## V8
## 1: shape
## 2: original_shape_SurfaceVolumeRatio
## 3:
## 4: 0.275227763
## 5: 0.240726824
## 6: 0.200765988## PatientID Histology Mstage Nstage SourceDataset Tstage age
## 1: 202 Adenocarcinoma 0 0 l2 2 66.0000
## 2: 371 large cell 0 2 l1 4 64.5722
## 3: 246 squamous cell carcinoma 0 3 l1 2 66.0452
## 4: 240 nos 0 2 l1 3 59.3566
## 5: 284 squamous cell carcinoma 0 3 l1 4 71.0554
## 6: 348 squamous cell carcinoma 0 2 l1 2 65.0212The radiomics features can be divided into 4 groups as follows (shown in row 1): - Group 1. First order statistics - Group 2. Shape and size based features - Group 3. Textural features - Group 4. Wavelet features
Each group can be subset into several sub-groups shown in row 2 of the radiomics dataset. To make the radiomics features numeric dataset we need to remove the two first rows and convert them to colnames.
groups <- radiomics[1:2,-1] %>%
t() %>%
as.data.frame() %>%
rename("Groups" = V1, "Features" = V2) #%>%
# remove_rownames()
head(groups)## Groups Features
## V2 shape original_shape_Compactness1
## V3 shape original_shape_Compactness2
## V4 shape original_shape_Maximum3DDiameter
## V5 shape original_shape_SphericalDisproportion
## V6 shape original_shape_Sphericity
## V7 shape original_shape_SurfaceAreaTo improve the esthetic of the dataframe, we note:
originalis repetitive word. we can omit it.The group label is included in Feature label except
texturalWe can remove
originalfrom Features and use use the rest as colnames of the radiomics dataset.
5.1 Plot the distribution of Goups and features
groups %>%
group_by(Groups, Features) %>%
summarise(n_Features = n()) %>%
ggplot() +
aes(x = Groups, y = n_Features, color = Features ) +
geom_col() +
theme(legend.position = "none") +
ggtitle("Number of Features by Group")
5.1.1 Set New Colnames of radiomics
new_colnames_radiomics <- groups %>%
mutate(Features = stringr::str_remove(Features,"original_")) %>%
pull(Features)
new_colnames_radiomics %>% head()## [1] "shape_Compactness1" "shape_Compactness2"
## [3] "shape_Maximum3DDiameter" "shape_SphericalDisproportion"
## [5] "shape_Sphericity" "shape_SurfaceArea"5.1.2 Get new radiomics style
old_names <- colnames(radiomics)
new_names <- c("PatientID", new_colnames_radiomics)
new_radiomics <- radiomics[-1:-3,] %>%
rename_at(vars(old_names), ~ new_names) %>%
mutate_if(is.character, as.numeric) #%>%
#as.matrix()
head(new_radiomics)[,1:8]## PatientID shape_Compactness1 shape_Compactness2 shape_Maximum3DDiameter
## 1 202 0.02781503 0.2748916 48.55924
## 2 371 0.02301549 0.1882100 75.70337
## 3 246 0.02734811 0.2657399 70.43437
## 4 240 0.02681111 0.2554064 46.81880
## 5 284 0.02369124 0.1994242 53.79591
## 6 348 0.03098136 0.3410383 63.74951
## shape_SphericalDisproportion shape_Sphericity shape_SurfaceArea
## 1 1.537964 0.6502103 5431.333
## 2 1.744961 0.5730787 10369.569
## 3 1.555420 0.6429131 10558.819
## 4 1.576120 0.6344693 4221.412
## 5 1.711620 0.5842418 5295.900
## 6 1.431305 0.6986630 8493.134
## shape_SurfaceVolumeRatio
## 1 0.2752278
## 2 0.2407268
## 3 0.2007660
## 4 0.3238780
## 5 0.3272407
## 6 0.19760175.2 Glimpse correlation between features (default order)
M <- cor(new_radiomics[-1])
#corrplot(M, method = "circle")
corrplot.mixed(M, tl.col="black", tl.pos = "lt")
5.2.1 Set the first principal component order of the features
5.3 Explore Clinical data for Train
p1 <- clinical %>%
group_by(Histology = stringi::stri_trans_totitle(Histology)) %>% # case insensitive of adenocarcinoma and Adenocarcinoma
group_by(Histology) %>%
summarise(Count = n()) %>%
ggplot()+
aes(x = Histology, y = Count, fill= Histology) +
geom_col()+
geom_text(aes(label = percent(Count/sum(Count))), vjust = -0.5)+
geom_text(aes(label = Count), vjust = -2) +
theme(axis.text.x = element_text(color="black",size=10,hjust=.5,vjust=.5, angle=5))
p2 <- ggplot(data=clinical[!is.na(clinical$age),]) +
aes(x= age) +
geom_histogram(fill="blue", bins = 60) +
geom_vline(xintercept = c(65,70, 72 ), color = "red")
#coord_flip()
p3 <- clinical %>%
mutate(Nstage = as.factor(Nstage)) %>%
group_by(Mstage, Nstage, Tstage) %>%
summarise(Count = n()) %>%
ggplot() +
aes(x = Tstage, y = Count, color = Nstage) +
facet_grid(Mstage~ .) +
geom_point(size=4, alpha = 0.8)
p4 <- clinical %>%
group_by(SourceDataset) %>%
summarise(Count = n()) %>%
ggplot()+
aes(x = "", y = Count, fill = SourceDataset) +
geom_bar(width = 1, stat = "identity") +
coord_polar("y", start=0) +
theme(legend.position = "top")
grid.arrange(p1,p2,p3,p4, layout_matrix = rbind(c(1),c(2, 3, 4)), nrow = 2)
The most frequente cases is
Adenocarcinomafollowed byAquamous Cell Carcinoma.NOS: not otherwise specified
It seems
NOSandNsclc Noscorespond to the same categoryNanis not available ?The density plot shows that the must frequent cases are
65, 70, 72years old.
_ The most frequent Nstage class is also 0, followed by 2, 3, and 1.
The third plots shows that the most cases are in
Mstage == 0. We can focus only in this class.There are two sources of dataset.
5.4 Explore output_train and output_test
output_train <- fread("output_train.csv")
output_test <- fread("output_test.csv")
head(output_train)## PatientID SurvivalTime Event
## 1: 202 1378 0
## 2: 371 379 1
## 3: 246 573 1
## 4: 240 959 0
## 5: 284 2119 0
## 6: 348 706 1## PatientID SurvivalTime Event
## 1: 13 788.4177 NaN
## 2: 155 427.6501 NaN
## 3: 404 173.5872 NaN
## 4: 407 389.8780 NaN
## 5: 9 1580.7672 NaN
## 6: 49 472.5234 NaN- The goal is the fill
Eventvariable in output_test by0or1.
6 Preprocessing of Train and Test dataset
The output of this section is to clean and unify variables and merge clinical, radimoics, and output_train dataset.
6.1 Train wrangling
# Convert character variables to numeric
new_clinical <- clinical %>%
mutate(Histology = stringi::stri_trans_totitle(Histology)) %>%
mutate_if(is.character, as.factor) %>%
mutate_if(is.factor, as.numeric)
#mutate(Histo = as.numeric(as.factor(Histology))) %>%
#mutate(Source = as.numeric(as.factor(SourceDataset))) %>%
#select(everything(), - Histology, -SourceDataset)
train_features <- new_clinical %>%
mutate_if(is.character, as.factor) %>%
left_join(y = output_train, by = "PatientID") %>%
left_join(y = new_radiomics, by = "PatientID") %>%
select(PatientID, Event, everything()) %>%
setDT()
fwrite(train_features, "train_features.csv")
train_features[,1:10] %>% head()## PatientID Event Histology Mstage Nstage SourceDataset Tstage age
## 1: 202 0 1 0 0 2 2 66.0000
## 2: 371 1 2 0 2 1 4 64.5722
## 3: 246 1 6 0 3 1 2 66.0452
## 4: 240 0 4 0 2 1 3 59.3566
## 5: 284 0 6 0 3 1 4 71.0554
## 6: 348 1 6 0 2 1 2 65.0212
## SurvivalTime shape_Compactness1
## 1: 1378 0.02781503
## 2: 379 0.02301549
## 3: 573 0.02734811
## 4: 959 0.02681111
## 5: 2119 0.02369124
## 6: 706 0.03098136
6.2 Test wrangling
radiomics_test <- fread("test/features/radiomics.csv", quote = "")
clinical_test <- fread("test/features/clinical_data.csv")
output_test <- fread("output_test.csv")6.2.1 Transform radiomics test dataset
groups_test <- radiomics_test[1:2,-1] %>%
t() %>%
as.data.frame() %>%
rename("Groups" = V1, "Features" = V2)
new_colnames_radiomics_test <- groups_test %>%
mutate(Features = stringr::str_remove(Features,"original_")) %>%
pull(Features)
old_names_test <- colnames(radiomics_test)
new_names_test <- c("PatientID", new_colnames_radiomics_test)
new_radiomics_test <- radiomics_test[-1:-3,] %>%
rename_at(vars(old_names_test), ~ new_names_test) %>%
mutate_if(is.character, as.numeric) #%>%
#as.matrix()
head(new_radiomics_test)[,1:8]## PatientID shape_Compactness1 shape_Compactness2 shape_Maximum3DDiameter
## 1 13 0.02888522 0.29645143 106.90182
## 2 155 0.03194837 0.36266005 18.81489
## 3 404 0.01599883 0.09094503 105.08092
## 4 407 0.03135766 0.34937318 46.96807
## 5 9 0.01781454 0.11275905 56.54202
## 6 49 0.03816202 0.51744596 20.12461
## shape_SphericalDisproportion shape_Sphericity shape_SurfaceArea
## 1 1.499738 0.6667830 29085.5414
## 2 1.402276 0.7131265 629.4436
## 3 2.223687 0.4497036 12509.2654
## 4 1.419832 0.7043089 4067.6574
## 5 2.069901 0.4831149 7093.3657
## 6 1.245599 0.8028264 844.2344
## shape_SurfaceVolumeRatio
## 1 0.1145278
## 2 0.7038788
## 3 0.3152977
## 4 0.2821040
## 5 0.3760316
## 6 0.50881766.2.2 Transform clinical test dataset
6.2.3 Explore clinical data for Test
p1 <- new_clinical_test %>%
group_by(Histology = stringi::stri_trans_totitle(Histology)) %>% # case insensitive of adenocarcinoma and Adenocarcinoma
group_by(Histology) %>%
summarise(Count = n()) %>%
ggplot()+
aes(x = Histology, y = Count, fill= Histology) +
geom_col()+
geom_text(aes(label = percent(Count/sum(Count))), vjust = -0.5)+
geom_text(aes(label = Count), vjust = -2) +
theme(axis.text.x = element_text(color="black",size=10,hjust=.5,vjust=.5, angle=5))
p2 <- ggplot(data=new_clinical_test[!is.na(new_clinical_test$age),]) +
aes(x= age) +
geom_histogram(fill="blue", bins = 60) +
geom_vline(xintercept = c(65,70, 72 ), color = "red")
#coord_flip()
p3 <- new_clinical_test %>%
mutate(Nstage = as.factor(Nstage)) %>%
group_by(Mstage, Nstage, Tstage) %>%
summarise(Count = n()) %>%
ggplot() +
aes(x = Tstage, y = Count, color = Nstage) +
facet_grid(Mstage~ .) +
geom_point(size=4, alpha = 0.8)
p4 <- new_clinical_test %>%
mutate(SourceDataset = as.factor(SourceDataset)) %>%
group_by(SourceDataset) %>%
summarise(Count = n()) %>%
ggplot()+
aes(x = "", y = Count, fill = SourceDataset) +
geom_bar(width = 1, stat = "identity") +
coord_polar("y", start=0) +
theme(legend.position = "top")
grid.arrange(p1,p2,p3,p4, layout_matrix = rbind(c(1),c(2, 3, 4)), nrow = 2)
- There is fourth class for
Nstagein test data taht is not available in train. - The average
agein test seems tobe younger in test data than in train. - The Histology seems to have the same distribution
6.2.4 Merge clinical, radiomics, and output_test dataset
test_features <- new_clinical_test %>%
mutate_if(is.character, as.factor) %>%
left_join(y = output_test, by = "PatientID") %>%
left_join(y = new_radiomics_test, by = "PatientID") %>%
select(PatientID, Event, everything()) %>%
setDT() # convert to data.table
fwrite(test_features, "test_features.csv")
test_features[,1:10] %>% head()## PatientID Event Histology Mstage Nstage SourceDataset Tstage age
## 1: 13 NaN 4 0 0 1 4 44.3970
## 2: 155 NaN 1 0 3 1 1 63.3183
## 3: 404 NaN 2 0 2 1 2 64.7255
## 4: 407 NaN 4 0 0 1 2 65.3635
## 5: 9 NaN 1 0 0 2 2 50.0000
## 6: 49 NaN 6 0 0 1 2 86.1410
## SurvivalTime shape_Compactness1
## 1: 788.4177 0.02888522
## 2: 427.6501 0.03194837
## 3: 173.5872 0.01599883
## 4: 389.8780 0.03135766
## 5: 1580.7672 0.01781454
## 6: 472.5234 0.03816202
7 Pull Radiomics, Clinical data and the best Masks
8 R Xgboost modeling with Radiomics, Clinical and Masks
8.1 Scaling Train and Test dataset
trainremoveCols <- c('PatientID','Event')
testremoveCols <- c('PatientID', 'Event')
Event <- train$Event
PatientID <- test$PatientID
train[,(trainremoveCols) := NULL]
test[,(testremoveCols) := NULL]
# Do scaling
dt <- rbind(train, test)
scale.cols <- colnames(dt)
dt[, (scale.cols) := lapply(.SD, scale), .SDcols = scale.cols]
train <- cbind(Event, head(dt,nrow(train)))
test <- cbind(PatientID, tail(dt, nrow(test)))
rm(dt)
invisible(gc())8.2 Split Train dataset into Train & Valid sets
require(rsample)
set.seed(100)
train_valid_split <- rsample::initial_split(train, prop = 0.8)
train_valid_split## <241/59/300>- We can retrieve our training and testing sets using training() and testing() functions.
# Retrieve train and test sets
train_8 <- rsample::training(train_valid_split)
valid_2 <- rsample::testing(train_valid_split)
train_8[1:10, 1:10]## Event Histology Mstage Nstage SourceDataset Tstage age
## 1: 0 -1.0235305 -0.1207812 -0.8392371 1.4175490 -0.1386218 -0.2504355
## 2: 1 -0.5217999 -0.1207812 0.8392371 -0.7037831 1.7024495 -0.3972837
## 3: 1 1.4851227 -0.1207812 1.6784742 -0.7037831 -0.1386218 -0.2457867
## 4: 0 1.4851227 -0.1207812 1.6784742 -0.7037831 1.7024495 0.2695086
## 5: 1 1.4851227 -0.1207812 0.8392371 -0.7037831 -0.1386218 -0.3511044
## 6: 1 -1.0235305 -0.1207812 -0.8392371 1.4175490 -1.0591575 0.1609615
## 7: 1 -1.0235305 -0.1207812 -0.8392371 -0.7037831 1.7024495 0.6186818
## 8: 1 -1.0235305 -0.1207812 0.8392371 -0.7037831 1.7024495 -1.5788159
## 9: 0 -0.5217999 -0.1207812 0.8392371 -0.7037831 -0.1386218 -2.0372357
## 10: 1 1.4851227 -0.1207812 0.8392371 1.4175490 -0.1386218 1.1894541
## SurvivalTime shape_Compactness1 shape_Compactness2
## 1: 0.7487397 0.3273910 0.2206572
## 2: -0.7068626 -0.4508739 -0.5451008
## 3: -0.4241931 0.2516768 0.1398098
## 4: 1.8284207 -0.3412982 -0.4460329
## 5: -0.2304042 0.8408228 0.8050072
## 6: 0.7356262 -0.8618943 -0.8911634
## 7: -0.9720474 0.3619137 0.2579747
## 8: -0.9735045 -1.1924952 -1.1402475
## 9: 0.3815607 0.9177119 0.8979347
## 10: -0.7345467 -0.0934834 -0.21140978.3 Format train and test to DMatrix
require(Matrix)
require(xgboost)
# the option na.pass avoids missing value in age column
options(na.action='na.pass')
train_8_sparse <- sparse.model.matrix(Event ~., data=train_8)
dtrain_8 <- xgb.DMatrix(data=train_8_sparse, label = train_8$Event)
options(na.action='na.pass')
valid_2_sparse <- sparse.model.matrix(Event ~., data=valid_2)
dvalid_2 <- xgb.DMatrix(data=valid_2_sparse, label = valid_2$Event)8.4 Optimize features with Cross validation
Here, we can see after how many rounds, we achieved the smallest test error.
params <- list(booster = "gbtree",
tree_method = "auto",
objective = "binary:logistic",
eval_metric = "auc", # for Binary classification error rate
max_depth = 2, # 6 makes training heavy, there is no correlation between features #1 is not better
eta = 0.03, # learning rate
subsample = 0.8, # prevent overfitting
colsample_bytree = 0.1 # specify the fraction of columns to be subsampled. # 0.5 is not better
)
tme <- Sys.time()
cv_model <- xgb.cv(params = params,
data = dtrain_8,
nthread = parallel::detectCores(all.tests = FALSE, logical = TRUE), #2,
nrounds = 25000,
verbose = TRUE,
nfold = 7,
print_every_n = 500,
early_stopping_rounds = 1000,
maximize = TRUE,
prediction = TRUE) # prediction of cv folds## [1] train-auc:0.718051+0.043889 test-auc:0.619140+0.061644
## Multiple eval metrics are present. Will use test_auc for early stopping.
## Will train until test_auc hasn't improved in 1000 rounds.
##
## [501] train-auc:0.999879+0.000097 test-auc:0.749731+0.075059
## [1001] train-auc:1.000000+0.000000 test-auc:0.753281+0.076136
## [1501] train-auc:1.000000+0.000000 test-auc:0.761041+0.071028
## [2001] train-auc:1.000000+0.000000 test-auc:0.757107+0.069419
## [2501] train-auc:1.000000+0.000000 test-auc:0.756282+0.072293
## Stopping. Best iteration:
## [1561] train-auc:1.000000+0.000000 test-auc:0.762555+0.071525## Time difference of 15.72488 mins8.5 Train the model
watchlist <- list(train = dtrain_8, eval = dvalid_2)
tme <- Sys.time()
xgboost_tree <- xgb.train(data = dtrain_8,
params = params,
watchlist = watchlist,
nrounds = cv_model$best_iteration, # more than 12000 ~0.897
print_every_n = 500,
verbose = TRUE)## [1] train-auc:0.688073 eval-auc:0.543103
## [501] train-auc:0.999444 eval-auc:0.842529
## [1001] train-auc:1.000000 eval-auc:0.865517
## [1501] train-auc:1.000000 eval-auc:0.864368
## [1561] train-auc:1.000000 eval-auc:0.864368## Time difference of 1.606111 mins8.6 Predict valid_2 dataset
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.002944 0.064929 0.499536 0.434123 0.738628 0.998919- We suppose that if Prob > 0.5 (Median), the Event is 1, else 0
8.7 Transform propability to binary classification
##
## 0 1
## 34 258.8 Confusion matrix for Tree model and performances
# data.frame(prediction = as.numeric(pred_bin),
# label = as.numeric(valid_2$Event)) %>%
# count(prediction, label)
pred_valid_bin <- as.factor(ifelse(pred_valid > 0.63,1,0))
valid_2_event <- as.factor(valid_2$Event)
caret::confusionMatrix(pred_valid_bin, valid_2_event)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 25 9
## 1 4 21
##
## Accuracy : 0.7797
## 95% CI : (0.6527, 0.8771)
## No Information Rate : 0.5085
## P-Value [Acc > NIR] : 1.683e-05
##
## Kappa : 0.5605
##
## Mcnemar's Test P-Value : 0.2673
##
## Sensitivity : 0.8621
## Specificity : 0.7000
## Pos Pred Value : 0.7353
## Neg Pred Value : 0.8400
## Prevalence : 0.4915
## Detection Rate : 0.4237
## Detection Prevalence : 0.5763
## Balanced Accuracy : 0.7810
##
## 'Positive' Class : 0
## pred_valid_error <- ROCR::prediction(pred_valid , valid_2$Event)
auc.valid <- ROCR::performance(pred_valid_error, "auc")
print("AUC: "); as.numeric(auc.valid@y.values)## [1] "AUC: "## [1] 0.86436788.9 Extract the most important features from tree xgboost model
8.9.1 List the most important features
features <- colnames(train_8)
importance_matrix_tree <- xgb.importance(features, model = xgboost_tree)
importance_matrix_tree## Feature Gain Cover Frequency
## 1: SurvivalTime 1.518797e-01 6.403812e-02 0.0451349512
## 2: glcm_Correlation 2.110504e-02 2.498131e-02 0.0242685416
## 3: age 2.073723e-02 2.646743e-02 0.0215468360
## 4: glcm_MaximumProbability 2.024262e-02 1.942644e-02 0.0176910864
## 5: glrlm_GrayLevelNonUniformity 1.741357e-02 1.557860e-02 0.0151961896
## ---
## 884: V3718 1.371769e-05 3.366216e-05 0.0002268088
## 885: V3809 9.926757e-06 3.106980e-05 0.0002268088
## 886: V6129 8.795324e-06 3.016645e-05 0.0002268088
## 887: V4196 2.153746e-06 3.204075e-05 0.0002268088
## 888: V3894 8.746036e-07 4.291979e-05 0.0002268088- Survival Time is the most important feature, followed by age, and 8 texture description.
8.10 Test Xgboost Prediction
8.10.1 Load test data and format to DMatrix
test_sparse <- sparse.model.matrix(PatientID ~., data=test)
dtest <- xgb.DMatrix(data=test_sparse, label = test$PatientID)pred_test <- predict(xgboost_tree, dtest)
pred_test_bin <- as.numeric(pred_test >= 0.63)
print("ratio of predicted Events in test datset: "); table(pred_test_bin)## [1] "ratio of predicted Events in test datset: "## pred_test_bin
## 0 1
## 73 52## [1] "ratio of Events in train datset: "##
## 0 1
## 138 1628.11 submission
pred_test_bin <- as.factor(ifelse(pred_test > 0.63,1,0))
output_test <- fread("output_test.csv")
pred <- data.frame(
PatientID = output_test$PatientID,
Event = pred_test_bin
)
submission <- output_test %>%
select(PatientID, SurvivalTime) %>%
left_join(pred, by = "PatientID")
fwrite(submission, "submission_fea_img_r.csv")
submission %>% head(10)## PatientID SurvivalTime Event
## 1 13 788.4177 0
## 2 155 427.6501 1
## 3 404 173.5872 1
## 4 407 389.8780 1
## 5 9 1580.7672 0
## 6 49 472.5234 1
## 7 55 1970.9725 0
## 8 200 530.4248 0
## 9 170 1067.4630 0
## 10 387 378.3248 19 Python xgboost Prediction (Python, Radiomics, Clinical, Masks datasets)
import matplotlib
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import seaborn as sns
from sklearn.model_selection import train_test_split
import pandas as pd
test = pd.read_csv("test_fea_img.csv")
train = pd.read_csv("train_fea_img.csv")
train.head()## PatientID Event Histology Mstage ... V8461 V8462 V8463 V8464
## 0 202 0 1 0 ... 0 0 0 0
## 1 371 1 2 0 ... 0 0 0 0
## 2 246 1 6 0 ... 0 0 0 0
## 3 240 0 4 0 ... 0 0 0 0
## 4 284 0 6 0 ... 0 0 0 0
##
## [5 rows x 8526 columns]# impute age to median
train['age'] = train['age'].fillna(train['age'].mean())
test['age'] = test['age'].fillna(test['age'].mean())
test.head()## PatientID Event Histology Mstage ... V8461 V8462 V8463 V8464
## 0 13 NaN 4 0 ... 0 0 0 0
## 1 155 NaN 1 0 ... 0 0 0 0
## 2 404 NaN 2 0 ... 0 0 0 0
## 3 407 NaN 4 0 ... 0 0 0 0
## 4 9 NaN 1 0 ... 0 0 0 0
##
## [5 rows x 8526 columns]# Set weed
SEED = 1423
train = train.drop('PatientID', axis=1)
test = test.drop(['PatientID', 'Event'], axis = 1)
def prepare_data_for_model(raw_dataframe, target_columns, drop_first = True, make_na_col = False):
# dummy all categorical fields
dataframe_dummy = pd.get_dummies(raw_dataframe, columns=target_columns,
drop_first=drop_first,
dummy_na=make_na_col)
return (dataframe_dummy)
# create dummy features
train_xgboost = prepare_data_for_model(train, target_columns=['Histology', 'Tstage']) #, 'Nstage' : 3 classes
train_xgboost = train_xgboost.dropna()
# create dummy features for test
test_xgboost = prepare_data_for_model(test, target_columns=['Histology', 'Tstage']) #, 'Nstage' : 4 classes
test_xgboost = test_xgboost.dropna()
train_xgboost.head()## Event Mstage Nstage SourceDataset ... Tstage_2 Tstage_3 Tstage_4 Tstage_5
## 0 0 0 0 2 ... 1 0 0 0
## 1 1 0 2 1 ... 0 0 1 0
## 2 1 0 3 1 ... 1 0 0 0
## 3 0 0 2 1 ... 0 1 0 0
## 4 0 0 3 1 ... 0 0 1 0
##
## [5 rows x 8532 columns]## Mstage Nstage SourceDataset ... Tstage_3 Tstage_4 Tstage_5
## 0 0 0 1 ... 0 1 0
## 1 0 3 1 ... 0 0 0
## 2 0 2 1 ... 0 0 0
## 3 0 0 1 ... 0 0 0
## 4 0 0 2 ... 0 0 0
##
## [5 rows x 8531 columns]# split data into train and test portions and model
features = [feat for feat in list(train_xgboost) if feat != 'Event']
X_train, X_valid, y_train, y_valid = train_test_split(train_xgboost[features],
train_xgboost[['Event']],
test_size=0.3,
random_state=SEED)
import xgboost as xgb
xgb_params = {
'max_depth':3,
'eta':0.01,
'silent':0,
'eval_metric':'auc',
'subsample': 0.8,
'colsample_bytree': 0.8,
'objective':'binary:logistic',
'seed' : 1423
}
dtrain = xgb.DMatrix(X_train, y_train, feature_names=X_train.columns.values)
dvalid = xgb.DMatrix(X_valid, y_valid, feature_names=X_valid.columns.values)
evals = [(dtrain,'train'),(dvalid,'eval')]
xgb_model_fea = xgb.train ( params = xgb_params,
dtrain = dtrain,
num_boost_round = 5000,
verbose_eval=200,
early_stopping_rounds = 500,
evals=evals,
maximize = True)## [0] train-auc:0.865973 eval-auc:0.842391
## Multiple eval metrics have been passed: 'eval-auc' will be used for early stopping.
##
## Will train until eval-auc hasn't improved in 500 rounds.
## [200] train-auc:0.986367 eval-auc:0.837945
## [400] train-auc:0.999171 eval-auc:0.839427
## Stopping. Best iteration:
## [3] train-auc:0.928519 eval-auc:0.845109# get dataframe version of important feature for model
xgb_fea_imp=pd.DataFrame(list(xgb_model_fea.get_fscore().items()),
columns=['feature','importance']).sort_values('importance', ascending=False)
xgb_fea_imp.head(10)## feature importance
## 0 SurvivalTime 490
## 3 glcm_MaximumProbability 101
## 2 age 99
## 6 glcm_ClusterShade 81
## 19 glrlm_LongRunLowGrayLevelEmphasis 67
## 32 glcm_Correlation 61
## 8 glrlm_ShortRunLowGrayLevelEmphasis 59
## 70 firstorder_Median 57
## 33 glcm_ClusterProminence 56
## 13 glrlm_LowGrayLevelRunEmphasis 52# Confusion matrix
dval_predictions = xgb_model_fea.predict(dvalid)
from sklearn.metrics import confusion_matrix
cm = confusion_matrix(y_valid, [1 if p > 0.5 else 0 for p in dval_predictions])
plt.figure(figsize = (6,4))
plt.ticklabel_format(style='plain', axis='y', useOffset=False)
sns.set(font_scale=1.4)
sns.heatmap(cm, annot=True, annot_kws={"size": 16})
plt.show()
# evaluate predictions
from sklearn.metrics import accuracy_score
dval_predictions[dval_predictions > 0.5] = 1
dval_predictions[dval_predictions <= 0.5] = 0
predictions = [round(value) for value in dval_predictions]
accuracy = accuracy_score(y_valid, predictions)
print("Accuracy: %.2f%%" % (accuracy * 100.0))## Accuracy: 72.22%9.1 Prediction with Python, features, Masks
dtest = xgb.DMatrix(test_xgboost, feature_names = X_train.columns.values)
dtest_predictions = xgb_model_fea.predict(dtest)
dtest_predictions[dtest_predictions > 0.5] = 1
dtest_predictions[dtest_predictions <= 0.5] = 0
output_test = pd.read_csv('output_test.csv', index_col = False)
output_test['Event'] = dtest_predictions
# submission_fea_img_p['Event'] = np.where(submission_fea_img_p['Event'] >0.5, 1, 0)
output_test.to_csv("submission_fea_img_p.csv", index=False)
output_test.head()## PatientID SurvivalTime Event
## 0 13 788.417673 0.0
## 1 155 427.650092 1.0
## 2 404 173.587222 1.0
## 3 407 389.877973 1.0
## 4 9 1580.767244 0.010 Random Forest Survival model (ranger package)
This method will give us an outcome probability over a time continuum (flipping the non-event to event probability)
Let’s take a quick look at the time period range in the training portion of our data set:
test <- fread("test_features.csv" )
train <- fread("train_features.csv")
# # reset train and test dataset
# train <-new_clinical %>%
# mutate_if(is.character, as.factor) %>%
# left_join(y = output_train, by = "PatientID") %>%
# left_join(y = new_radiomics, by = "PatientID") %>%
# select(PatientID, Event, everything()) %>%
# setDT() # convert to data.table
#
#
# test <- new_clinical_test %>%
# mutate_if(is.character, as.factor) %>%
# left_join(y = output_test, by = "PatientID") %>%
# left_join(y = new_radiomics_test, by = "PatientID") %>%
# select(PatientID, Event, everything()) %>%
# setDT() # convert to data.table
plot(sort(train$SurvivalTime), pch='.', type='o',
col='blue', lwd=2 ,
main = 'Survival Days of Lung Cancer')
10.1 Dealing with missing Age
10.1.1 Check the data for missing values.
## PatientID Event
## 0 0
## Histology Mstage
## 0 0
## Nstage SourceDataset
## 0 0
## Tstage age
## 0 16
## SurvivalTime shape_Compactness1
## 0 0
## shape_Compactness2 shape_Maximum3DDiameter
## 0 0
## shape_SphericalDisproportion shape_Sphericity
## 0 0
## shape_SurfaceArea shape_SurfaceVolumeRatio
## 0 0
## shape_VoxelVolume firstorder_Energy
## 0 0
## firstorder_Entropy firstorder_Kurtosis
## 0 0
## firstorder_Maximum firstorder_Mean
## 0 0
## firstorder_MeanAbsoluteDeviation firstorder_Median
## 0 0
## firstorder_Minimum firstorder_Range
## 0 0
## firstorder_RootMeanSquared firstorder_Skewness
## 0 0
## firstorder_StandardDeviation firstorder_Uniformity
## 0 0
## firstorder_Variance glcm_Autocorrelation
## 0 0
## glcm_ClusterProminence glcm_ClusterShade
## 0 0
## glcm_ClusterTendency glcm_Contrast
## 0 0
## glcm_Correlation glcm_DifferenceEntropy
## 0 0
## glcm_DifferenceAverage glcm_JointEnergy
## 0 0
## glcm_JointEntropy glcm_Id
## 0 0
## glcm_Idm glcm_Imc1
## 0 0
## glcm_Imc2 glcm_Idmn
## 0 0
## glcm_Idn glcm_InverseVariance
## 0 0
## glcm_MaximumProbability glcm_SumAverage
## 0 0
## glcm_SumEntropy glrlm_ShortRunEmphasis
## 0 0
## glrlm_LongRunEmphasis glrlm_GrayLevelNonUniformity
## 0 0
## glrlm_RunLengthNonUniformity glrlm_RunPercentage
## 0 0
## glrlm_LowGrayLevelRunEmphasis glrlm_HighGrayLevelRunEmphasis
## 0 0
## glrlm_ShortRunLowGrayLevelEmphasis glrlm_ShortRunHighGrayLevelEmphasis
## 0 0
## glrlm_LongRunLowGrayLevelEmphasis glrlm_LongRunHighGrayLevelEmphasis
## 0 010.1.2 Imputation processing for train data
## Warning: Number of logged events: 1- We may not want to use a certain variable as predictors. For example, the PatitenID variable does not have any predictive value.
- If we want to skip a variable from imputation use the code below. This variable will be used for prediction.
- Now let specify the methods for imputing the missing values. There are specific methods for continues, binary and ordinal variables.
meth[c("age")]="cart" # pmm (Predictive Mean Matching suitable for numeric variables )
# pmm generate error. it is seems working with cart
# (https://stackoverflow.com/questions/48355250/
#do-imputation-in-r-when-mice-returns-error-that-system-is-computationally-singu)- Now it is time to run the multiple (m=5) imputation.
##
## iter imp variable
## 1 1 age
## 1 2 age
## 1 3 age
## 1 4 age
## 1 5 age
## 2 1 age
## 2 2 age
## 2 3 age
## 2 4 age
## 2 5 age
## 3 1 age
## 3 2 age
## 3 3 age
## 3 4 age
## 3 5 age
## 4 1 age
## 4 2 age
## 4 3 age
## 4 4 age
## 4 5 age
## 5 1 age
## 5 2 age
## 5 3 age
## 5 4 age
## 5 5 age## Warning: Number of logged events: 25- Create a dataset after imputation.
- Check for missings in the imputed dataset.
## PatientID Event
## 0 0
## Histology Mstage
## 0 0
## Nstage SourceDataset
## 0 0
## Tstage age
## 0 0
## SurvivalTime shape_Compactness1
## 0 0
## shape_Compactness2 shape_Maximum3DDiameter
## 0 0
## shape_SphericalDisproportion shape_Sphericity
## 0 0
## shape_SurfaceArea shape_SurfaceVolumeRatio
## 0 0
## shape_VoxelVolume firstorder_Energy
## 0 0
## firstorder_Entropy firstorder_Kurtosis
## 0 0
## firstorder_Maximum firstorder_Mean
## 0 0
## firstorder_MeanAbsoluteDeviation firstorder_Median
## 0 0
## firstorder_Minimum firstorder_Range
## 0 0
## firstorder_RootMeanSquared firstorder_Skewness
## 0 0
## firstorder_StandardDeviation firstorder_Uniformity
## 0 0
## firstorder_Variance glcm_Autocorrelation
## 0 0
## glcm_ClusterProminence glcm_ClusterShade
## 0 0
## glcm_ClusterTendency glcm_Contrast
## 0 0
## glcm_Correlation glcm_DifferenceEntropy
## 0 0
## glcm_DifferenceAverage glcm_JointEnergy
## 0 0
## glcm_JointEntropy glcm_Id
## 0 0
## glcm_Idm glcm_Imc1
## 0 0
## glcm_Imc2 glcm_Idmn
## 0 0
## glcm_Idn glcm_InverseVariance
## 0 0
## glcm_MaximumProbability glcm_SumAverage
## 0 0
## glcm_SumEntropy glrlm_ShortRunEmphasis
## 0 0
## glrlm_LongRunEmphasis glrlm_GrayLevelNonUniformity
## 0 0
## glrlm_RunLengthNonUniformity glrlm_RunPercentage
## 0 0
## glrlm_LowGrayLevelRunEmphasis glrlm_HighGrayLevelRunEmphasis
## 0 0
## glrlm_ShortRunLowGrayLevelEmphasis glrlm_ShortRunHighGrayLevelEmphasis
## 0 0
## glrlm_LongRunLowGrayLevelEmphasis glrlm_LongRunHighGrayLevelEmphasis
## 0 0- Accuracy of imputation
## [1] "train$age"## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 42.51 62.98 69.95 68.77 76.20 87.13 16## [1] "imputed$age"## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 42.51 63.00 70.00 68.94 76.42 87.13- Well done :-)
10.1.3 Do the same imputation for test dataset
## Warning: Number of logged events: 2meth = init$method
predM = init$predictorMatrix
predM[, c("PatientID")] <- 0
meth[c("PatientID")]=""
meth[c("age")]="cart"
set.seed(103)
imputed_test = mice(test, method=meth, predictorMatrix=predM, m=5)##
## iter imp variable
## 1 1 age
## 1 2 age
## 1 3 age
## 1 4 age
## 1 5 age
## 2 1 age
## 2 2 age
## 2 3 age
## 2 4 age
## 2 5 age
## 3 1 age
## 3 2 age
## 3 3 age
## 3 4 age
## 3 5 age
## 4 1 age
## 4 2 age
## 4 3 age
## 4 4 age
## 4 5 age
## 5 1 age
## 5 2 age
## 5 3 age
## 5 4 age
## 5 5 age## Warning: Number of logged events: 25imputed_test <- complete(imputed_test)
fwrite(imputed_test, "test_features_imputed.csv")
imputed_test[1:10,1:10]## PatientID Event Histology Mstage Nstage SourceDataset Tstage age
## 1 13 NA 4 0 0 1 4 44.3970
## 2 155 NA 1 0 3 1 1 63.3183
## 3 404 NA 2 0 2 1 2 64.7255
## 4 407 NA 4 0 0 1 2 65.3635
## 5 9 NA 1 0 0 2 2 50.0000
## 6 49 NA 6 0 0 1 2 86.1410
## 7 55 NA 3 0 0 1 1 75.2663
## 8 200 NA 3 0 0 1 1 85.4511
## 9 170 NA 2 0 3 1 1 69.8727
## 10 387 NA 2 0 3 1 2 52.8569
## SurvivalTime shape_Compactness1
## 1 788.4177 0.02888522
## 2 427.6501 0.03194837
## 3 173.5872 0.01599883
## 4 389.8780 0.03135766
## 5 1580.7672 0.01781454
## 6 472.5234 0.03816202
## 7 1970.9725 0.03699879
## 8 530.4248 0.03373779
## 9 1067.4630 0.01929334
## 10 378.3248 0.0253147010.2 Preprocessing Train and Test
In order to measure the AUC of each model we need to split the data randomly (with seed) into two equal parts:
set.seed(1234)
random_splits <- runif(nrow(imputed))
train_df_official <- imputed[random_splits < .5,]
dim(train_df_official)## [1] 151 62## [1] 149 62In order to align the survival and the classification models, we will focus on the probability of reaching event over the 825 days. We tried the Median, mean, quantile but it seems not well as 825 days.
- We also need to create a classification-centric outcome variable. This will measure how many patients reached event or not within the chosen period. Here we look for a censor feature of 1 (i.e. the event happened) under the chosen period to set the outcome to 1, everything else is set to 0:
# classification data set
train_df_classificaiton <- train_df_official
train_df_classificaiton$ReachedEvent <- ifelse((train_df_classificaiton$Event == 1 &
train_df_classificaiton$SurvivalTime <= period_choice), 1, 0)
summary(train_df_classificaiton$ReachedEvent)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 0.000 0.457 1.000 1.000validate_df_classification <- validate_df_official
validate_df_classification$ReachedEvent <- ifelse((validate_df_classification$Event == 1 &
validate_df_classification$SurvivalTime <= period_choice), 1, 0)
summary(validate_df_classification$ReachedEvent)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0000 0.0000 0.4228 1.0000 1.0000- Now we can easily get an AUC score on the probability of reaching event within our allotted period choice
10.3 Survival Model (ranger)
train_df_classificaiton <- as.data.table(train_df_classificaiton)
# omit PatientID and S3:integer64 from variable importance, Event and SurvivalTime will be used in formula
var <- paste(colnames(train_df_classificaiton)[train_df_classificaiton[, !names(train_df_classificaiton) %in% c("PatientID",
"Event",
"SurvivalTime",
"ReachedEvent",
"firstorder_Energy")]], # first_orderEnergy is not double
collapse ="+")
survival_formula <- formula(paste('Surv(', 'SurvivalTime', ',', 'Event', ') ~ ', var))
survival_formula## Surv(SurvivalTime, Event) ~ Histology + Mstage + Nstage + SourceDataset +
## Tstage + age + shape_Compactness1 + shape_Compactness2 +
## shape_Maximum3DDiameter + shape_SphericalDisproportion +
## shape_Sphericity + shape_SurfaceArea + shape_SurfaceVolumeRatio +
## shape_VoxelVolume + firstorder_Entropy + firstorder_Kurtosis +
## firstorder_Maximum + firstorder_Mean + firstorder_MeanAbsoluteDeviation +
## firstorder_Median + firstorder_Minimum + firstorder_Range +
## firstorder_RootMeanSquared + firstorder_Skewness + firstorder_StandardDeviation +
## firstorder_Uniformity + firstorder_Variance + glcm_Autocorrelation +
## glcm_ClusterProminence + glcm_ClusterShade + glcm_ClusterTendency +
## glcm_Contrast + glcm_Correlation + glcm_DifferenceEntropy +
## glcm_DifferenceAverage + glcm_JointEnergy + glcm_JointEntropy +
## glcm_Id + glcm_Idm + glcm_Imc1 + glcm_Imc2 + glcm_Idmn +
## glcm_Idn + glcm_InverseVariance + glcm_MaximumProbability +
## glcm_SumAverage + glcm_SumEntropy + glrlm_ShortRunEmphasis +
## glrlm_LongRunEmphasis + glrlm_GrayLevelNonUniformity + glrlm_RunLengthNonUniformity +
## glrlm_RunPercentage + glrlm_LowGrayLevelRunEmphasis + glrlm_HighGrayLevelRunEmphasis +
## glrlm_ShortRunLowGrayLevelEmphasis + glrlm_ShortRunHighGrayLevelEmphasis +
## glrlm_LongRunLowGrayLevelEmphasis + glrlm_LongRunHighGrayLevelEmphasissurvival_model <- ranger(survival_formula,
data = train_df_classificaiton,
seed = 1234,
importance = 'permutation',
mtry = 2,
verbose = TRUE,
num.trees = 50,
write.forest=TRUE)
# print out coefficients
sort(survival_model$variable.importance, decreasing = TRUE) %>% head(10) %>% names()## [1] "firstorder_Skewness" "glcm_Idm"
## [3] "glrlm_LongRunEmphasis" "glcm_Idmn"
## [5] "Tstage" "glrlm_ShortRunEmphasis"
## [7] "glcm_JointEnergy" "glrlm_GrayLevelNonUniformity"
## [9] "firstorder_Kurtosis" "glcm_JointEntropy"- Once we have our survival_model model object, we can take a look at some probabilities of survival (this is just for illustrative purposes as we haven’t split our data set yet). Let’s look at two patients - row 1 and row 56:
plot(survival_model$unique.death.times, survival_model$survival[1,],
type='l', col='orange', ylim=c(0.2,1))
lines(survival_model$unique.death.times,
survival_model$survival[56,], col='blue')
- The orange PatientID has more probability to survive.
## [1] "Orange PatientID: "## Event Tstage age SurvivalTime
## 1 0 2 66 1378## [1] "Blue PatientID: "## Event Tstage age SurvivalTime
## 56 1 4 62.4476 30310.3.1 Scoring the Random Forest Survival Model
First we get the basic survival prediction using our validation split set and then we flip the probability of the period of choice and get the AUC score:
feature_names <- setdiff(names(train_df_classificaiton),
c('PatientID', 'ReachedEvent',
'SurvivalTime', 'Event'))
suvival_predictions <- predict(survival_model,
validate_df_official[, feature_names])
roc(response = validate_df_classification$ReachedEvent,
predictor = 1 - suvival_predictions$survival[,which(suvival_predictions$unique.death.times
== period_choice)])## Setting levels: control = 0, case = 1## Setting direction: controls < cases##
## Call:
## roc.default(response = validate_df_classification$ReachedEvent, predictor = 1 - suvival_predictions$survival[, which(suvival_predictions$unique.death.times == period_choice)])
##
## Data: 1 - suvival_predictions$survival[, which(suvival_predictions$unique.death.times == period_choice)] in 86 controls (validate_df_classification$ReachedEvent 0) < 63 cases (validate_df_classification$ReachedEvent 1).
## Area under the curve: 0.709710.3.2 RF survival Prediction
survival_predictions_test <- predict( survival_model,imputed_test[, feature_names])
predictor <- 1 -
survival_predictions_test$survival[,which(survival_predictions_test$unique.death.times
== period_choice)]
pred_survival <- data.frame(
PatientID = imputed_test$PatientID,
Event = predictor
)
output_test <- fread("output_test.csv")
submission_surv <- output_test %>%
select(PatientID, SurvivalTime) %>%
left_join(pred_survival, by = "PatientID")
submission_surv["Event"] <- ifelse(submission_surv$Event > 0.42, 1,0)
fwrite(submission_surv, "submission_surv.csv")
pred_bin_survival <- as.numeric(predictor > 0.5)
print("ratio of predicted Events in test datset: "); table(pred_bin_survival)## [1] "ratio of predicted Events in test datset: "## pred_bin_survival
## 0 1
## 67 58## [1] "ratio of Events in traindatset: "##
## 0 1
## 138 16210.3.3 CoxPH model
#sapply(train_df_official, function(x) sum(is.na(x)))
tr <- train_df_classificaiton %>%
mutate_if(is.integer, as.numeric) %>%
mutate(Event = ifelse(Event == 0, 1, 2)) #%>%
#select(which(sapply(.,is.numeric)))
res.cox <- coxph(survival_formula, data = tr)
summary(res.cox)## Call:
## coxph(formula = survival_formula, data = tr)
##
## n= 151, number of events= 80
##
## coef exp(coef) se(coef) z
## Histology -5.797e-03 9.942e-01 9.858e-02 -0.059
## Mstage 4.333e-01 1.542e+00 3.529e-01 1.228
## Nstage 6.196e-01 1.858e+00 1.819e-01 3.406
## SourceDataset -1.113e+00 3.286e-01 1.485e+00 -0.749
## Tstage -3.498e-01 7.048e-01 2.411e-01 -1.451
## age 5.479e-02 1.056e+00 2.056e-02 2.665
## shape_Compactness1 3.078e+04 Inf 3.961e+04 0.777
## shape_Compactness2 -2.631e+02 5.230e-115 3.740e+02 -0.704
## shape_Maximum3DDiameter 3.260e-02 1.033e+00 1.495e-02 2.181
## shape_SphericalDisproportion -6.115e+01 2.775e-27 6.672e+01 -0.916
## shape_Sphericity -1.766e+03 0.000e+00 2.221e+03 -0.795
## shape_SurfaceArea 2.328e-04 1.000e+00 1.434e-04 1.623
## shape_SurfaceVolumeRatio 1.475e+01 2.557e+06 8.935e+00 1.651
## shape_VoxelVolume -2.941e-05 1.000e+00 1.894e-05 -1.552
## firstorder_Entropy -3.371e+01 2.301e-15 1.225e+01 -2.751
## firstorder_Kurtosis 6.347e-02 1.066e+00 4.481e-02 1.416
## firstorder_Maximum -2.742e-03 9.973e-01 1.845e-03 -1.486
## firstorder_Mean 6.984e-03 1.007e+00 3.387e-02 0.206
## firstorder_MeanAbsoluteDeviation 2.020e-03 1.002e+00 7.495e-02 0.027
## firstorder_Median -2.204e-02 9.782e-01 1.713e-02 -1.286
## firstorder_Minimum 9.557e-03 1.010e+00 2.600e-02 0.368
## firstorder_Range NA NA 0.000e+00 NA
## firstorder_RootMeanSquared -3.392e-02 9.666e-01 1.959e-02 -1.732
## firstorder_Skewness 7.280e-01 2.071e+00 5.530e-01 1.316
## firstorder_StandardDeviation 3.563e-02 1.036e+00 6.281e-02 0.567
## firstorder_Uniformity -1.163e+02 3.124e-51 9.259e+01 -1.256
## firstorder_Variance 1.868e-04 1.000e+00 1.884e-04 0.991
## glcm_Autocorrelation 1.831e-02 1.018e+00 2.400e-02 0.763
## glcm_ClusterProminence -1.956e-06 1.000e+00 4.026e-06 -0.486
## glcm_ClusterShade -2.373e-04 9.998e-01 2.042e-04 -1.162
## glcm_ClusterTendency -2.179e-02 9.784e-01 2.769e-02 -0.787
## glcm_Contrast 4.032e-01 1.497e+00 3.658e-01 1.102
## glcm_Correlation -1.155e+01 9.612e-06 8.828e+00 -1.309
## glcm_DifferenceEntropy 8.310e+00 4.066e+03 6.158e+00 1.350
## glcm_DifferenceAverage -2.328e+01 7.756e-11 1.656e+01 -1.406
## glcm_JointEnergy 1.985e+02 1.675e+86 1.199e+02 1.656
## glcm_JointEntropy 9.067e+00 8.664e+03 5.628e+00 1.611
## glcm_Id -1.372e+03 0.000e+00 1.006e+03 -1.364
## glcm_Idm 9.665e+02 Inf 7.964e+02 1.214
## glcm_Imc1 -4.851e+01 8.536e-22 2.510e+01 -1.932
## glcm_Imc2 -3.449e+00 3.179e-02 1.188e+01 -0.290
## glcm_Idmn -3.589e+02 1.298e-156 2.749e+02 -1.306
## glcm_Idn 2.433e+02 4.510e+105 1.734e+02 1.403
## glcm_InverseVariance -5.010e+01 1.754e-22 1.039e+02 -0.482
## glcm_MaximumProbability -2.376e+01 4.786e-11 1.512e+01 -1.571
## glcm_SumAverage -4.526e-01 6.360e-01 4.397e-01 -1.029
## glcm_SumEntropy 7.811e+00 2.468e+03 7.712e+00 1.013
## glrlm_ShortRunEmphasis 3.310e+01 2.384e+14 4.115e+01 0.805
## glrlm_LongRunEmphasis -8.420e-01 4.308e-01 9.536e-01 -0.883
## glrlm_GrayLevelNonUniformity 7.652e-05 1.000e+00 9.188e-05 0.833
## glrlm_RunLengthNonUniformity 2.938e-07 1.000e+00 2.161e-05 0.014
## glrlm_RunPercentage -1.199e+02 8.732e-53 8.680e+01 -1.381
## glrlm_LowGrayLevelRunEmphasis -4.078e+02 7.494e-178 6.236e+02 -0.654
## glrlm_HighGrayLevelRunEmphasis -2.196e-03 9.978e-01 2.740e-02 -0.080
## glrlm_ShortRunLowGrayLevelEmphasis 5.478e+02 8.391e+237 7.039e+02 0.778
## glrlm_ShortRunHighGrayLevelEmphasis 1.913e-03 1.002e+00 1.737e-02 0.110
## glrlm_LongRunLowGrayLevelEmphasis 6.043e+00 4.212e+02 3.135e+01 0.193
## glrlm_LongRunHighGrayLevelEmphasis -1.846e-04 9.998e-01 5.328e-04 -0.347
## Pr(>|z|)
## Histology 0.953109
## Mstage 0.219558
## Nstage 0.000659 ***
## SourceDataset 0.453630
## Tstage 0.146770
## age 0.007702 **
## shape_Compactness1 0.437107
## shape_Compactness2 0.481730
## shape_Maximum3DDiameter 0.029198 *
## shape_SphericalDisproportion 0.359411
## shape_Sphericity 0.426525
## shape_SurfaceArea 0.104510
## shape_SurfaceVolumeRatio 0.098677 .
## shape_VoxelVolume 0.120607
## firstorder_Entropy 0.005933 **
## firstorder_Kurtosis 0.156668
## firstorder_Maximum 0.137265
## firstorder_Mean 0.836644
## firstorder_MeanAbsoluteDeviation 0.978502
## firstorder_Median 0.198289
## firstorder_Minimum 0.713172
## firstorder_Range NA
## firstorder_RootMeanSquared 0.083272 .
## firstorder_Skewness 0.188034
## firstorder_StandardDeviation 0.570550
## firstorder_Uniformity 0.209134
## firstorder_Variance 0.321452
## glcm_Autocorrelation 0.445304
## glcm_ClusterProminence 0.626993
## glcm_ClusterShade 0.245185
## glcm_ClusterTendency 0.431256
## glcm_Contrast 0.270354
## glcm_Correlation 0.190681
## glcm_DifferenceEntropy 0.177133
## glcm_DifferenceAverage 0.159747
## glcm_JointEnergy 0.097787 .
## glcm_JointEntropy 0.107165
## glcm_Id 0.172725
## glcm_Idm 0.224908
## glcm_Imc1 0.053311 .
## glcm_Imc2 0.771574
## glcm_Idmn 0.191627
## glcm_Idn 0.160661
## glcm_InverseVariance 0.629627
## glcm_MaximumProbability 0.116116
## glcm_SumAverage 0.303326
## glcm_SumEntropy 0.311145
## glrlm_ShortRunEmphasis 0.421085
## glrlm_LongRunEmphasis 0.377249
## glrlm_GrayLevelNonUniformity 0.404953
## glrlm_RunLengthNonUniformity 0.989153
## glrlm_RunPercentage 0.167266
## glrlm_LowGrayLevelRunEmphasis 0.513083
## glrlm_HighGrayLevelRunEmphasis 0.936131
## glrlm_ShortRunLowGrayLevelEmphasis 0.436394
## glrlm_ShortRunHighGrayLevelEmphasis 0.912313
## glrlm_LongRunLowGrayLevelEmphasis 0.847143
## glrlm_LongRunHighGrayLevelEmphasis 0.728912
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Histology 9.942e-01 1.006e+00 8.195e-01 1.206e+00
## Mstage 1.542e+00 6.484e-01 7.723e-01 3.080e+00
## Nstage 1.858e+00 5.382e-01 1.301e+00 2.654e+00
## SourceDataset 3.286e-01 3.043e+00 1.789e-02 6.036e+00
## Tstage 7.048e-01 1.419e+00 4.394e-01 1.131e+00
## age 1.056e+00 9.467e-01 1.015e+00 1.100e+00
## shape_Compactness1 Inf 0.000e+00 0.000e+00 Inf
## shape_Compactness2 5.230e-115 1.912e+114 0.000e+00 1.255e+204
## shape_Maximum3DDiameter 1.033e+00 9.679e-01 1.003e+00 1.064e+00
## shape_SphericalDisproportion 2.775e-27 3.604e+26 4.466e-84 1.724e+30
## shape_Sphericity 0.000e+00 Inf 0.000e+00 Inf
## shape_SurfaceArea 1.000e+00 9.998e-01 1.000e+00 1.001e+00
## shape_SurfaceVolumeRatio 2.557e+06 3.911e-07 6.343e-02 1.031e+14
## shape_VoxelVolume 1.000e+00 1.000e+00 9.999e-01 1.000e+00
## firstorder_Entropy 2.301e-15 4.347e+14 8.604e-26 6.152e-05
## firstorder_Kurtosis 1.066e+00 9.385e-01 9.759e-01 1.163e+00
## firstorder_Maximum 9.973e-01 1.003e+00 9.937e-01 1.001e+00
## firstorder_Mean 1.007e+00 9.930e-01 9.423e-01 1.076e+00
## firstorder_MeanAbsoluteDeviation 1.002e+00 9.980e-01 8.651e-01 1.161e+00
## firstorder_Median 9.782e-01 1.022e+00 9.459e-01 1.012e+00
## firstorder_Minimum 1.010e+00 9.905e-01 9.594e-01 1.062e+00
## firstorder_Range NA NA NA NA
## firstorder_RootMeanSquared 9.666e-01 1.035e+00 9.302e-01 1.004e+00
## firstorder_Skewness 2.071e+00 4.829e-01 7.006e-01 6.122e+00
## firstorder_StandardDeviation 1.036e+00 9.650e-01 9.162e-01 1.172e+00
## firstorder_Uniformity 3.124e-51 3.201e+50 4.776e-130 2.043e+28
## firstorder_Variance 1.000e+00 9.998e-01 9.998e-01 1.001e+00
## glcm_Autocorrelation 1.018e+00 9.819e-01 9.717e-01 1.068e+00
## glcm_ClusterProminence 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## glcm_ClusterShade 9.998e-01 1.000e+00 9.994e-01 1.000e+00
## glcm_ClusterTendency 9.784e-01 1.022e+00 9.268e-01 1.033e+00
## glcm_Contrast 1.497e+00 6.682e-01 7.307e-01 3.065e+00
## glcm_Correlation 9.612e-06 1.040e+05 2.938e-13 3.144e+02
## glcm_DifferenceEntropy 4.066e+03 2.459e-04 2.333e-02 7.088e+08
## glcm_DifferenceAverage 7.756e-11 1.289e+10 6.238e-25 9.644e+03
## glcm_JointEnergy 1.675e+86 5.970e-87 1.424e-16 1.971e+188
## glcm_JointEntropy 8.664e+03 1.154e-04 1.404e-01 5.349e+08
## glcm_Id 0.000e+00 Inf 0.000e+00 4.144e+260
## glcm_Idm Inf 0.000e+00 7.064e-259 Inf
## glcm_Imc1 8.536e-22 1.172e+21 3.646e-43 1.998e+00
## glcm_Imc2 3.179e-02 3.146e+01 2.458e-12 4.110e+08
## glcm_Idmn 1.298e-156 7.706e+155 0.000e+00 1.252e+78
## glcm_Idn 4.510e+105 2.217e-106 1.101e-42 1.847e+253
## glcm_InverseVariance 1.754e-22 5.701e+21 6.663e-111 4.617e+66
## glcm_MaximumProbability 4.786e-11 2.090e+10 6.413e-24 3.571e+02
## glcm_SumAverage 6.360e-01 1.572e+00 2.686e-01 1.506e+00
## glcm_SumEntropy 2.468e+03 4.052e-04 6.724e-04 9.057e+09
## glrlm_ShortRunEmphasis 2.384e+14 4.195e-15 2.251e-21 2.525e+49
## glrlm_LongRunEmphasis 4.308e-01 2.321e+00 6.646e-02 2.793e+00
## glrlm_GrayLevelNonUniformity 1.000e+00 9.999e-01 9.999e-01 1.000e+00
## glrlm_RunLengthNonUniformity 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## glrlm_RunPercentage 8.732e-53 1.145e+52 1.147e-126 6.647e+21
## glrlm_LowGrayLevelRunEmphasis 7.494e-178 1.334e+177 0.000e+00 Inf
## glrlm_HighGrayLevelRunEmphasis 9.978e-01 1.002e+00 9.456e-01 1.053e+00
## glrlm_ShortRunLowGrayLevelEmphasis 8.391e+237 1.192e-238 0.000e+00 Inf
## glrlm_ShortRunHighGrayLevelEmphasis 1.002e+00 9.981e-01 9.684e-01 1.037e+00
## glrlm_LongRunLowGrayLevelEmphasis 4.212e+02 2.374e-03 8.700e-25 2.039e+29
## glrlm_LongRunHighGrayLevelEmphasis 9.998e-01 1.000e+00 9.988e-01 1.001e+00
##
## Concordance= 0.824 (se = 0.026 )
## Likelihood ratio test= 132.2 on 57 df, p=7e-08
## Wald test = 55.79 on 57 df, p=0.5
## Score (logrank) test = 134.4 on 57 df, p=3e-08- restart the model of the most significant
cox2 <- coxph(Surv(SurvivalTime, Event) ~ Mstage + Nstage + SourceDataset + age + shape_Compactness1 + shape_Compactness2 + shape_SphericalDisproportion +shape_Sphericity+ glrlm_ShortRunEmphasis, data = tr )
summary(cox2)## Call:
## coxph(formula = Surv(SurvivalTime, Event) ~ Mstage + Nstage +
## SourceDataset + age + shape_Compactness1 + shape_Compactness2 +
## shape_SphericalDisproportion + shape_Sphericity + glrlm_ShortRunEmphasis,
## data = tr)
##
## n= 151, number of events= 80
##
## coef exp(coef) se(coef) z
## Mstage 2.813e-01 1.325e+00 2.461e-01 1.143
## Nstage 2.949e-01 1.343e+00 1.096e-01 2.691
## SourceDataset -6.354e-01 5.297e-01 3.725e-01 -1.706
## age 4.591e-02 1.047e+00 1.334e-02 3.442
## shape_Compactness1 3.849e+02 1.439e+167 2.648e+04 0.015
## shape_Compactness2 4.138e+00 6.265e+01 2.515e+02 0.016
## shape_SphericalDisproportion -3.083e+00 4.583e-02 4.440e+01 -0.069
## shape_Sphericity -3.712e+01 7.583e-17 1.484e+03 -0.025
## glrlm_ShortRunEmphasis -3.916e+00 1.991e-02 1.383e+00 -2.832
## Pr(>|z|)
## Mstage 0.253016
## Nstage 0.007124 **
## SourceDataset 0.088075 .
## age 0.000577 ***
## shape_Compactness1 0.988404
## shape_Compactness2 0.986872
## shape_SphericalDisproportion 0.944653
## shape_Sphericity 0.980040
## glrlm_ShortRunEmphasis 0.004633 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Mstage 1.325e+00 7.548e-01 8.179e-01 2.146e+00
## Nstage 1.343e+00 7.446e-01 1.083e+00 1.665e+00
## SourceDataset 5.297e-01 1.888e+00 2.553e-01 1.099e+00
## age 1.047e+00 9.551e-01 1.020e+00 1.075e+00
## shape_Compactness1 1.439e+167 6.949e-168 0.000e+00 Inf
## shape_Compactness2 6.265e+01 1.596e-02 5.732e-213 6.848e+215
## shape_SphericalDisproportion 4.583e-02 2.182e+01 7.304e-40 2.876e+36
## shape_Sphericity 7.583e-17 1.319e+16 0.000e+00 Inf
## glrlm_ShortRunEmphasis 1.991e-02 5.022e+01 1.324e-03 2.995e-01
##
## Concordance= 0.721 (se = 0.028 )
## Likelihood ratio test= 46.96 on 9 df, p=4e-07
## Wald test = 41 on 9 df, p=5e-06
## Score (logrank) test = 49.23 on 9 df, p=2e-0710.3.3.1 Testing proportional Hazards assumption
## chisq df p
## Mstage 9.73549 1 0.0018
## Nstage 0.81714 1 0.3660
## SourceDataset 0.00128 1 0.9714
## age 0.07673 1 0.7818
## shape_Compactness1 1.08386 1 0.2978
## shape_Compactness2 0.97642 1 0.3231
## shape_SphericalDisproportion 0.99967 1 0.3174
## shape_Sphericity 1.09885 1 0.2945
## glrlm_ShortRunEmphasis 0.25219 1 0.6155
## GLOBAL 14.81042 9 0.0963
- In the figure above, the solid line is a smoothing spline fit to the plot, with the dashed lines representing a +/- 2-standard-error band around the fit.
#Var <- stringr::str_split(string = var, pattern = "\\+", simplify = TRUE, )
#coxph.fit(tr %>% select(-Event), tr$Event)
fit <- survfit(cox2, newdata = validate_df_classification, data = train_df_classificaiton)
#ggsurvplot(fit, conf.int = TRUE, palette = "Dark2",
# censor = FALSE)
summary(fit)## Call: survfit(formula = cox2, newdata = validate_df_classification,
## data = train_df_classificaiton)
##
## time n.risk n.event survival1 survival2 survival3 survival4 survival5
## 24 150 1 0.994 0.9881 0.996 0.9875 0.990
## 25 149 1 0.988 0.9763 0.992 0.9751 0.979
## 48 148 1 0.982 0.9645 0.987 0.9627 0.969
## 65 147 1 0.976 0.9527 0.983 0.9504 0.959
## 71 146 1 0.970 0.9411 0.979 0.9382 0.948
## 76 145 1 0.964 0.9294 0.974 0.9259 0.938
## 77 144 1 0.957 0.9176 0.970 0.9136 0.928
## 78 143 1 0.951 0.9059 0.966 0.9014 0.917
## 79 142 1 0.945 0.8942 0.961 0.8891 0.907
## 86 141 1 0.939 0.8825 0.957 0.8769 0.896
## 96 140 1 0.932 0.8710 0.952 0.8649 0.886
## 98 139 1 0.926 0.8594 0.948 0.8529 0.876
## 113 138 1 0.920 0.8479 0.943 0.8409 0.866
## 120 137 2 0.907 0.8249 0.934 0.8169 0.845
## 131 135 1 0.901 0.8135 0.929 0.8050 0.835
## 132 134 1 0.894 0.8016 0.925 0.7926 0.824
## 136 133 1 0.887 0.7897 0.920 0.7803 0.813
## 141 132 1 0.880 0.7778 0.915 0.7680 0.803
## 143 131 1 0.874 0.7661 0.910 0.7558 0.792
## 159 130 1 0.867 0.7544 0.905 0.7437 0.781
## 166 129 1 0.860 0.7429 0.900 0.7318 0.771
## 177 128 1 0.853 0.7314 0.895 0.7199 0.760
## 183 127 1 0.847 0.7198 0.890 0.7079 0.750
## 192 126 1 0.840 0.7083 0.885 0.6960 0.739
## 193 125 1 0.833 0.6968 0.880 0.6841 0.729
## 195 124 1 0.825 0.6848 0.874 0.6718 0.718
## 210 123 1 0.818 0.6730 0.869 0.6596 0.707
## 213 122 1 0.811 0.6612 0.863 0.6475 0.696
## 220 121 1 0.803 0.6494 0.858 0.6354 0.685
## 258 119 1 0.796 0.6375 0.852 0.6231 0.674
## 259 117 1 0.788 0.6251 0.846 0.6104 0.663
## 261 116 1 0.780 0.6129 0.841 0.5979 0.651
## 265 115 1 0.772 0.6008 0.835 0.5855 0.640
## 287 114 1 0.765 0.5889 0.829 0.5733 0.629
## 291 113 1 0.757 0.5770 0.823 0.5612 0.618
## 303 111 1 0.749 0.5649 0.817 0.5488 0.607
## 321 108 1 0.740 0.5522 0.810 0.5359 0.595
## 325 107 1 0.731 0.5394 0.803 0.5228 0.583
## 336 106 1 0.723 0.5268 0.797 0.5099 0.571
## 340 105 1 0.714 0.5142 0.790 0.4972 0.559
## 342 104 1 0.705 0.5019 0.783 0.4846 0.547
## 360 103 1 0.696 0.4896 0.776 0.4723 0.535
## 370 102 1 0.688 0.4776 0.769 0.4601 0.524
## 377 100 1 0.679 0.4657 0.762 0.4480 0.512
## 401 99 1 0.670 0.4535 0.755 0.4357 0.500
## 409 98 1 0.661 0.4416 0.748 0.4237 0.489
## 426 97 1 0.652 0.4298 0.741 0.4119 0.478
## 433 96 1 0.643 0.4183 0.734 0.4002 0.466
## 456 95 1 0.634 0.4069 0.727 0.3888 0.455
## 463 94 1 0.625 0.3957 0.720 0.3775 0.444
## 465 93 1 0.616 0.3847 0.712 0.3665 0.433
## 472 91 1 0.607 0.3735 0.705 0.3553 0.422
## 508 88 1 0.598 0.3621 0.697 0.3440 0.411
## 512 87 1 0.588 0.3509 0.690 0.3328 0.400
## 515 86 2 0.569 0.3292 0.674 0.3112 0.378
## 527 81 1 0.559 0.3179 0.666 0.3000 0.367
## 539 80 1 0.549 0.3068 0.657 0.2889 0.355
## 575 77 1 0.539 0.2950 0.648 0.2773 0.343
## 618 75 1 0.527 0.2831 0.639 0.2655 0.331
## 632 73 1 0.516 0.2712 0.629 0.2538 0.319
## 635 72 1 0.505 0.2597 0.620 0.2425 0.307
## 639 71 1 0.494 0.2484 0.610 0.2315 0.296
## 646 70 1 0.483 0.2375 0.600 0.2208 0.284
## 685 68 1 0.471 0.2264 0.590 0.2100 0.272
## 703 66 1 0.459 0.2152 0.580 0.1991 0.261
## 754 63 1 0.446 0.2034 0.568 0.1876 0.248
## 815 59 1 0.432 0.1914 0.556 0.1760 0.235
## 907 53 1 0.417 0.1783 0.542 0.1634 0.221
## 911 52 1 0.402 0.1657 0.528 0.1513 0.207
## 991 51 1 0.387 0.1539 0.515 0.1400 0.194
## 1028 49 1 0.372 0.1425 0.501 0.1291 0.182
## 1076 48 1 0.358 0.1318 0.487 0.1189 0.170
## 1141 47 1 0.344 0.1215 0.473 0.1092 0.158
## 1213 41 1 0.327 0.1101 0.457 0.0984 0.145
## 1280 37 1 0.309 0.0988 0.440 0.0878 0.132
## 1295 35 1 0.292 0.0882 0.422 0.0780 0.119
## 1369 32 1 0.272 0.0769 0.402 0.0675 0.106
## 1548 22 1 0.240 0.0598 0.368 0.0519 0.085
## survival6 survival7 survival8 survival9 survival10 survival11 survival12
## 0.991 0.995 0.997 0.992 0.997 0.997 0.994
## 0.983 0.989 0.995 0.985 0.994 0.995 0.989
## 0.974 0.984 0.992 0.977 0.990 0.992 0.983
## 0.966 0.978 0.989 0.969 0.987 0.989 0.977
## 0.957 0.973 0.987 0.961 0.984 0.986 0.971
## 0.949 0.967 0.984 0.954 0.981 0.983 0.966
## 0.940 0.961 0.981 0.946 0.977 0.980 0.960
## 0.932 0.956 0.978 0.938 0.974 0.978 0.954
## 0.923 0.950 0.976 0.930 0.971 0.975 0.948
## 0.914 0.944 0.973 0.922 0.967 0.972 0.942
## 0.906 0.939 0.970 0.914 0.964 0.969 0.936
## 0.897 0.933 0.967 0.906 0.960 0.966 0.930
## 0.889 0.927 0.964 0.898 0.957 0.963 0.924
## 0.871 0.916 0.958 0.883 0.950 0.957 0.912
## 0.863 0.910 0.955 0.875 0.946 0.954 0.906
## 0.854 0.904 0.952 0.866 0.943 0.951 0.899
## 0.845 0.898 0.949 0.858 0.939 0.947 0.893
## 0.836 0.892 0.946 0.849 0.935 0.944 0.887
## 0.826 0.885 0.943 0.841 0.931 0.941 0.880
## 0.817 0.879 0.940 0.833 0.928 0.937 0.874
## 0.808 0.873 0.936 0.825 0.924 0.934 0.867
## 0.800 0.867 0.933 0.816 0.920 0.931 0.861
## 0.790 0.861 0.930 0.808 0.916 0.927 0.854
## 0.781 0.854 0.927 0.799 0.912 0.924 0.848
## 0.772 0.848 0.923 0.791 0.908 0.920 0.841
## 0.763 0.841 0.920 0.782 0.904 0.917 0.834
## 0.753 0.834 0.916 0.773 0.900 0.913 0.827
## 0.744 0.828 0.913 0.764 0.896 0.910 0.820
## 0.734 0.821 0.909 0.756 0.891 0.906 0.813
## 0.725 0.814 0.905 0.747 0.887 0.902 0.806
## 0.715 0.807 0.901 0.737 0.882 0.898 0.798
## 0.705 0.800 0.897 0.728 0.878 0.894 0.791
## 0.695 0.792 0.894 0.718 0.873 0.890 0.783
## 0.685 0.785 0.890 0.709 0.868 0.886 0.776
## 0.675 0.778 0.886 0.700 0.864 0.882 0.768
## 0.665 0.770 0.881 0.690 0.859 0.877 0.761
## 0.654 0.762 0.877 0.680 0.854 0.873 0.752
## 0.643 0.754 0.872 0.670 0.848 0.868 0.744
## 0.632 0.746 0.868 0.660 0.843 0.863 0.736
## 0.621 0.738 0.863 0.649 0.838 0.859 0.727
## 0.611 0.730 0.859 0.639 0.832 0.854 0.719
## 0.600 0.722 0.854 0.629 0.827 0.849 0.710
## 0.589 0.713 0.849 0.619 0.821 0.844 0.702
## 0.579 0.705 0.845 0.609 0.816 0.839 0.693
## 0.568 0.697 0.840 0.598 0.810 0.834 0.685
## 0.557 0.688 0.835 0.588 0.804 0.829 0.676
## 0.547 0.680 0.830 0.578 0.799 0.824 0.667
## 0.536 0.671 0.825 0.568 0.793 0.819 0.659
## 0.526 0.663 0.820 0.558 0.787 0.814 0.650
## 0.515 0.655 0.815 0.548 0.781 0.808 0.641
## 0.505 0.646 0.810 0.538 0.775 0.803 0.633
## 0.494 0.638 0.804 0.528 0.769 0.798 0.624
## 0.484 0.629 0.799 0.517 0.763 0.792 0.615
## 0.473 0.620 0.793 0.507 0.757 0.787 0.605
## 0.452 0.602 0.782 0.486 0.744 0.775 0.587
## 0.441 0.592 0.776 0.475 0.737 0.769 0.577
## 0.429 0.583 0.770 0.464 0.730 0.763 0.568
## 0.418 0.572 0.763 0.453 0.722 0.756 0.557
## 0.405 0.562 0.757 0.441 0.715 0.749 0.546
## 0.393 0.551 0.749 0.429 0.706 0.741 0.535
## 0.381 0.540 0.742 0.417 0.698 0.734 0.524
## 0.369 0.529 0.735 0.405 0.690 0.727 0.513
## 0.358 0.518 0.728 0.393 0.682 0.719 0.502
## 0.346 0.507 0.720 0.381 0.673 0.711 0.491
## 0.333 0.496 0.712 0.369 0.664 0.703 0.479
## 0.320 0.483 0.703 0.356 0.654 0.694 0.466
## 0.306 0.470 0.694 0.342 0.644 0.684 0.453
## 0.291 0.455 0.683 0.326 0.632 0.673 0.438
## 0.276 0.440 0.672 0.311 0.620 0.662 0.423
## 0.262 0.425 0.661 0.297 0.607 0.651 0.408
## 0.248 0.410 0.650 0.282 0.595 0.640 0.393
## 0.235 0.396 0.639 0.268 0.583 0.628 0.379
## 0.221 0.382 0.628 0.254 0.570 0.617 0.364
## 0.206 0.365 0.614 0.239 0.556 0.603 0.347
## 0.191 0.347 0.599 0.222 0.540 0.588 0.330
## 0.176 0.330 0.585 0.207 0.524 0.573 0.312
## 0.160 0.310 0.567 0.189 0.505 0.555 0.292
## 0.133 0.276 0.537 0.161 0.472 0.524 0.259
## survival13 survival14 survival15 survival16 survival17 survival18 survival19
## 0.998 0.993 0.997 0.999 0.999 0.999 0.997
## 0.996 0.986 0.994 0.999 0.997 0.997 0.994
## 0.994 0.979 0.991 0.998 0.996 0.996 0.991
## 0.991 0.972 0.988 0.997 0.995 0.994 0.988
## 0.989 0.965 0.986 0.997 0.994 0.993 0.985
## 0.987 0.958 0.983 0.996 0.992 0.991 0.982
## 0.985 0.951 0.980 0.995 0.991 0.990 0.979
## 0.982 0.943 0.977 0.995 0.990 0.988 0.976
## 0.980 0.936 0.974 0.994 0.988 0.986 0.973
## 0.978 0.929 0.971 0.993 0.987 0.985 0.970
## 0.976 0.922 0.968 0.992 0.986 0.983 0.967
## 0.973 0.915 0.964 0.992 0.984 0.982 0.964
## 0.971 0.907 0.961 0.991 0.983 0.980 0.960
## 0.966 0.893 0.955 0.990 0.980 0.977 0.954
## 0.964 0.885 0.952 0.989 0.979 0.975 0.951
## 0.961 0.878 0.948 0.988 0.977 0.973 0.947
## 0.959 0.870 0.945 0.987 0.976 0.972 0.944
## 0.956 0.862 0.942 0.986 0.974 0.970 0.940
## 0.953 0.855 0.938 0.986 0.972 0.968 0.937
## 0.951 0.847 0.935 0.985 0.971 0.966 0.933
## 0.948 0.839 0.931 0.984 0.969 0.964 0.930
## 0.946 0.831 0.928 0.983 0.968 0.962 0.926
## 0.943 0.824 0.924 0.982 0.966 0.961 0.923
## 0.940 0.816 0.921 0.981 0.964 0.959 0.919
## 0.937 0.808 0.917 0.980 0.963 0.957 0.915
## 0.934 0.800 0.913 0.979 0.961 0.955 0.911
## 0.932 0.792 0.910 0.979 0.959 0.953 0.908
## 0.929 0.783 0.906 0.978 0.958 0.951 0.904
## 0.926 0.775 0.902 0.977 0.956 0.949 0.900
## 0.923 0.767 0.898 0.976 0.954 0.946 0.896
## 0.919 0.758 0.894 0.975 0.952 0.944 0.891
## 0.916 0.749 0.890 0.974 0.950 0.942 0.887
## 0.913 0.740 0.885 0.972 0.948 0.940 0.883
## 0.910 0.732 0.881 0.971 0.946 0.937 0.878
## 0.906 0.723 0.877 0.970 0.944 0.935 0.874
## 0.903 0.714 0.872 0.969 0.942 0.933 0.870
## 0.899 0.704 0.868 0.968 0.940 0.930 0.865
## 0.895 0.695 0.863 0.967 0.937 0.927 0.860
## 0.892 0.685 0.858 0.966 0.935 0.925 0.855
## 0.888 0.675 0.853 0.964 0.933 0.922 0.850
## 0.884 0.666 0.848 0.963 0.930 0.919 0.845
## 0.880 0.656 0.843 0.962 0.928 0.916 0.840
## 0.876 0.647 0.838 0.960 0.925 0.914 0.834
## 0.872 0.637 0.833 0.959 0.923 0.911 0.829
## 0.868 0.627 0.828 0.958 0.920 0.908 0.824
## 0.864 0.617 0.822 0.956 0.918 0.905 0.819
## 0.860 0.608 0.817 0.955 0.915 0.902 0.813
## 0.856 0.598 0.812 0.953 0.913 0.899 0.808
## 0.851 0.588 0.807 0.952 0.910 0.896 0.802
## 0.847 0.579 0.801 0.951 0.907 0.893 0.797
## 0.843 0.569 0.796 0.949 0.905 0.890 0.791
## 0.838 0.559 0.790 0.947 0.902 0.887 0.786
## 0.834 0.549 0.784 0.946 0.899 0.883 0.780
## 0.829 0.539 0.778 0.944 0.896 0.880 0.774
## 0.820 0.519 0.767 0.941 0.890 0.873 0.762
## 0.815 0.509 0.760 0.939 0.887 0.869 0.755
## 0.809 0.498 0.754 0.937 0.883 0.866 0.749
## 0.804 0.487 0.747 0.935 0.880 0.861 0.742
## 0.798 0.475 0.739 0.933 0.876 0.857 0.734
## 0.792 0.463 0.732 0.931 0.872 0.853 0.726
## 0.786 0.451 0.724 0.929 0.868 0.848 0.719
## 0.779 0.440 0.717 0.927 0.864 0.844 0.711
## 0.773 0.428 0.709 0.924 0.860 0.839 0.703
## 0.767 0.416 0.701 0.922 0.856 0.834 0.695
## 0.760 0.404 0.693 0.919 0.851 0.829 0.686
## 0.752 0.391 0.683 0.916 0.846 0.823 0.677
## 0.744 0.377 0.673 0.913 0.841 0.817 0.667
## 0.734 0.362 0.662 0.910 0.834 0.810 0.656
## 0.725 0.346 0.651 0.906 0.828 0.803 0.644
## 0.715 0.332 0.639 0.903 0.822 0.796 0.632
## 0.706 0.317 0.627 0.899 0.815 0.788 0.621
## 0.696 0.303 0.616 0.895 0.808 0.781 0.609
## 0.686 0.288 0.604 0.891 0.801 0.773 0.597
## 0.674 0.272 0.590 0.886 0.793 0.764 0.583
## 0.661 0.255 0.575 0.881 0.784 0.754 0.567
## 0.648 0.239 0.560 0.876 0.775 0.743 0.552
## 0.632 0.220 0.541 0.869 0.764 0.731 0.534
## 0.604 0.190 0.510 0.857 0.744 0.709 0.502
## survival20 survival21 survival22 survival23 survival24 survival25 survival26
## 0.997 0.997 0.999 0.994 0.994 0.998 0.994
## 0.995 0.993 0.997 0.988 0.988 0.995 0.989
## 0.992 0.990 0.996 0.982 0.981 0.993 0.983
## 0.990 0.986 0.995 0.976 0.975 0.990 0.977
## 0.987 0.983 0.994 0.970 0.969 0.987 0.971
## 0.984 0.979 0.992 0.964 0.963 0.985 0.966
## 0.981 0.976 0.991 0.958 0.956 0.982 0.960
## 0.979 0.972 0.990 0.952 0.950 0.980 0.954
## 0.976 0.968 0.988 0.946 0.944 0.977 0.948
## 0.973 0.965 0.987 0.940 0.937 0.974 0.942
## 0.970 0.961 0.986 0.934 0.931 0.972 0.936
## 0.968 0.957 0.984 0.928 0.924 0.969 0.930
## 0.965 0.954 0.983 0.921 0.918 0.966 0.924
## 0.959 0.946 0.980 0.909 0.905 0.961 0.912
## 0.956 0.942 0.979 0.903 0.898 0.958 0.906
## 0.953 0.938 0.977 0.896 0.892 0.955 0.899
## 0.950 0.934 0.976 0.889 0.885 0.952 0.893
## 0.947 0.930 0.974 0.883 0.878 0.949 0.887
## 0.944 0.926 0.972 0.876 0.871 0.946 0.880
## 0.941 0.922 0.971 0.869 0.864 0.943 0.874
## 0.937 0.918 0.969 0.863 0.857 0.940 0.867
## 0.934 0.914 0.968 0.856 0.850 0.937 0.861
## 0.931 0.910 0.966 0.849 0.843 0.934 0.854
## 0.928 0.905 0.965 0.843 0.836 0.931 0.848
## 0.925 0.901 0.963 0.836 0.829 0.928 0.841
## 0.921 0.897 0.961 0.829 0.822 0.925 0.834
## 0.918 0.892 0.959 0.821 0.814 0.921 0.827
## 0.914 0.888 0.958 0.814 0.807 0.918 0.820
## 0.910 0.883 0.956 0.807 0.799 0.914 0.813
## 0.907 0.878 0.954 0.800 0.792 0.911 0.806
## 0.903 0.873 0.952 0.792 0.784 0.907 0.798
## 0.899 0.868 0.950 0.784 0.776 0.904 0.791
## 0.895 0.863 0.948 0.777 0.768 0.900 0.783
## 0.891 0.858 0.946 0.769 0.760 0.896 0.776
## 0.887 0.853 0.944 0.761 0.752 0.892 0.768
## 0.883 0.848 0.942 0.753 0.744 0.888 0.761
## 0.879 0.843 0.940 0.745 0.735 0.884 0.752
## 0.875 0.837 0.937 0.736 0.726 0.880 0.744
## 0.870 0.831 0.935 0.727 0.717 0.876 0.736
## 0.865 0.825 0.933 0.719 0.708 0.871 0.727
## 0.861 0.820 0.930 0.710 0.699 0.867 0.719
## 0.856 0.814 0.928 0.702 0.690 0.862 0.710
## 0.852 0.808 0.926 0.693 0.681 0.858 0.702
## 0.847 0.802 0.923 0.684 0.673 0.854 0.693
## 0.842 0.796 0.921 0.675 0.663 0.849 0.685
## 0.837 0.790 0.918 0.666 0.654 0.844 0.676
## 0.832 0.784 0.915 0.658 0.645 0.840 0.667
## 0.828 0.778 0.913 0.649 0.636 0.835 0.659
## 0.823 0.772 0.910 0.640 0.627 0.830 0.650
## 0.818 0.765 0.907 0.631 0.618 0.825 0.641
## 0.813 0.759 0.905 0.622 0.609 0.820 0.633
## 0.807 0.753 0.902 0.613 0.600 0.815 0.624
## 0.802 0.746 0.899 0.604 0.590 0.810 0.615
## 0.797 0.739 0.896 0.595 0.581 0.805 0.606
## 0.786 0.726 0.890 0.576 0.562 0.794 0.587
## 0.780 0.719 0.887 0.566 0.552 0.789 0.578
## 0.774 0.711 0.884 0.556 0.542 0.783 0.568
## 0.767 0.703 0.880 0.545 0.531 0.777 0.557
## 0.760 0.695 0.876 0.534 0.519 0.770 0.546
## 0.753 0.686 0.872 0.523 0.508 0.763 0.535
## 0.746 0.678 0.868 0.512 0.497 0.756 0.524
## 0.739 0.669 0.864 0.501 0.485 0.749 0.513
## 0.732 0.661 0.860 0.490 0.474 0.742 0.502
## 0.724 0.652 0.856 0.478 0.463 0.735 0.491
## 0.716 0.642 0.851 0.466 0.451 0.727 0.479
## 0.708 0.632 0.846 0.454 0.438 0.719 0.466
## 0.698 0.621 0.841 0.440 0.424 0.710 0.453
## 0.688 0.608 0.835 0.425 0.409 0.700 0.438
## 0.677 0.596 0.828 0.410 0.393 0.689 0.423
## 0.666 0.583 0.822 0.395 0.379 0.679 0.408
## 0.655 0.570 0.815 0.380 0.364 0.668 0.393
## 0.644 0.557 0.809 0.366 0.349 0.657 0.379
## 0.633 0.545 0.802 0.351 0.335 0.646 0.364
## 0.619 0.529 0.794 0.334 0.318 0.633 0.348
## 0.605 0.513 0.785 0.317 0.301 0.619 0.330
## 0.590 0.497 0.775 0.300 0.284 0.605 0.313
## 0.573 0.477 0.764 0.280 0.264 0.588 0.293
## 0.542 0.444 0.745 0.247 0.232 0.558 0.260
## survival27 survival28 survival29 survival30 survival31 survival32 survival33
## 0.998 0.996 0.9845 0.998 0.998 0.999 0.992
## 0.995 0.992 0.9691 0.997 0.996 0.997 0.984
## 0.993 0.988 0.9538 0.995 0.994 0.996 0.976
## 0.990 0.984 0.9387 0.994 0.992 0.994 0.969
## 0.988 0.980 0.9237 0.992 0.990 0.993 0.961
## 0.985 0.976 0.9087 0.990 0.988 0.992 0.953
## 0.983 0.972 0.8938 0.988 0.986 0.990 0.945
## 0.980 0.967 0.8789 0.987 0.984 0.989 0.937
## 0.978 0.963 0.8641 0.985 0.982 0.987 0.929
## 0.975 0.959 0.8493 0.983 0.980 0.986 0.921
## 0.973 0.955 0.8348 0.982 0.978 0.984 0.913
## 0.970 0.950 0.8204 0.980 0.976 0.983 0.905
## 0.968 0.946 0.8061 0.978 0.973 0.981 0.897
## 0.962 0.937 0.7776 0.974 0.969 0.978 0.881
## 0.960 0.933 0.7636 0.973 0.967 0.976 0.872
## 0.957 0.928 0.7490 0.971 0.965 0.975 0.864
## 0.954 0.924 0.7345 0.969 0.962 0.973 0.855
## 0.951 0.919 0.7202 0.967 0.960 0.971 0.847
## 0.948 0.914 0.7059 0.965 0.958 0.969 0.838
## 0.945 0.910 0.6920 0.963 0.955 0.968 0.830
## 0.942 0.905 0.6782 0.961 0.953 0.966 0.822
## 0.939 0.900 0.6645 0.959 0.950 0.964 0.813
## 0.936 0.895 0.6508 0.957 0.948 0.962 0.805
## 0.933 0.891 0.6372 0.955 0.945 0.961 0.796
## 0.930 0.886 0.6237 0.952 0.943 0.959 0.788
## 0.927 0.880 0.6097 0.950 0.940 0.957 0.779
## 0.924 0.875 0.5960 0.948 0.938 0.955 0.770
## 0.921 0.870 0.5825 0.946 0.935 0.953 0.761
## 0.917 0.865 0.5689 0.944 0.932 0.951 0.752
## 0.914 0.860 0.5553 0.941 0.929 0.949 0.743
## 0.910 0.854 0.5412 0.939 0.926 0.947 0.733
## 0.907 0.848 0.5275 0.936 0.923 0.945 0.724
## 0.903 0.843 0.5139 0.934 0.920 0.942 0.714
## 0.900 0.837 0.5007 0.931 0.917 0.940 0.705
## 0.896 0.831 0.4875 0.929 0.914 0.938 0.695
## 0.892 0.825 0.4742 0.926 0.911 0.936 0.686
## 0.888 0.819 0.4603 0.923 0.908 0.933 0.675
## 0.884 0.813 0.4464 0.920 0.904 0.931 0.665
## 0.880 0.806 0.4328 0.917 0.901 0.928 0.655
## 0.876 0.800 0.4193 0.914 0.897 0.926 0.644
## 0.871 0.793 0.4062 0.911 0.894 0.923 0.634
## 0.867 0.787 0.3934 0.908 0.890 0.920 0.624
## 0.863 0.780 0.3808 0.905 0.887 0.918 0.614
## 0.858 0.773 0.3684 0.902 0.883 0.915 0.603
## 0.854 0.767 0.3558 0.899 0.879 0.912 0.593
## 0.849 0.760 0.3437 0.896 0.875 0.909 0.583
## 0.845 0.753 0.3318 0.892 0.872 0.906 0.572
## 0.840 0.746 0.3202 0.889 0.868 0.904 0.562
## 0.836 0.739 0.3089 0.886 0.864 0.901 0.552
## 0.831 0.732 0.2978 0.883 0.860 0.898 0.542
## 0.826 0.725 0.2870 0.879 0.856 0.895 0.532
## 0.821 0.718 0.2761 0.876 0.852 0.892 0.522
## 0.816 0.711 0.2652 0.872 0.848 0.889 0.511
## 0.811 0.703 0.2545 0.868 0.843 0.885 0.500
## 0.801 0.688 0.2341 0.861 0.834 0.879 0.480
## 0.795 0.680 0.2237 0.857 0.830 0.875 0.469
## 0.790 0.672 0.2135 0.853 0.825 0.872 0.458
## 0.784 0.663 0.2028 0.848 0.820 0.868 0.446
## 0.777 0.654 0.1922 0.844 0.814 0.863 0.434
## 0.771 0.645 0.1817 0.839 0.809 0.859 0.422
## 0.764 0.636 0.1717 0.834 0.803 0.855 0.410
## 0.757 0.626 0.1621 0.829 0.797 0.850 0.398
## 0.750 0.617 0.1528 0.824 0.791 0.846 0.387
## 0.743 0.607 0.1436 0.819 0.785 0.841 0.375
## 0.736 0.597 0.1343 0.813 0.779 0.836 0.362
## 0.728 0.585 0.1248 0.807 0.772 0.831 0.349
## 0.719 0.574 0.1152 0.800 0.764 0.825 0.335
## 0.709 0.560 0.1051 0.793 0.755 0.818 0.320
## 0.698 0.547 0.0955 0.785 0.746 0.811 0.305
## 0.688 0.533 0.0867 0.777 0.737 0.804 0.290
## 0.678 0.519 0.0784 0.769 0.728 0.797 0.276
## 0.667 0.506 0.0708 0.761 0.719 0.790 0.262
## 0.656 0.492 0.0637 0.753 0.709 0.783 0.248
## 0.644 0.476 0.0560 0.743 0.698 0.774 0.233
## 0.630 0.459 0.0486 0.732 0.686 0.764 0.217
## 0.616 0.442 0.0419 0.721 0.673 0.754 0.201
## 0.599 0.422 0.0350 0.708 0.658 0.742 0.183
## 0.570 0.388 0.0252 0.684 0.632 0.721 0.155
## survival34 survival35 survival36 survival37 survival38 survival39 survival40
## 0.999 0.994 0.9869 0.9890 0.999 0.9809 0.996
## 0.997 0.987 0.9739 0.9780 0.997 0.9620 0.991
## 0.995 0.981 0.9609 0.9670 0.996 0.9433 0.987
## 0.994 0.974 0.9481 0.9560 0.995 0.9248 0.983
## 0.992 0.968 0.9353 0.9452 0.993 0.9066 0.978
## 0.991 0.961 0.9225 0.9343 0.992 0.8885 0.974
## 0.989 0.954 0.9097 0.9233 0.991 0.8704 0.969
## 0.988 0.948 0.8969 0.9123 0.989 0.8526 0.965
## 0.986 0.941 0.8841 0.9014 0.988 0.8349 0.960
## 0.984 0.934 0.8714 0.8904 0.986 0.8173 0.956
## 0.983 0.928 0.8589 0.8796 0.985 0.8001 0.951
## 0.981 0.921 0.8464 0.8688 0.984 0.7831 0.946
## 0.980 0.914 0.8339 0.8580 0.982 0.7662 0.942
## 0.976 0.901 0.8090 0.8363 0.979 0.7329 0.932
## 0.974 0.894 0.7966 0.8256 0.978 0.7166 0.928
## 0.973 0.887 0.7838 0.8143 0.976 0.6998 0.923
## 0.971 0.880 0.7710 0.8031 0.975 0.6831 0.918
## 0.969 0.872 0.7583 0.7919 0.973 0.6666 0.913
## 0.967 0.865 0.7457 0.7808 0.971 0.6504 0.908
## 0.965 0.858 0.7332 0.7698 0.970 0.6346 0.903
## 0.963 0.851 0.7209 0.7588 0.968 0.6190 0.898
## 0.962 0.844 0.7086 0.7479 0.966 0.6035 0.893
## 0.960 0.837 0.6963 0.7369 0.965 0.5882 0.887
## 0.958 0.829 0.6840 0.7260 0.963 0.5731 0.882
## 0.956 0.822 0.6717 0.7150 0.961 0.5581 0.877
## 0.954 0.814 0.6591 0.7036 0.959 0.5428 0.871
## 0.952 0.807 0.6465 0.6923 0.958 0.5277 0.866
## 0.950 0.799 0.6341 0.6811 0.956 0.5129 0.860
## 0.947 0.791 0.6217 0.6698 0.954 0.4982 0.855
## 0.945 0.783 0.6091 0.6584 0.952 0.4835 0.849
## 0.943 0.775 0.5961 0.6465 0.950 0.4685 0.843
## 0.941 0.767 0.5833 0.6348 0.948 0.4538 0.837
## 0.938 0.758 0.5706 0.6231 0.946 0.4394 0.831
## 0.936 0.750 0.5582 0.6116 0.944 0.4255 0.825
## 0.933 0.742 0.5458 0.6002 0.942 0.4117 0.819
## 0.931 0.733 0.5332 0.5885 0.940 0.3978 0.813
## 0.928 0.724 0.5200 0.5762 0.937 0.3835 0.806
## 0.926 0.715 0.5067 0.5638 0.935 0.3692 0.799
## 0.923 0.706 0.4937 0.5515 0.932 0.3554 0.792
## 0.920 0.697 0.4807 0.5393 0.930 0.3418 0.785
## 0.917 0.688 0.4680 0.5272 0.927 0.3287 0.778
## 0.914 0.679 0.4555 0.5153 0.925 0.3158 0.771
## 0.912 0.670 0.4432 0.5035 0.922 0.3034 0.764
## 0.909 0.660 0.4310 0.4918 0.920 0.2912 0.757
## 0.906 0.651 0.4186 0.4799 0.917 0.2791 0.750
## 0.903 0.642 0.4065 0.4682 0.915 0.2674 0.743
## 0.900 0.632 0.3946 0.4566 0.912 0.2559 0.736
## 0.897 0.623 0.3830 0.4452 0.909 0.2449 0.729
## 0.894 0.614 0.3715 0.4340 0.906 0.2343 0.721
## 0.890 0.605 0.3602 0.4228 0.904 0.2239 0.714
## 0.887 0.595 0.3492 0.4119 0.901 0.2140 0.707
## 0.884 0.586 0.3380 0.4007 0.898 0.2040 0.699
## 0.881 0.576 0.3267 0.3894 0.895 0.1941 0.691
## 0.877 0.566 0.3156 0.3782 0.892 0.1845 0.683
## 0.870 0.547 0.2942 0.3564 0.886 0.1664 0.668
## 0.866 0.537 0.2831 0.3451 0.882 0.1573 0.659
## 0.862 0.526 0.2722 0.3338 0.879 0.1485 0.651
## 0.858 0.515 0.2607 0.3219 0.875 0.1394 0.642
## 0.854 0.504 0.2491 0.3098 0.871 0.1304 0.632
## 0.849 0.492 0.2376 0.2977 0.867 0.1217 0.622
## 0.845 0.481 0.2265 0.2859 0.863 0.1135 0.613
## 0.840 0.470 0.2157 0.2744 0.859 0.1056 0.603
## 0.835 0.458 0.2053 0.2632 0.855 0.0982 0.593
## 0.830 0.446 0.1948 0.2518 0.850 0.0909 0.583
## 0.825 0.434 0.1842 0.2401 0.845 0.0838 0.572
## 0.819 0.421 0.1731 0.2279 0.840 0.0765 0.561
## 0.813 0.407 0.1619 0.2154 0.835 0.0693 0.548
## 0.806 0.392 0.1497 0.2017 0.828 0.0618 0.534
## 0.798 0.377 0.1381 0.1884 0.822 0.0550 0.520
## 0.791 0.362 0.1273 0.1759 0.815 0.0488 0.507
## 0.783 0.347 0.1169 0.1638 0.808 0.0431 0.493
## 0.776 0.333 0.1073 0.1523 0.801 0.0380 0.479
## 0.768 0.318 0.0982 0.1413 0.794 0.0333 0.465
## 0.759 0.302 0.0880 0.1289 0.786 0.0284 0.449
## 0.748 0.285 0.0781 0.1166 0.777 0.0238 0.431
## 0.738 0.268 0.0690 0.1050 0.767 0.0199 0.414
## 0.725 0.248 0.0593 0.0924 0.756 0.0159 0.394
## 0.703 0.217 0.0450 0.0732 0.735 0.0106 0.359
## survival41 survival42 survival43 survival44 survival45 survival46 survival47
## 0.993 0.992 0.997 0.997 0.997 0.9894 0.999
## 0.986 0.985 0.993 0.993 0.994 0.9788 0.998
## 0.978 0.977 0.990 0.990 0.991 0.9682 0.997
## 0.971 0.970 0.986 0.986 0.988 0.9577 0.996
## 0.964 0.962 0.983 0.983 0.985 0.9472 0.994
## 0.957 0.955 0.980 0.980 0.982 0.9367 0.993
## 0.949 0.947 0.976 0.976 0.979 0.9261 0.992
## 0.942 0.939 0.972 0.973 0.976 0.9155 0.991
## 0.935 0.932 0.969 0.969 0.972 0.9049 0.990
## 0.927 0.924 0.965 0.965 0.969 0.8943 0.988
## 0.920 0.916 0.962 0.962 0.966 0.8839 0.987
## 0.912 0.909 0.958 0.958 0.963 0.8734 0.986
## 0.905 0.901 0.955 0.955 0.960 0.8629 0.985
## 0.890 0.885 0.947 0.947 0.953 0.8420 0.982
## 0.883 0.878 0.943 0.944 0.950 0.8315 0.981
## 0.875 0.869 0.939 0.940 0.946 0.8207 0.980
## 0.867 0.861 0.936 0.936 0.943 0.8098 0.978
## 0.859 0.853 0.932 0.932 0.939 0.7989 0.977
## 0.851 0.845 0.928 0.928 0.936 0.7881 0.976
## 0.843 0.837 0.924 0.924 0.932 0.7774 0.974
## 0.835 0.829 0.920 0.920 0.928 0.7668 0.973
## 0.828 0.821 0.916 0.916 0.925 0.7561 0.971
## 0.820 0.812 0.911 0.912 0.921 0.7455 0.970
## 0.812 0.804 0.907 0.908 0.917 0.7348 0.968
## 0.804 0.796 0.903 0.903 0.914 0.7241 0.967
## 0.795 0.787 0.899 0.899 0.910 0.7130 0.965
## 0.787 0.778 0.894 0.895 0.906 0.7019 0.964
## 0.779 0.770 0.890 0.890 0.902 0.6910 0.962
## 0.770 0.761 0.885 0.886 0.898 0.6800 0.961
## 0.762 0.752 0.881 0.881 0.894 0.6688 0.959
## 0.753 0.743 0.876 0.876 0.889 0.6572 0.957
## 0.744 0.734 0.871 0.871 0.885 0.6457 0.956
## 0.735 0.725 0.866 0.866 0.880 0.6343 0.954
## 0.726 0.715 0.861 0.862 0.876 0.6231 0.952
## 0.717 0.706 0.856 0.857 0.872 0.6118 0.950
## 0.708 0.697 0.851 0.852 0.867 0.6003 0.948
## 0.698 0.687 0.846 0.846 0.862 0.5882 0.946
## 0.688 0.677 0.840 0.841 0.857 0.5760 0.944
## 0.679 0.667 0.835 0.835 0.852 0.5640 0.942
## 0.669 0.657 0.829 0.829 0.847 0.5519 0.940
## 0.659 0.647 0.823 0.824 0.842 0.5401 0.938
## 0.649 0.637 0.818 0.818 0.837 0.5283 0.936
## 0.639 0.627 0.812 0.812 0.831 0.5167 0.934
## 0.630 0.617 0.806 0.806 0.826 0.5051 0.932
## 0.620 0.607 0.800 0.800 0.821 0.4933 0.929
## 0.610 0.596 0.794 0.795 0.815 0.4818 0.927
## 0.600 0.586 0.788 0.789 0.810 0.4703 0.925
## 0.590 0.576 0.782 0.782 0.804 0.4589 0.922
## 0.580 0.566 0.776 0.776 0.799 0.4478 0.920
## 0.571 0.556 0.770 0.770 0.793 0.4367 0.918
## 0.561 0.547 0.764 0.764 0.788 0.4259 0.915
## 0.551 0.536 0.757 0.758 0.782 0.4147 0.913
## 0.541 0.526 0.751 0.751 0.776 0.4035 0.910
## 0.531 0.516 0.744 0.745 0.770 0.3923 0.907
## 0.511 0.495 0.731 0.731 0.758 0.3705 0.902
## 0.500 0.484 0.724 0.724 0.751 0.3591 0.899
## 0.489 0.474 0.716 0.717 0.744 0.3479 0.896
## 0.478 0.462 0.709 0.709 0.737 0.3359 0.893
## 0.466 0.450 0.700 0.701 0.730 0.3238 0.889
## 0.454 0.438 0.692 0.693 0.722 0.3116 0.886
## 0.442 0.426 0.684 0.684 0.714 0.2997 0.882
## 0.431 0.415 0.675 0.676 0.706 0.2881 0.879
## 0.419 0.403 0.667 0.667 0.698 0.2768 0.875
## 0.407 0.391 0.658 0.658 0.690 0.2652 0.871
## 0.395 0.379 0.648 0.649 0.681 0.2534 0.867
## 0.382 0.365 0.638 0.639 0.672 0.2410 0.863
## 0.368 0.351 0.627 0.628 0.662 0.2282 0.858
## 0.352 0.336 0.615 0.616 0.650 0.2142 0.852
## 0.337 0.321 0.602 0.603 0.638 0.2007 0.846
## 0.322 0.306 0.590 0.591 0.627 0.1878 0.841
## 0.308 0.292 0.577 0.578 0.615 0.1753 0.835
## 0.293 0.278 0.564 0.565 0.603 0.1635 0.829
## 0.279 0.264 0.552 0.553 0.591 0.1521 0.822
## 0.263 0.248 0.537 0.537 0.576 0.1392 0.815
## 0.246 0.231 0.520 0.521 0.561 0.1264 0.807
## 0.230 0.215 0.504 0.505 0.545 0.1142 0.798
## 0.212 0.197 0.485 0.486 0.527 0.1010 0.788
## 0.182 0.169 0.452 0.453 0.495 0.0808 0.770
## survival48 survival49 survival50 survival51 survival52 survival53 survival54
## 0.998 0.995 0.991 0.992 0.9878 0.9884 0.9855
## 0.997 0.991 0.982 0.984 0.9756 0.9768 0.9711
## 0.995 0.986 0.973 0.976 0.9635 0.9653 0.9568
## 0.993 0.982 0.964 0.968 0.9515 0.9538 0.9426
## 0.991 0.977 0.955 0.959 0.9395 0.9424 0.9285
## 0.990 0.972 0.946 0.951 0.9275 0.9310 0.9144
## 0.988 0.968 0.937 0.943 0.9154 0.9195 0.9003
## 0.986 0.963 0.927 0.935 0.9034 0.9080 0.8863
## 0.984 0.958 0.918 0.927 0.8914 0.8965 0.8723
## 0.982 0.953 0.909 0.918 0.8795 0.8851 0.8584
## 0.980 0.949 0.900 0.910 0.8676 0.8737 0.8447
## 0.978 0.944 0.891 0.902 0.8558 0.8624 0.8311
## 0.977 0.939 0.882 0.894 0.8441 0.8512 0.8175
## 0.973 0.929 0.863 0.877 0.8205 0.8286 0.7905
## 0.971 0.924 0.854 0.869 0.8088 0.8174 0.7771
## 0.969 0.919 0.845 0.860 0.7967 0.8057 0.7633
## 0.967 0.914 0.835 0.851 0.7845 0.7940 0.7495
## 0.965 0.908 0.826 0.843 0.7724 0.7824 0.7357
## 0.962 0.903 0.816 0.834 0.7604 0.7708 0.7222
## 0.960 0.898 0.807 0.825 0.7486 0.7594 0.7088
## 0.958 0.893 0.797 0.817 0.7368 0.7480 0.6956
## 0.956 0.887 0.788 0.808 0.7250 0.7367 0.6824
## 0.954 0.882 0.778 0.799 0.7133 0.7253 0.6693
## 0.952 0.876 0.769 0.790 0.7015 0.7140 0.6562
## 0.949 0.871 0.759 0.782 0.6898 0.7026 0.6432
## 0.947 0.865 0.749 0.772 0.6777 0.6908 0.6297
## 0.945 0.859 0.739 0.763 0.6656 0.6791 0.6165
## 0.942 0.854 0.729 0.754 0.6537 0.6676 0.6034
## 0.940 0.848 0.719 0.745 0.6417 0.6560 0.5903
## 0.937 0.842 0.709 0.736 0.6296 0.6442 0.5770
## 0.935 0.836 0.699 0.726 0.6170 0.6319 0.5634
## 0.932 0.829 0.688 0.716 0.6047 0.6199 0.5500
## 0.929 0.823 0.678 0.706 0.5924 0.6079 0.5367
## 0.927 0.817 0.668 0.697 0.5803 0.5962 0.5238
## 0.924 0.810 0.657 0.687 0.5683 0.5844 0.5109
## 0.921 0.804 0.647 0.677 0.5560 0.5724 0.4978
## 0.918 0.797 0.636 0.667 0.5432 0.5598 0.4842
## 0.915 0.790 0.625 0.656 0.5302 0.5472 0.4705
## 0.912 0.783 0.613 0.646 0.5175 0.5346 0.4571
## 0.909 0.775 0.602 0.635 0.5048 0.5222 0.4438
## 0.906 0.768 0.591 0.625 0.4924 0.5099 0.4308
## 0.902 0.761 0.580 0.614 0.4800 0.4978 0.4180
## 0.899 0.754 0.569 0.604 0.4679 0.4858 0.4055
## 0.896 0.747 0.558 0.594 0.4559 0.4740 0.3932
## 0.892 0.739 0.547 0.583 0.4437 0.4619 0.3807
## 0.889 0.732 0.536 0.573 0.4317 0.4500 0.3685
## 0.886 0.724 0.525 0.562 0.4199 0.4383 0.3566
## 0.882 0.717 0.514 0.552 0.4083 0.4268 0.3449
## 0.879 0.709 0.504 0.542 0.3969 0.4155 0.3335
## 0.875 0.701 0.493 0.531 0.3856 0.4043 0.3223
## 0.872 0.694 0.483 0.521 0.3746 0.3933 0.3113
## 0.868 0.686 0.472 0.511 0.3634 0.3821 0.3003
## 0.864 0.678 0.461 0.500 0.3521 0.3707 0.2892
## 0.860 0.670 0.450 0.490 0.3409 0.3595 0.2783
## 0.852 0.654 0.429 0.469 0.3192 0.3378 0.2574
## 0.848 0.645 0.417 0.458 0.3080 0.3264 0.2467
## 0.844 0.636 0.406 0.447 0.2969 0.3153 0.2361
## 0.839 0.627 0.394 0.435 0.2851 0.3034 0.2251
## 0.834 0.617 0.382 0.423 0.2733 0.2914 0.2141
## 0.829 0.607 0.370 0.411 0.2615 0.2795 0.2031
## 0.824 0.597 0.358 0.399 0.2501 0.2679 0.1926
## 0.818 0.587 0.346 0.387 0.2390 0.2565 0.1825
## 0.813 0.577 0.334 0.375 0.2282 0.2455 0.1728
## 0.808 0.567 0.322 0.363 0.2173 0.2343 0.1630
## 0.802 0.556 0.310 0.351 0.2062 0.2229 0.1531
## 0.795 0.544 0.297 0.338 0.1946 0.2110 0.1430
## 0.788 0.531 0.283 0.324 0.1828 0.1988 0.1327
## 0.780 0.517 0.268 0.308 0.1699 0.1855 0.1217
## 0.772 0.503 0.254 0.294 0.1577 0.1727 0.1113
## 0.764 0.489 0.240 0.279 0.1461 0.1607 0.1017
## 0.756 0.475 0.226 0.265 0.1350 0.1490 0.0925
## 0.747 0.461 0.213 0.251 0.1246 0.1381 0.0841
## 0.738 0.447 0.200 0.238 0.1146 0.1276 0.0762
## 0.728 0.430 0.186 0.222 0.1035 0.1158 0.0675
## 0.717 0.413 0.171 0.206 0.0926 0.1042 0.0592
## 0.705 0.395 0.157 0.191 0.0825 0.0933 0.0515
## 0.691 0.375 0.141 0.174 0.0716 0.0816 0.0436
## 0.667 0.341 0.117 0.147 0.0553 0.0639 0.0321
## survival55 survival56 survival57 survival58 survival59 survival60 survival61
## 0.9862 0.9897 0.995 0.9902 0.9835 0.992 0.996
## 0.9724 0.9794 0.990 0.9804 0.9672 0.984 0.992
## 0.9587 0.9691 0.985 0.9705 0.9509 0.976 0.989
## 0.9451 0.9588 0.980 0.9608 0.9349 0.968 0.985
## 0.9316 0.9486 0.975 0.9510 0.9190 0.959 0.981
## 0.9181 0.9384 0.970 0.9413 0.9031 0.951 0.977
## 0.9046 0.9281 0.965 0.9314 0.8873 0.943 0.973
## 0.8911 0.9177 0.959 0.9216 0.8715 0.935 0.969
## 0.8777 0.9074 0.954 0.9117 0.8559 0.927 0.965
## 0.8643 0.8971 0.949 0.9019 0.8404 0.918 0.961
## 0.8511 0.8869 0.944 0.8921 0.8251 0.910 0.957
## 0.8380 0.8767 0.938 0.8823 0.8099 0.902 0.953
## 0.8249 0.8665 0.933 0.8725 0.7949 0.894 0.949
## 0.7988 0.8461 0.922 0.8529 0.7650 0.877 0.941
## 0.7859 0.8359 0.917 0.8431 0.7503 0.869 0.936
## 0.7725 0.8252 0.911 0.8329 0.7351 0.860 0.932
## 0.7592 0.8146 0.905 0.8227 0.7199 0.851 0.928
## 0.7459 0.8040 0.900 0.8125 0.7050 0.843 0.923
## 0.7327 0.7934 0.894 0.8023 0.6902 0.834 0.919
## 0.7198 0.7829 0.888 0.7922 0.6756 0.825 0.914
## 0.7069 0.7725 0.883 0.7822 0.6613 0.817 0.910
## 0.6942 0.7621 0.877 0.7722 0.6470 0.808 0.905
## 0.6814 0.7516 0.871 0.7621 0.6329 0.799 0.901
## 0.6687 0.7412 0.865 0.7520 0.6188 0.790 0.896
## 0.6560 0.7307 0.859 0.7419 0.6049 0.782 0.892
## 0.6429 0.7198 0.853 0.7313 0.5905 0.772 0.887
## 0.6299 0.7089 0.847 0.7208 0.5763 0.763 0.882
## 0.6172 0.6982 0.840 0.7105 0.5624 0.754 0.877
## 0.6043 0.6874 0.834 0.7000 0.5485 0.745 0.872
## 0.5914 0.6764 0.828 0.6893 0.5345 0.736 0.867
## 0.5780 0.6650 0.821 0.6782 0.5201 0.726 0.861
## 0.5649 0.6537 0.814 0.6673 0.5060 0.716 0.856
## 0.5519 0.6425 0.807 0.6564 0.4922 0.707 0.851
## 0.5391 0.6314 0.800 0.6456 0.4787 0.697 0.845
## 0.5265 0.6203 0.794 0.6348 0.4653 0.687 0.840
## 0.5136 0.6090 0.787 0.6238 0.4517 0.677 0.834
## 0.5001 0.5971 0.779 0.6122 0.4377 0.667 0.828
## 0.4866 0.5850 0.771 0.6004 0.4236 0.656 0.822
## 0.4734 0.5731 0.764 0.5887 0.4099 0.646 0.816
## 0.4602 0.5612 0.756 0.5771 0.3963 0.635 0.809
## 0.4473 0.5495 0.748 0.5656 0.3831 0.625 0.803
## 0.4347 0.5379 0.741 0.5542 0.3702 0.615 0.797
## 0.4222 0.5264 0.733 0.5430 0.3576 0.604 0.791
## 0.4099 0.5149 0.725 0.5317 0.3452 0.594 0.784
## 0.3975 0.5032 0.717 0.5202 0.3327 0.583 0.778
## 0.3853 0.4917 0.709 0.5089 0.3207 0.573 0.771
## 0.3734 0.4803 0.701 0.4977 0.3088 0.562 0.765
## 0.3617 0.4691 0.693 0.4866 0.2974 0.552 0.758
## 0.3503 0.4580 0.685 0.4756 0.2862 0.542 0.751
## 0.3390 0.4470 0.677 0.4648 0.2752 0.531 0.745
## 0.3280 0.4362 0.669 0.4540 0.2646 0.521 0.738
## 0.3169 0.4251 0.661 0.4431 0.2540 0.511 0.731
## 0.3057 0.4139 0.652 0.4319 0.2433 0.500 0.724
## 0.2947 0.4027 0.644 0.4208 0.2329 0.490 0.717
## 0.2735 0.3810 0.627 0.3992 0.2131 0.469 0.703
## 0.2626 0.3696 0.618 0.3878 0.2030 0.458 0.695
## 0.2519 0.3583 0.608 0.3766 0.1931 0.447 0.687
## 0.2406 0.3463 0.599 0.3646 0.1829 0.435 0.678
## 0.2293 0.3342 0.588 0.3524 0.1727 0.423 0.670
## 0.2181 0.3220 0.578 0.3401 0.1627 0.411 0.661
## 0.2074 0.3100 0.567 0.3281 0.1531 0.399 0.651
## 0.1969 0.2984 0.557 0.3163 0.1440 0.387 0.642
## 0.1869 0.2869 0.546 0.3048 0.1353 0.375 0.633
## 0.1767 0.2753 0.536 0.2930 0.1266 0.363 0.624
## 0.1665 0.2633 0.524 0.2809 0.1179 0.351 0.614
## 0.1559 0.2508 0.512 0.2681 0.1090 0.338 0.603
## 0.1452 0.2379 0.499 0.2550 0.1002 0.324 0.591
## 0.1337 0.2237 0.484 0.2405 0.0908 0.309 0.578
## 0.1228 0.2099 0.470 0.2264 0.0820 0.294 0.565
## 0.1126 0.1969 0.455 0.2129 0.0740 0.279 0.552
## 0.1029 0.1841 0.441 0.1998 0.0664 0.265 0.538
## 0.0940 0.1720 0.427 0.1873 0.0596 0.251 0.525
## 0.0855 0.1603 0.412 0.1752 0.0532 0.238 0.512
## 0.0762 0.1472 0.395 0.1614 0.0464 0.222 0.496
## 0.0671 0.1339 0.378 0.1476 0.0399 0.206 0.479
## 0.0588 0.1214 0.360 0.1345 0.0341 0.191 0.462
## 0.0501 0.1078 0.340 0.1200 0.0282 0.174 0.443
## 0.0374 0.0867 0.306 0.0975 0.0199 0.147 0.409
## survival62 survival63 survival64 survival65 survival66 survival67 survival68
## 0.996 0.998 0.9862 0.999 0.999 0.9852 0.998
## 0.993 0.997 0.9725 0.997 0.998 0.9705 0.996
## 0.989 0.995 0.9588 0.996 0.997 0.9559 0.994
## 0.985 0.993 0.9452 0.994 0.996 0.9414 0.992
## 0.981 0.992 0.9317 0.993 0.995 0.9271 0.990
## 0.978 0.990 0.9183 0.991 0.993 0.9127 0.988
## 0.974 0.988 0.9048 0.990 0.992 0.8983 0.986
## 0.970 0.987 0.8913 0.988 0.991 0.8840 0.984
## 0.966 0.985 0.8780 0.987 0.990 0.8698 0.982
## 0.962 0.983 0.8646 0.985 0.989 0.8557 0.979
## 0.958 0.981 0.8515 0.984 0.988 0.8417 0.977
## 0.954 0.980 0.8384 0.982 0.987 0.8279 0.975
## 0.950 0.978 0.8253 0.981 0.985 0.8141 0.973
## 0.942 0.974 0.7993 0.977 0.983 0.7866 0.968
## 0.938 0.972 0.7864 0.976 0.982 0.7730 0.966
## 0.934 0.970 0.7730 0.974 0.980 0.7589 0.964
## 0.929 0.969 0.7597 0.972 0.979 0.7449 0.961
## 0.925 0.967 0.7465 0.971 0.978 0.7310 0.959
## 0.921 0.965 0.7333 0.969 0.976 0.7173 0.957
## 0.916 0.963 0.7204 0.967 0.975 0.7037 0.954
## 0.912 0.961 0.7076 0.965 0.974 0.6903 0.952
## 0.908 0.959 0.6948 0.964 0.972 0.6770 0.949
## 0.903 0.956 0.6821 0.962 0.971 0.6637 0.947
## 0.899 0.954 0.6694 0.960 0.970 0.6504 0.944
## 0.894 0.952 0.6567 0.958 0.968 0.6373 0.942
## 0.889 0.950 0.6436 0.956 0.967 0.6237 0.939
## 0.884 0.948 0.6307 0.954 0.965 0.6102 0.936
## 0.880 0.946 0.6179 0.952 0.964 0.5970 0.934
## 0.875 0.943 0.6051 0.950 0.962 0.5838 0.931
## 0.870 0.941 0.5922 0.948 0.961 0.5704 0.928
## 0.864 0.938 0.5788 0.946 0.959 0.5566 0.925
## 0.859 0.936 0.5657 0.944 0.957 0.5431 0.922
## 0.854 0.933 0.5527 0.941 0.955 0.5298 0.919
## 0.849 0.931 0.5400 0.939 0.954 0.5167 0.916
## 0.843 0.928 0.5273 0.937 0.952 0.5037 0.913
## 0.838 0.926 0.5145 0.934 0.950 0.4906 0.909
## 0.832 0.923 0.5010 0.932 0.948 0.4769 0.906
## 0.826 0.920 0.4875 0.929 0.946 0.4631 0.902
## 0.820 0.917 0.4743 0.927 0.944 0.4496 0.899
## 0.814 0.914 0.4611 0.924 0.942 0.4363 0.895
## 0.808 0.911 0.4483 0.921 0.940 0.4233 0.892
## 0.801 0.908 0.4356 0.919 0.938 0.4105 0.888
## 0.795 0.905 0.4231 0.916 0.936 0.3979 0.884
## 0.789 0.902 0.4108 0.913 0.934 0.3855 0.881
## 0.783 0.898 0.3984 0.910 0.932 0.3730 0.877
## 0.776 0.895 0.3863 0.908 0.929 0.3609 0.873
## 0.770 0.892 0.3743 0.905 0.927 0.3489 0.869
## 0.763 0.889 0.3626 0.902 0.925 0.3373 0.865
## 0.757 0.885 0.3512 0.899 0.923 0.3259 0.861
## 0.750 0.882 0.3399 0.896 0.920 0.3147 0.857
## 0.744 0.879 0.3289 0.893 0.918 0.3038 0.853
## 0.737 0.875 0.3178 0.890 0.916 0.2928 0.849
## 0.730 0.871 0.3066 0.886 0.913 0.2818 0.845
## 0.723 0.868 0.2956 0.883 0.911 0.2709 0.840
## 0.709 0.860 0.2744 0.876 0.905 0.2502 0.831
## 0.701 0.856 0.2635 0.873 0.903 0.2395 0.826
## 0.693 0.852 0.2528 0.869 0.900 0.2291 0.822
## 0.685 0.848 0.2415 0.865 0.896 0.2182 0.816
## 0.676 0.843 0.2302 0.861 0.893 0.2073 0.811
## 0.667 0.838 0.2190 0.856 0.890 0.1965 0.805
## 0.658 0.833 0.2082 0.852 0.886 0.1861 0.799
## 0.649 0.828 0.1977 0.848 0.883 0.1761 0.793
## 0.640 0.823 0.1877 0.843 0.879 0.1665 0.787
## 0.631 0.818 0.1775 0.838 0.876 0.1569 0.781
## 0.621 0.812 0.1673 0.833 0.872 0.1472 0.774
## 0.610 0.806 0.1567 0.828 0.867 0.1372 0.767
## 0.599 0.799 0.1459 0.822 0.862 0.1272 0.760
## 0.586 0.792 0.1344 0.815 0.857 0.1164 0.751
## 0.573 0.784 0.1234 0.808 0.851 0.1063 0.742
## 0.560 0.776 0.1133 0.801 0.846 0.0969 0.733
## 0.546 0.768 0.1035 0.793 0.840 0.0880 0.723
## 0.533 0.760 0.0945 0.786 0.834 0.0799 0.714
## 0.520 0.752 0.0860 0.779 0.828 0.0722 0.704
## 0.504 0.742 0.0767 0.770 0.821 0.0638 0.693
## 0.488 0.731 0.0676 0.760 0.813 0.0558 0.680
## 0.471 0.720 0.0593 0.750 0.805 0.0484 0.668
## 0.451 0.706 0.0505 0.737 0.795 0.0408 0.653
## 0.418 0.683 0.0377 0.716 0.777 0.0298 0.626
## survival69 survival70 survival71 survival72 survival73 survival74 survival75
## 0.991 0.995 0.996 0.995 0.997 0.992 0.994
## 0.982 0.990 0.992 0.989 0.994 0.985 0.987
## 0.973 0.985 0.989 0.984 0.991 0.977 0.981
## 0.965 0.981 0.985 0.978 0.988 0.970 0.975
## 0.956 0.976 0.981 0.973 0.985 0.962 0.968
## 0.947 0.971 0.977 0.967 0.982 0.955 0.962
## 0.938 0.966 0.973 0.962 0.979 0.947 0.956
## 0.929 0.961 0.969 0.956 0.976 0.940 0.949
## 0.920 0.956 0.965 0.950 0.973 0.932 0.943
## 0.911 0.951 0.961 0.945 0.970 0.924 0.936
## 0.902 0.946 0.957 0.939 0.966 0.917 0.929
## 0.893 0.941 0.953 0.933 0.963 0.909 0.923
## 0.884 0.936 0.949 0.928 0.960 0.901 0.916
## 0.866 0.925 0.941 0.916 0.954 0.886 0.903
## 0.857 0.920 0.937 0.910 0.950 0.878 0.896
## 0.848 0.915 0.932 0.904 0.947 0.870 0.890
## 0.839 0.909 0.928 0.898 0.943 0.862 0.882
## 0.829 0.903 0.923 0.892 0.940 0.853 0.875
## 0.820 0.898 0.919 0.886 0.936 0.845 0.868
## 0.811 0.892 0.914 0.880 0.933 0.837 0.861
## 0.801 0.887 0.910 0.874 0.929 0.829 0.854
## 0.792 0.881 0.905 0.867 0.926 0.821 0.847
## 0.783 0.876 0.901 0.861 0.922 0.813 0.840
## 0.773 0.870 0.896 0.855 0.918 0.805 0.833
## 0.764 0.864 0.892 0.849 0.915 0.796 0.826
## 0.754 0.858 0.887 0.842 0.911 0.788 0.818
## 0.745 0.852 0.882 0.835 0.907 0.779 0.811
## 0.735 0.846 0.877 0.829 0.903 0.770 0.803
## 0.725 0.840 0.872 0.822 0.899 0.762 0.796
## 0.715 0.834 0.867 0.815 0.895 0.753 0.788
## 0.705 0.827 0.861 0.808 0.890 0.744 0.780
## 0.694 0.821 0.856 0.801 0.886 0.734 0.772
## 0.684 0.814 0.851 0.793 0.882 0.725 0.764
## 0.674 0.807 0.845 0.786 0.877 0.716 0.756
## 0.664 0.801 0.840 0.779 0.873 0.707 0.747
## 0.654 0.794 0.834 0.771 0.868 0.698 0.739
## 0.643 0.787 0.828 0.764 0.863 0.688 0.730
## 0.631 0.779 0.822 0.755 0.858 0.678 0.721
## 0.620 0.772 0.816 0.747 0.853 0.668 0.712
## 0.609 0.764 0.810 0.739 0.848 0.657 0.703
## 0.598 0.757 0.803 0.731 0.843 0.647 0.694
## 0.588 0.749 0.797 0.723 0.838 0.637 0.685
## 0.577 0.742 0.791 0.715 0.833 0.628 0.676
## 0.566 0.734 0.785 0.707 0.828 0.618 0.667
## 0.555 0.727 0.778 0.698 0.822 0.607 0.658
## 0.544 0.719 0.771 0.690 0.817 0.597 0.649
## 0.533 0.711 0.765 0.681 0.812 0.587 0.640
## 0.522 0.703 0.758 0.673 0.806 0.577 0.630
## 0.512 0.695 0.752 0.665 0.801 0.567 0.621
## 0.501 0.688 0.745 0.656 0.795 0.557 0.612
## 0.491 0.680 0.738 0.648 0.790 0.547 0.603
## 0.480 0.672 0.731 0.639 0.784 0.537 0.594
## 0.469 0.663 0.724 0.630 0.778 0.527 0.584
## 0.458 0.655 0.717 0.621 0.772 0.517 0.574
## 0.437 0.638 0.703 0.604 0.760 0.496 0.555
## 0.426 0.629 0.695 0.594 0.753 0.485 0.545
## 0.415 0.620 0.687 0.585 0.747 0.475 0.535
## 0.403 0.611 0.679 0.574 0.740 0.463 0.524
## 0.391 0.601 0.670 0.564 0.732 0.451 0.513
## 0.378 0.590 0.661 0.553 0.724 0.439 0.501
## 0.366 0.580 0.652 0.542 0.717 0.427 0.490
## 0.354 0.570 0.643 0.531 0.709 0.416 0.478
## 0.343 0.559 0.634 0.520 0.701 0.404 0.467
## 0.331 0.549 0.624 0.509 0.693 0.392 0.456
## 0.318 0.538 0.614 0.498 0.684 0.380 0.443
## 0.305 0.525 0.603 0.485 0.675 0.366 0.430
## 0.292 0.513 0.592 0.472 0.665 0.353 0.417
## 0.277 0.498 0.578 0.457 0.653 0.337 0.401
## 0.262 0.484 0.565 0.442 0.641 0.322 0.386
## 0.248 0.470 0.552 0.427 0.630 0.307 0.371
## 0.234 0.455 0.539 0.413 0.618 0.293 0.356
## 0.221 0.441 0.525 0.398 0.606 0.279 0.342
## 0.208 0.427 0.512 0.384 0.594 0.265 0.328
## 0.193 0.410 0.496 0.367 0.580 0.249 0.311
## 0.178 0.392 0.479 0.349 0.564 0.232 0.294
## 0.164 0.375 0.463 0.332 0.549 0.216 0.277
## 0.148 0.355 0.443 0.312 0.530 0.198 0.257
## 0.123 0.321 0.409 0.278 0.499 0.169 0.225
## survival76 survival77 survival78 survival79 survival80 survival81 survival82
## 0.997 0.998 0.993 0.990 0.998 0.996 0.991
## 0.994 0.995 0.987 0.981 0.996 0.992 0.982
## 0.990 0.993 0.980 0.971 0.994 0.988 0.974
## 0.987 0.990 0.973 0.961 0.991 0.984 0.965
## 0.984 0.988 0.967 0.952 0.989 0.980 0.956
## 0.981 0.985 0.960 0.942 0.987 0.975 0.947
## 0.977 0.982 0.953 0.932 0.985 0.971 0.939
## 0.974 0.980 0.946 0.923 0.982 0.967 0.930
## 0.971 0.977 0.939 0.913 0.980 0.963 0.921
## 0.967 0.975 0.932 0.903 0.978 0.958 0.912
## 0.964 0.972 0.926 0.894 0.975 0.954 0.903
## 0.960 0.969 0.919 0.884 0.973 0.950 0.894
## 0.957 0.967 0.912 0.874 0.971 0.946 0.885
## 0.950 0.961 0.898 0.855 0.966 0.937 0.868
## 0.946 0.958 0.891 0.845 0.964 0.932 0.859
## 0.943 0.956 0.884 0.835 0.961 0.928 0.849
## 0.939 0.953 0.876 0.825 0.958 0.923 0.840
## 0.935 0.950 0.869 0.815 0.956 0.918 0.831
## 0.931 0.947 0.861 0.805 0.953 0.914 0.821
## 0.927 0.944 0.854 0.795 0.951 0.909 0.812
## 0.924 0.941 0.847 0.785 0.948 0.904 0.803
## 0.920 0.938 0.839 0.775 0.945 0.899 0.794
## 0.916 0.935 0.832 0.765 0.943 0.894 0.785
## 0.912 0.932 0.824 0.755 0.940 0.890 0.775
## 0.908 0.928 0.817 0.745 0.937 0.885 0.766
## 0.904 0.925 0.809 0.735 0.934 0.879 0.756
## 0.899 0.922 0.801 0.724 0.931 0.874 0.747
## 0.895 0.919 0.793 0.714 0.928 0.869 0.737
## 0.891 0.915 0.785 0.704 0.925 0.864 0.727
## 0.887 0.912 0.777 0.693 0.922 0.858 0.717
## 0.882 0.908 0.769 0.682 0.919 0.853 0.707
## 0.877 0.904 0.760 0.671 0.916 0.847 0.697
## 0.873 0.901 0.752 0.661 0.912 0.841 0.687
## 0.868 0.897 0.744 0.650 0.909 0.836 0.677
## 0.863 0.893 0.735 0.639 0.906 0.830 0.667
## 0.858 0.889 0.726 0.628 0.902 0.824 0.656
## 0.853 0.885 0.717 0.617 0.899 0.818 0.645
## 0.848 0.881 0.708 0.605 0.895 0.811 0.634
## 0.842 0.877 0.699 0.593 0.891 0.805 0.623
## 0.837 0.872 0.689 0.582 0.887 0.798 0.612
## 0.832 0.868 0.680 0.570 0.883 0.791 0.601
## 0.826 0.864 0.671 0.559 0.880 0.785 0.590
## 0.821 0.859 0.661 0.548 0.876 0.778 0.580
## 0.815 0.855 0.652 0.537 0.872 0.772 0.569
## 0.809 0.850 0.642 0.525 0.867 0.765 0.558
## 0.804 0.845 0.633 0.514 0.863 0.758 0.547
## 0.798 0.841 0.623 0.503 0.859 0.751 0.536
## 0.792 0.836 0.614 0.492 0.855 0.744 0.526
## 0.786 0.831 0.605 0.481 0.851 0.737 0.515
## 0.780 0.827 0.595 0.470 0.846 0.730 0.505
## 0.774 0.822 0.586 0.459 0.842 0.723 0.494
## 0.768 0.817 0.576 0.449 0.838 0.716 0.484
## 0.762 0.812 0.566 0.437 0.833 0.709 0.473
## 0.756 0.806 0.557 0.426 0.828 0.701 0.462
## 0.743 0.796 0.537 0.405 0.819 0.686 0.441
## 0.736 0.790 0.527 0.393 0.814 0.678 0.429
## 0.729 0.784 0.516 0.382 0.809 0.670 0.418
## 0.721 0.778 0.505 0.370 0.803 0.661 0.406
## 0.713 0.772 0.494 0.358 0.797 0.652 0.394
## 0.705 0.765 0.482 0.346 0.791 0.642 0.382
## 0.697 0.758 0.470 0.334 0.785 0.633 0.370
## 0.689 0.751 0.459 0.322 0.778 0.623 0.358
## 0.681 0.744 0.447 0.310 0.772 0.614 0.346
## 0.672 0.737 0.436 0.298 0.766 0.604 0.334
## 0.663 0.729 0.423 0.286 0.759 0.594 0.322
## 0.653 0.721 0.410 0.273 0.751 0.583 0.309
## 0.643 0.712 0.396 0.260 0.743 0.571 0.295
## 0.630 0.702 0.381 0.246 0.733 0.557 0.280
## 0.618 0.691 0.366 0.231 0.724 0.543 0.265
## 0.606 0.681 0.351 0.218 0.714 0.530 0.251
## 0.594 0.670 0.336 0.205 0.704 0.516 0.237
## 0.582 0.659 0.322 0.192 0.695 0.503 0.224
## 0.569 0.649 0.307 0.180 0.685 0.489 0.211
## 0.554 0.636 0.291 0.166 0.673 0.473 0.196
## 0.538 0.622 0.274 0.152 0.660 0.456 0.181
## 0.522 0.607 0.257 0.139 0.646 0.439 0.167
## 0.503 0.590 0.238 0.124 0.630 0.419 0.151
## 0.471 0.561 0.207 0.101 0.603 0.385 0.125
## survival83 survival84 survival85 survival86 survival87 survival88 survival89
## 0.997 0.992 0.992 0.991 0.995 0.9885 0.999
## 0.994 0.984 0.984 0.981 0.990 0.9770 0.999
## 0.991 0.976 0.976 0.972 0.984 0.9655 0.998
## 0.988 0.969 0.968 0.962 0.979 0.9542 0.997
## 0.985 0.961 0.960 0.953 0.974 0.9428 0.996
## 0.982 0.953 0.952 0.944 0.969 0.9315 0.996
## 0.979 0.945 0.944 0.934 0.963 0.9201 0.995
## 0.976 0.937 0.936 0.925 0.958 0.9086 0.994
## 0.973 0.929 0.928 0.915 0.953 0.8973 0.993
## 0.970 0.921 0.920 0.906 0.947 0.8859 0.993
## 0.966 0.913 0.912 0.897 0.942 0.8747 0.992
## 0.963 0.905 0.903 0.887 0.936 0.8634 0.991
## 0.960 0.897 0.895 0.878 0.931 0.8522 0.990
## 0.954 0.881 0.879 0.859 0.920 0.8298 0.989
## 0.950 0.872 0.871 0.849 0.914 0.8186 0.988
## 0.947 0.864 0.862 0.840 0.909 0.8070 0.987
## 0.943 0.856 0.854 0.830 0.903 0.7954 0.986
## 0.940 0.847 0.845 0.820 0.897 0.7839 0.985
## 0.936 0.839 0.836 0.810 0.891 0.7723 0.984
## 0.933 0.830 0.828 0.800 0.885 0.7610 0.983
## 0.929 0.822 0.819 0.791 0.879 0.7497 0.982
## 0.926 0.813 0.811 0.781 0.873 0.7384 0.981
## 0.922 0.805 0.802 0.771 0.867 0.7271 0.981
## 0.918 0.796 0.794 0.761 0.861 0.7158 0.980
## 0.915 0.788 0.785 0.752 0.855 0.7045 0.979
## 0.911 0.779 0.776 0.741 0.849 0.6928 0.978
## 0.907 0.770 0.767 0.731 0.842 0.6812 0.977
## 0.903 0.761 0.758 0.721 0.836 0.6697 0.976
## 0.899 0.752 0.749 0.711 0.829 0.6581 0.975
## 0.895 0.743 0.740 0.701 0.823 0.6464 0.973
## 0.890 0.733 0.730 0.690 0.816 0.6342 0.972
## 0.886 0.724 0.720 0.679 0.809 0.6222 0.971
## 0.882 0.714 0.711 0.669 0.802 0.6103 0.970
## 0.877 0.705 0.701 0.658 0.795 0.5986 0.969
## 0.873 0.695 0.692 0.648 0.788 0.5869 0.968
## 0.868 0.686 0.682 0.637 0.781 0.5749 0.966
## 0.864 0.675 0.672 0.625 0.773 0.5624 0.965
## 0.859 0.665 0.661 0.614 0.765 0.5497 0.964
## 0.854 0.655 0.651 0.603 0.758 0.5372 0.962
## 0.849 0.644 0.640 0.591 0.750 0.5248 0.961
## 0.843 0.634 0.630 0.580 0.742 0.5126 0.960
## 0.838 0.624 0.620 0.569 0.734 0.5005 0.958
## 0.833 0.614 0.609 0.558 0.726 0.4886 0.957
## 0.828 0.604 0.599 0.547 0.718 0.4767 0.955
## 0.823 0.593 0.589 0.535 0.710 0.4646 0.954
## 0.817 0.583 0.578 0.524 0.702 0.4528 0.952
## 0.812 0.572 0.568 0.513 0.694 0.4411 0.951
## 0.806 0.562 0.558 0.502 0.686 0.4296 0.949
## 0.801 0.552 0.547 0.491 0.677 0.4183 0.948
## 0.795 0.542 0.537 0.481 0.669 0.4071 0.946
## 0.790 0.532 0.527 0.470 0.661 0.3961 0.945
## 0.784 0.522 0.517 0.459 0.653 0.3849 0.943
## 0.778 0.511 0.506 0.448 0.644 0.3736 0.941
## 0.772 0.501 0.496 0.437 0.635 0.3624 0.939
## 0.760 0.480 0.475 0.416 0.618 0.3406 0.936
## 0.754 0.469 0.464 0.404 0.609 0.3293 0.934
## 0.747 0.458 0.453 0.393 0.599 0.3181 0.932
## 0.740 0.446 0.441 0.381 0.589 0.3062 0.930
## 0.732 0.434 0.429 0.369 0.579 0.2943 0.927
## 0.725 0.422 0.417 0.357 0.568 0.2823 0.925
## 0.717 0.410 0.405 0.345 0.558 0.2706 0.923
## 0.709 0.398 0.393 0.333 0.547 0.2593 0.920
## 0.701 0.387 0.382 0.321 0.536 0.2482 0.918
## 0.693 0.375 0.370 0.309 0.525 0.2370 0.915
## 0.684 0.362 0.357 0.297 0.514 0.2255 0.912
## 0.675 0.349 0.344 0.284 0.502 0.2136 0.909
## 0.665 0.335 0.330 0.271 0.489 0.2013 0.906
## 0.653 0.320 0.315 0.256 0.474 0.1880 0.902
## 0.642 0.305 0.300 0.242 0.459 0.1751 0.898
## 0.630 0.290 0.285 0.228 0.445 0.1630 0.894
## 0.618 0.276 0.271 0.214 0.430 0.1512 0.890
## 0.606 0.262 0.257 0.202 0.416 0.1402 0.886
## 0.594 0.248 0.244 0.189 0.401 0.1296 0.882
## 0.580 0.233 0.228 0.175 0.384 0.1178 0.876
## 0.565 0.217 0.212 0.161 0.367 0.1060 0.871
## 0.549 0.201 0.197 0.147 0.349 0.0951 0.865
## 0.531 0.184 0.179 0.132 0.329 0.0832 0.858
## 0.499 0.156 0.151 0.108 0.295 0.0652 0.845
## survival90 survival91 survival92 survival93 survival94 survival95 survival96
## 0.992 0.9898 0.993 0.998 0.9881 0.9828 0.9879
## 0.983 0.9796 0.986 0.996 0.9761 0.9658 0.9759
## 0.975 0.9694 0.979 0.994 0.9642 0.9488 0.9638
## 0.967 0.9593 0.972 0.992 0.9525 0.9322 0.9519
## 0.958 0.9492 0.965 0.990 0.9407 0.9156 0.9400
## 0.950 0.9391 0.958 0.988 0.9290 0.8992 0.9281
## 0.942 0.9289 0.951 0.985 0.9171 0.8827 0.9162
## 0.933 0.9187 0.944 0.983 0.9053 0.8664 0.9042
## 0.925 0.9085 0.937 0.981 0.8936 0.8502 0.8923
## 0.916 0.8983 0.930 0.979 0.8818 0.8341 0.8805
## 0.908 0.8882 0.923 0.977 0.8702 0.8183 0.8687
## 0.899 0.8781 0.916 0.974 0.8586 0.8027 0.8570
## 0.891 0.8680 0.909 0.972 0.8470 0.7871 0.8453
## 0.874 0.8478 0.894 0.968 0.8239 0.7563 0.8219
## 0.865 0.8377 0.887 0.965 0.8124 0.7411 0.8103
## 0.856 0.8272 0.879 0.963 0.8005 0.7254 0.7983
## 0.848 0.8166 0.872 0.961 0.7885 0.7099 0.7862
## 0.839 0.8061 0.864 0.958 0.7766 0.6945 0.7742
## 0.830 0.7956 0.856 0.956 0.7648 0.6793 0.7622
## 0.821 0.7853 0.849 0.953 0.7531 0.6644 0.7505
## 0.812 0.7749 0.841 0.951 0.7415 0.6496 0.7388
## 0.803 0.7646 0.834 0.948 0.7299 0.6351 0.7271
## 0.794 0.7543 0.826 0.945 0.7183 0.6206 0.7154
## 0.785 0.7439 0.818 0.943 0.7068 0.6062 0.7037
## 0.776 0.7335 0.811 0.940 0.6952 0.5920 0.6921
## 0.767 0.7227 0.802 0.937 0.6832 0.5773 0.6800
## 0.758 0.7119 0.794 0.935 0.6713 0.5628 0.6680
## 0.748 0.7013 0.786 0.932 0.6595 0.5487 0.6562
## 0.739 0.6905 0.778 0.929 0.6477 0.5345 0.6442
## 0.729 0.6796 0.770 0.926 0.6357 0.5203 0.6322
## 0.719 0.6683 0.761 0.923 0.6233 0.5057 0.6197
## 0.710 0.6571 0.752 0.920 0.6110 0.4915 0.6073
## 0.700 0.6460 0.744 0.917 0.5989 0.4775 0.5951
## 0.690 0.6350 0.735 0.914 0.5870 0.4638 0.5831
## 0.680 0.6239 0.726 0.910 0.5750 0.4503 0.5711
## 0.670 0.6127 0.717 0.907 0.5629 0.4366 0.5589
## 0.660 0.6009 0.708 0.904 0.5502 0.4224 0.5461
## 0.649 0.5889 0.698 0.900 0.5373 0.4083 0.5332
## 0.638 0.5770 0.689 0.896 0.5247 0.3945 0.5205
## 0.627 0.5652 0.679 0.893 0.5121 0.3809 0.5079
## 0.617 0.5536 0.670 0.889 0.4997 0.3677 0.4954
## 0.606 0.5420 0.660 0.885 0.4875 0.3548 0.4832
## 0.596 0.5305 0.651 0.882 0.4754 0.3422 0.4711
## 0.585 0.5191 0.641 0.878 0.4634 0.3298 0.4590
## 0.575 0.5075 0.631 0.874 0.4513 0.3174 0.4468
## 0.564 0.4960 0.622 0.870 0.4394 0.3054 0.4349
## 0.553 0.4847 0.612 0.866 0.4276 0.2937 0.4231
## 0.543 0.4735 0.602 0.862 0.4160 0.2823 0.4115
## 0.533 0.4624 0.593 0.858 0.4046 0.2712 0.4002
## 0.522 0.4514 0.583 0.854 0.3934 0.2604 0.3889
## 0.512 0.4406 0.574 0.850 0.3824 0.2500 0.3779
## 0.502 0.4296 0.564 0.845 0.3712 0.2395 0.3667
## 0.491 0.4184 0.554 0.841 0.3598 0.2290 0.3553
## 0.480 0.4072 0.544 0.836 0.3486 0.2188 0.3441
## 0.459 0.3855 0.524 0.827 0.3269 0.1994 0.3224
## 0.448 0.3742 0.514 0.822 0.3156 0.1896 0.3112
## 0.437 0.3629 0.503 0.817 0.3045 0.1800 0.3001
## 0.425 0.3509 0.492 0.812 0.2927 0.1700 0.2883
## 0.413 0.3387 0.480 0.806 0.2808 0.1602 0.2765
## 0.401 0.3265 0.468 0.800 0.2690 0.1505 0.2647
## 0.389 0.3145 0.457 0.794 0.2575 0.1413 0.2532
## 0.377 0.3028 0.445 0.788 0.2463 0.1325 0.2420
## 0.365 0.2914 0.434 0.782 0.2354 0.1242 0.2312
## 0.353 0.2796 0.422 0.776 0.2243 0.1158 0.2202
## 0.341 0.2677 0.409 0.769 0.2131 0.1076 0.2091
## 0.328 0.2551 0.396 0.762 0.2014 0.0992 0.1974
## 0.314 0.2421 0.382 0.754 0.1894 0.0908 0.1855
## 0.299 0.2278 0.367 0.745 0.1764 0.0819 0.1726
## 0.284 0.2140 0.352 0.736 0.1639 0.0736 0.1602
## 0.269 0.2008 0.337 0.727 0.1521 0.0662 0.1486
## 0.255 0.1879 0.322 0.717 0.1407 0.0591 0.1374
## 0.242 0.1758 0.308 0.708 0.1301 0.0528 0.1269
## 0.228 0.1640 0.294 0.698 0.1199 0.0470 0.1168
## 0.213 0.1506 0.277 0.686 0.1086 0.0407 0.1056
## 0.197 0.1373 0.260 0.674 0.0973 0.0348 0.0946
## 0.182 0.1246 0.244 0.661 0.0869 0.0295 0.0843
## 0.166 0.1107 0.225 0.645 0.0757 0.0242 0.0733
## 0.139 0.0893 0.194 0.618 0.0588 0.0168 0.0568
## survival97 survival98 survival99 survival100 survival101 survival102
## 0.9878 0.998 0.9846 0.992 0.998 0.994
## 0.9757 0.997 0.9694 0.983 0.995 0.988
## 0.9636 0.995 0.9542 0.975 0.993 0.982
## 0.9516 0.993 0.9392 0.967 0.991 0.977
## 0.9396 0.992 0.9243 0.959 0.988 0.971
## 0.9276 0.990 0.9095 0.950 0.986 0.965
## 0.9156 0.988 0.8946 0.942 0.984 0.959
## 0.9036 0.987 0.8798 0.934 0.981 0.953
## 0.8916 0.985 0.8651 0.925 0.979 0.947
## 0.8797 0.983 0.8505 0.917 0.976 0.941
## 0.8679 0.981 0.8361 0.909 0.974 0.935
## 0.8561 0.980 0.8218 0.900 0.972 0.929
## 0.8443 0.978 0.8076 0.892 0.969 0.923
## 0.8208 0.974 0.7793 0.875 0.964 0.910
## 0.8091 0.972 0.7653 0.866 0.961 0.904
## 0.7970 0.971 0.7509 0.858 0.959 0.898
## 0.7849 0.969 0.7365 0.849 0.956 0.891
## 0.7728 0.967 0.7222 0.840 0.953 0.885
## 0.7608 0.965 0.7081 0.831 0.950 0.878
## 0.7490 0.963 0.6942 0.822 0.948 0.871
## 0.7372 0.961 0.6804 0.813 0.945 0.865
## 0.7255 0.959 0.6668 0.805 0.942 0.858
## 0.7137 0.956 0.6532 0.796 0.939 0.852
## 0.7020 0.954 0.6397 0.787 0.936 0.845
## 0.6903 0.952 0.6263 0.778 0.933 0.838
## 0.6781 0.950 0.6124 0.769 0.930 0.831
## 0.6661 0.948 0.5987 0.760 0.927 0.824
## 0.6542 0.946 0.5852 0.750 0.924 0.817
## 0.6422 0.943 0.5717 0.741 0.921 0.810
## 0.6301 0.941 0.5581 0.731 0.918 0.803
## 0.6176 0.938 0.5441 0.722 0.914 0.795
## 0.6052 0.936 0.5304 0.712 0.911 0.787
## 0.5930 0.933 0.5169 0.702 0.907 0.780
## 0.5809 0.931 0.5037 0.692 0.904 0.772
## 0.5689 0.928 0.4905 0.683 0.901 0.765
## 0.5567 0.926 0.4772 0.673 0.897 0.757
## 0.5438 0.923 0.4634 0.662 0.893 0.748
## 0.5309 0.920 0.4495 0.651 0.889 0.740
## 0.5181 0.917 0.4359 0.641 0.885 0.731
## 0.5055 0.914 0.4225 0.630 0.881 0.723
## 0.4930 0.911 0.4094 0.620 0.877 0.714
## 0.4807 0.908 0.3965 0.609 0.873 0.706
## 0.4686 0.905 0.3840 0.599 0.869 0.697
## 0.4566 0.902 0.3716 0.588 0.864 0.689
## 0.4443 0.899 0.3590 0.577 0.860 0.680
## 0.4324 0.895 0.3469 0.567 0.856 0.671
## 0.4206 0.892 0.3350 0.556 0.851 0.662
## 0.4090 0.889 0.3233 0.546 0.847 0.653
## 0.3976 0.885 0.3120 0.536 0.843 0.645
## 0.3863 0.882 0.3009 0.525 0.838 0.636
## 0.3753 0.879 0.2901 0.515 0.834 0.627
## 0.3641 0.875 0.2792 0.505 0.829 0.618
## 0.3528 0.872 0.2683 0.494 0.824 0.609
## 0.3416 0.868 0.2576 0.483 0.819 0.600
## 0.3199 0.860 0.2371 0.462 0.809 0.581
## 0.3086 0.856 0.2266 0.451 0.804 0.571
## 0.2975 0.852 0.2164 0.440 0.798 0.562
## 0.2858 0.848 0.2057 0.428 0.792 0.551
## 0.2740 0.843 0.1950 0.416 0.786 0.540
## 0.2622 0.838 0.1844 0.404 0.780 0.529
## 0.2508 0.833 0.1744 0.392 0.773 0.518
## 0.2396 0.828 0.1646 0.380 0.767 0.507
## 0.2289 0.823 0.1553 0.368 0.760 0.496
## 0.2179 0.818 0.1460 0.356 0.754 0.484
## 0.2068 0.812 0.1367 0.344 0.746 0.472
## 0.1952 0.806 0.1271 0.331 0.738 0.460
## 0.1834 0.800 0.1174 0.317 0.730 0.446
## 0.1705 0.792 0.1071 0.302 0.720 0.431
## 0.1582 0.784 0.0975 0.287 0.710 0.416
## 0.1466 0.776 0.0885 0.273 0.700 0.401
## 0.1355 0.768 0.0801 0.258 0.690 0.386
## 0.1251 0.760 0.0724 0.245 0.680 0.372
## 0.1151 0.752 0.0652 0.231 0.669 0.357
## 0.1040 0.742 0.0574 0.216 0.657 0.340
## 0.0930 0.731 0.0499 0.200 0.643 0.323
## 0.0829 0.720 0.0431 0.185 0.630 0.306
## 0.0720 0.707 0.0360 0.168 0.613 0.286
## 0.0556 0.683 0.0260 0.141 0.585 0.253
## survival103 survival104 survival105 survival106 survival107 survival108
## 0.997 0.97916 0.992 0.997 0.997 0.997
## 0.995 0.95859 0.984 0.994 0.993 0.994
## 0.992 0.93819 0.976 0.991 0.990 0.991
## 0.989 0.91819 0.968 0.988 0.986 0.988
## 0.986 0.89844 0.960 0.985 0.983 0.985
## 0.984 0.87886 0.952 0.982 0.980 0.982
## 0.981 0.85936 0.944 0.979 0.976 0.979
## 0.978 0.84009 0.936 0.976 0.973 0.976
## 0.975 0.82105 0.928 0.973 0.969 0.973
## 0.972 0.80223 0.920 0.969 0.965 0.970
## 0.969 0.78381 0.912 0.966 0.962 0.967
## 0.966 0.76561 0.904 0.963 0.958 0.964
## 0.963 0.74763 0.895 0.960 0.955 0.961
## 0.957 0.71221 0.879 0.953 0.947 0.954
## 0.954 0.69488 0.871 0.950 0.944 0.951
## 0.951 0.67707 0.862 0.946 0.940 0.948
## 0.948 0.65946 0.854 0.943 0.936 0.944
## 0.945 0.64213 0.845 0.939 0.932 0.941
## 0.941 0.62508 0.837 0.936 0.928 0.938
## 0.938 0.60845 0.828 0.932 0.924 0.934
## 0.935 0.59212 0.820 0.929 0.920 0.931
## 0.932 0.57603 0.811 0.925 0.916 0.927
## 0.928 0.56011 0.802 0.921 0.912 0.923
## 0.925 0.54438 0.794 0.918 0.908 0.920
## 0.921 0.52888 0.785 0.914 0.903 0.916
## 0.918 0.51297 0.776 0.910 0.899 0.912
## 0.914 0.49741 0.767 0.906 0.895 0.909
## 0.911 0.48225 0.758 0.902 0.890 0.905
## 0.907 0.46718 0.749 0.898 0.886 0.901
## 0.903 0.45213 0.740 0.894 0.881 0.897
## 0.899 0.43678 0.730 0.890 0.876 0.892
## 0.895 0.42187 0.721 0.885 0.872 0.888
## 0.891 0.40730 0.711 0.881 0.867 0.884
## 0.887 0.39317 0.702 0.877 0.862 0.880
## 0.883 0.37928 0.692 0.872 0.857 0.875
## 0.879 0.36536 0.682 0.868 0.852 0.871
## 0.874 0.35100 0.672 0.863 0.846 0.866
## 0.870 0.33677 0.661 0.858 0.841 0.861
## 0.865 0.32299 0.651 0.853 0.835 0.856
## 0.860 0.30954 0.641 0.847 0.830 0.851
## 0.855 0.29655 0.630 0.842 0.824 0.846
## 0.851 0.28394 0.620 0.837 0.818 0.841
## 0.846 0.27175 0.610 0.832 0.813 0.836
## 0.841 0.25987 0.599 0.827 0.807 0.831
## 0.836 0.24803 0.589 0.821 0.801 0.826
## 0.831 0.23669 0.579 0.816 0.795 0.820
## 0.826 0.22567 0.568 0.811 0.789 0.815
## 0.821 0.21509 0.558 0.805 0.783 0.810
## 0.816 0.20490 0.548 0.800 0.777 0.804
## 0.811 0.19503 0.538 0.794 0.771 0.799
## 0.805 0.18556 0.527 0.788 0.765 0.794
## 0.800 0.17613 0.517 0.783 0.758 0.788
## 0.795 0.16681 0.507 0.777 0.752 0.782
## 0.789 0.15781 0.496 0.771 0.745 0.776
## 0.778 0.14100 0.475 0.758 0.732 0.764
## 0.771 0.13258 0.464 0.752 0.725 0.758
## 0.765 0.12450 0.453 0.745 0.718 0.751
## 0.758 0.11618 0.442 0.738 0.710 0.744
## 0.751 0.10805 0.430 0.731 0.701 0.737
## 0.744 0.10018 0.417 0.723 0.693 0.729
## 0.737 0.09279 0.405 0.715 0.685 0.721
## 0.730 0.08583 0.394 0.707 0.676 0.714
## 0.722 0.07930 0.382 0.699 0.668 0.706
## 0.714 0.07288 0.370 0.691 0.659 0.698
## 0.706 0.06661 0.357 0.682 0.649 0.689
## 0.697 0.06033 0.344 0.673 0.639 0.680
## 0.688 0.05418 0.331 0.663 0.628 0.670
## 0.677 0.04782 0.315 0.651 0.616 0.659
## 0.666 0.04204 0.300 0.639 0.604 0.647
## 0.655 0.03690 0.286 0.628 0.591 0.636
## 0.643 0.03220 0.271 0.616 0.578 0.624
## 0.632 0.02807 0.257 0.604 0.566 0.612
## 0.620 0.02433 0.244 0.592 0.553 0.600
## 0.607 0.02044 0.228 0.578 0.538 0.586
## 0.592 0.01688 0.212 0.562 0.522 0.571
## 0.577 0.01383 0.197 0.547 0.506 0.556
## 0.559 0.01086 0.180 0.528 0.486 0.537
## 0.529 0.00698 0.152 0.496 0.453 0.506
## survival109 survival110 survival111 survival112 survival113 survival114
## 0.999 0.999 0.9868 0.997 0.996 0.997
## 0.997 0.998 0.9736 0.994 0.991 0.995
## 0.996 0.996 0.9605 0.990 0.986 0.992
## 0.995 0.995 0.9475 0.987 0.982 0.989
## 0.994 0.994 0.9346 0.984 0.977 0.987
## 0.992 0.993 0.9216 0.981 0.973 0.984
## 0.991 0.991 0.9087 0.978 0.968 0.981
## 0.990 0.990 0.8957 0.974 0.963 0.978
## 0.988 0.989 0.8828 0.971 0.959 0.975
## 0.987 0.988 0.8700 0.967 0.954 0.973
## 0.985 0.986 0.8573 0.964 0.949 0.970
## 0.984 0.985 0.8447 0.961 0.944 0.967
## 0.983 0.984 0.8321 0.957 0.940 0.964
## 0.980 0.981 0.8070 0.950 0.930 0.958
## 0.978 0.980 0.7945 0.947 0.925 0.955
## 0.977 0.978 0.7816 0.943 0.920 0.952
## 0.975 0.977 0.7687 0.939 0.915 0.949
## 0.974 0.975 0.7558 0.936 0.910 0.946
## 0.972 0.974 0.7431 0.932 0.904 0.942
## 0.971 0.972 0.7305 0.928 0.899 0.939
## 0.969 0.971 0.7181 0.924 0.894 0.936
## 0.967 0.969 0.7057 0.921 0.889 0.933
## 0.966 0.968 0.6933 0.917 0.883 0.930
## 0.964 0.966 0.6809 0.913 0.878 0.926
## 0.962 0.964 0.6686 0.909 0.873 0.923
## 0.961 0.963 0.6558 0.905 0.867 0.919
## 0.959 0.961 0.6432 0.901 0.861 0.916
## 0.957 0.959 0.6307 0.896 0.856 0.912
## 0.955 0.958 0.6182 0.892 0.850 0.908
## 0.953 0.956 0.6055 0.888 0.844 0.905
## 0.951 0.954 0.5924 0.883 0.838 0.901
## 0.949 0.952 0.5796 0.879 0.831 0.897
## 0.947 0.950 0.5669 0.874 0.825 0.893
## 0.945 0.948 0.5543 0.869 0.819 0.889
## 0.943 0.946 0.5419 0.865 0.813 0.885
## 0.941 0.944 0.5292 0.860 0.806 0.881
## 0.939 0.942 0.5160 0.855 0.799 0.876
## 0.937 0.940 0.5027 0.849 0.792 0.872
## 0.934 0.938 0.4896 0.844 0.785 0.867
## 0.932 0.936 0.4766 0.839 0.778 0.863
## 0.930 0.933 0.4638 0.833 0.771 0.858
## 0.927 0.931 0.4513 0.828 0.764 0.853
## 0.925 0.929 0.4389 0.822 0.757 0.848
## 0.922 0.926 0.4267 0.817 0.750 0.844
## 0.920 0.924 0.4143 0.811 0.742 0.839
## 0.917 0.921 0.4022 0.806 0.735 0.834
## 0.914 0.919 0.3903 0.800 0.727 0.829
## 0.912 0.916 0.3786 0.794 0.720 0.824
## 0.909 0.914 0.3672 0.788 0.713 0.819
## 0.906 0.911 0.3559 0.783 0.705 0.814
## 0.904 0.909 0.3449 0.777 0.698 0.809
## 0.901 0.906 0.3337 0.771 0.690 0.803
## 0.898 0.903 0.3224 0.764 0.682 0.798
## 0.895 0.900 0.3113 0.758 0.674 0.792
## 0.889 0.895 0.2899 0.745 0.658 0.781
## 0.886 0.892 0.2789 0.738 0.649 0.775
## 0.882 0.888 0.2680 0.732 0.641 0.769
## 0.879 0.885 0.2565 0.724 0.631 0.762
## 0.875 0.881 0.2451 0.716 0.621 0.755
## 0.871 0.878 0.2336 0.708 0.611 0.748
## 0.867 0.874 0.2226 0.700 0.601 0.741
## 0.863 0.870 0.2119 0.692 0.592 0.734
## 0.859 0.866 0.2015 0.684 0.582 0.726
## 0.854 0.862 0.1911 0.675 0.571 0.719
## 0.850 0.857 0.1805 0.666 0.560 0.711
## 0.845 0.853 0.1696 0.656 0.549 0.702
## 0.839 0.847 0.1584 0.646 0.536 0.692
## 0.833 0.841 0.1464 0.634 0.522 0.682
## 0.827 0.835 0.1349 0.622 0.508 0.671
## 0.820 0.829 0.1243 0.610 0.494 0.660
## 0.813 0.823 0.1140 0.597 0.480 0.648
## 0.807 0.816 0.1045 0.585 0.466 0.637
## 0.800 0.810 0.0955 0.573 0.452 0.626
## 0.792 0.802 0.0856 0.558 0.435 0.612
## 0.782 0.793 0.0758 0.542 0.418 0.598
## 0.773 0.784 0.0669 0.526 0.400 0.583
## 0.762 0.773 0.0574 0.507 0.380 0.565
## 0.742 0.754 0.0434 0.475 0.346 0.535
## survival115 survival116 survival117 survival118 survival119 survival120
## 0.995 0.992 0.998 0.9829 0.995 0.999
## 0.990 0.984 0.997 0.9659 0.990 0.997
## 0.985 0.976 0.995 0.9490 0.986 0.996
## 0.980 0.969 0.993 0.9324 0.981 0.994
## 0.975 0.961 0.992 0.9159 0.976 0.993
## 0.970 0.953 0.990 0.8994 0.971 0.992
## 0.965 0.945 0.988 0.8830 0.966 0.990
## 0.960 0.937 0.986 0.8667 0.961 0.989
## 0.955 0.929 0.985 0.8506 0.956 0.987
## 0.950 0.921 0.983 0.8346 0.951 0.986
## 0.944 0.913 0.981 0.8188 0.946 0.984
## 0.939 0.905 0.979 0.8032 0.941 0.983
## 0.934 0.897 0.977 0.7876 0.936 0.981
## 0.923 0.881 0.974 0.7569 0.926 0.978
## 0.918 0.873 0.972 0.7417 0.921 0.977
## 0.912 0.864 0.970 0.7261 0.916 0.975
## 0.907 0.856 0.968 0.7106 0.910 0.973
## 0.901 0.847 0.966 0.6952 0.905 0.972
## 0.895 0.839 0.964 0.6800 0.899 0.970
## 0.890 0.831 0.962 0.6651 0.894 0.968
## 0.884 0.822 0.960 0.6505 0.888 0.967
## 0.878 0.814 0.958 0.6359 0.883 0.965
## 0.873 0.805 0.956 0.6214 0.877 0.963
## 0.867 0.797 0.953 0.6071 0.872 0.961
## 0.861 0.788 0.951 0.5929 0.866 0.959
## 0.855 0.779 0.949 0.5782 0.860 0.958
## 0.849 0.770 0.947 0.5638 0.854 0.956
## 0.842 0.761 0.944 0.5496 0.848 0.954
## 0.836 0.752 0.942 0.5355 0.842 0.952
## 0.830 0.743 0.940 0.5213 0.836 0.950
## 0.823 0.734 0.937 0.5067 0.829 0.948
## 0.816 0.724 0.934 0.4925 0.823 0.945
## 0.810 0.715 0.932 0.4785 0.816 0.943
## 0.803 0.705 0.929 0.4648 0.810 0.941
## 0.796 0.696 0.927 0.4513 0.803 0.939
## 0.789 0.686 0.924 0.4377 0.796 0.937
## 0.782 0.676 0.921 0.4235 0.789 0.934
## 0.774 0.666 0.918 0.4093 0.782 0.932
## 0.767 0.655 0.915 0.3955 0.775 0.929
## 0.759 0.645 0.912 0.3820 0.767 0.927
## 0.751 0.635 0.909 0.3688 0.760 0.924
## 0.744 0.625 0.906 0.3558 0.752 0.921
## 0.736 0.614 0.903 0.3433 0.745 0.919
## 0.729 0.604 0.900 0.3309 0.737 0.916
## 0.721 0.594 0.896 0.3185 0.730 0.913
## 0.713 0.584 0.893 0.3065 0.722 0.911
## 0.705 0.573 0.890 0.2947 0.714 0.908
## 0.697 0.563 0.886 0.2833 0.707 0.905
## 0.689 0.553 0.883 0.2723 0.699 0.902
## 0.681 0.543 0.880 0.2614 0.691 0.899
## 0.673 0.533 0.876 0.2510 0.683 0.896
## 0.665 0.523 0.873 0.2405 0.675 0.893
## 0.656 0.512 0.869 0.2300 0.667 0.890
## 0.648 0.501 0.865 0.2197 0.659 0.887
## 0.631 0.481 0.857 0.2003 0.642 0.880
## 0.622 0.470 0.853 0.1905 0.633 0.877
## 0.613 0.459 0.849 0.1809 0.624 0.873
## 0.603 0.447 0.845 0.1709 0.615 0.869
## 0.593 0.435 0.840 0.1610 0.605 0.865
## 0.582 0.423 0.835 0.1513 0.594 0.861
## 0.572 0.411 0.830 0.1421 0.584 0.857
## 0.561 0.399 0.825 0.1333 0.574 0.853
## 0.551 0.388 0.820 0.1249 0.564 0.848
## 0.540 0.376 0.814 0.1166 0.553 0.844
## 0.529 0.363 0.808 0.1083 0.542 0.839
## 0.517 0.350 0.802 0.0998 0.530 0.833
## 0.504 0.336 0.795 0.0914 0.517 0.827
## 0.489 0.321 0.788 0.0825 0.503 0.821
## 0.475 0.306 0.780 0.0742 0.488 0.814
## 0.460 0.291 0.772 0.0667 0.474 0.807
## 0.446 0.277 0.764 0.0596 0.460 0.800
## 0.432 0.263 0.755 0.0533 0.446 0.793
## 0.417 0.249 0.747 0.0474 0.432 0.785
## 0.401 0.234 0.737 0.0411 0.415 0.777
## 0.383 0.217 0.726 0.0351 0.397 0.767
## 0.366 0.202 0.715 0.0298 0.380 0.757
## 0.345 0.184 0.701 0.0244 0.360 0.745
## 0.311 0.156 0.677 0.0170 0.325 0.724
## survival121 survival122 survival123 survival124 survival125 survival126
## 0.9879 0.9881 0.998 0.997 0.993 0.998
## 0.9758 0.9761 0.996 0.995 0.985 0.996
## 0.9637 0.9642 0.994 0.992 0.977 0.995
## 0.9518 0.9525 0.992 0.990 0.970 0.993
## 0.9399 0.9407 0.990 0.987 0.963 0.991
## 0.9280 0.9290 0.988 0.984 0.955 0.989
## 0.9160 0.9171 0.986 0.981 0.947 0.987
## 0.9040 0.9053 0.984 0.979 0.940 0.986
## 0.8921 0.8936 0.982 0.976 0.932 0.984
## 0.8802 0.8818 0.980 0.973 0.924 0.982
## 0.8685 0.8702 0.978 0.970 0.917 0.980
## 0.8567 0.8586 0.976 0.968 0.909 0.978
## 0.8450 0.8470 0.974 0.965 0.901 0.976
## 0.8216 0.8239 0.969 0.959 0.886 0.972
## 0.8100 0.8124 0.967 0.956 0.878 0.970
## 0.7979 0.8004 0.965 0.953 0.870 0.968
## 0.7858 0.7885 0.963 0.950 0.862 0.966
## 0.7738 0.7766 0.960 0.947 0.854 0.964
## 0.7618 0.7648 0.958 0.944 0.846 0.962
## 0.7500 0.7531 0.956 0.941 0.838 0.959
## 0.7383 0.7415 0.953 0.937 0.829 0.957
## 0.7266 0.7299 0.951 0.934 0.821 0.955
## 0.7149 0.7183 0.948 0.931 0.813 0.953
## 0.7032 0.7068 0.946 0.928 0.805 0.951
## 0.6916 0.6952 0.943 0.924 0.797 0.948
## 0.6794 0.6832 0.941 0.921 0.788 0.946
## 0.6674 0.6713 0.938 0.917 0.779 0.943
## 0.6556 0.6595 0.935 0.914 0.771 0.941
## 0.6436 0.6477 0.933 0.910 0.762 0.939
## 0.6316 0.6357 0.930 0.907 0.753 0.936
## 0.6190 0.6233 0.927 0.903 0.744 0.933
## 0.6067 0.6110 0.924 0.899 0.735 0.931
## 0.5945 0.5989 0.921 0.895 0.726 0.928
## 0.5825 0.5870 0.918 0.891 0.717 0.925
## 0.5705 0.5750 0.915 0.887 0.708 0.922
## 0.5583 0.5629 0.912 0.883 0.698 0.920
## 0.5454 0.5502 0.909 0.879 0.688 0.916
## 0.5325 0.5373 0.905 0.874 0.678 0.913
## 0.5198 0.5247 0.902 0.870 0.668 0.910
## 0.5072 0.5121 0.898 0.865 0.658 0.907
## 0.4947 0.4997 0.895 0.861 0.648 0.904
## 0.4824 0.4875 0.891 0.856 0.638 0.900
## 0.4703 0.4754 0.888 0.852 0.628 0.897
## 0.4583 0.4634 0.884 0.847 0.618 0.894
## 0.4461 0.4512 0.880 0.842 0.608 0.890
## 0.4342 0.4394 0.876 0.837 0.598 0.887
## 0.4224 0.4276 0.873 0.832 0.588 0.883
## 0.4108 0.4160 0.869 0.827 0.578 0.880
## 0.3994 0.4046 0.865 0.822 0.568 0.876
## 0.3881 0.3934 0.861 0.817 0.558 0.873
## 0.3771 0.3824 0.857 0.812 0.548 0.869
## 0.3659 0.3712 0.853 0.807 0.538 0.865
## 0.3546 0.3598 0.849 0.802 0.528 0.861
## 0.3434 0.3486 0.845 0.796 0.517 0.857
## 0.3217 0.3269 0.836 0.785 0.497 0.849
## 0.3104 0.3156 0.831 0.779 0.486 0.845
## 0.2993 0.3045 0.826 0.773 0.475 0.841
## 0.2876 0.2927 0.821 0.767 0.464 0.836
## 0.2757 0.2808 0.816 0.760 0.452 0.831
## 0.2639 0.2690 0.810 0.753 0.440 0.826
## 0.2525 0.2575 0.804 0.746 0.428 0.820
## 0.2413 0.2462 0.799 0.739 0.416 0.815
## 0.2305 0.2354 0.793 0.732 0.405 0.810
## 0.2195 0.2243 0.787 0.724 0.393 0.804
## 0.2084 0.2131 0.780 0.716 0.380 0.798
## 0.1968 0.2014 0.773 0.707 0.367 0.791
## 0.1849 0.1894 0.766 0.698 0.353 0.784
## 0.1720 0.1763 0.757 0.687 0.338 0.776
## 0.1596 0.1639 0.748 0.677 0.323 0.768
## 0.1480 0.1521 0.739 0.666 0.308 0.760
## 0.1368 0.1407 0.730 0.655 0.293 0.751
## 0.1264 0.1301 0.721 0.644 0.279 0.743
## 0.1163 0.1199 0.712 0.632 0.265 0.734
## 0.1051 0.1086 0.700 0.619 0.250 0.723
## 0.0941 0.0973 0.688 0.605 0.233 0.712
## 0.0839 0.0869 0.676 0.590 0.217 0.700
## 0.0729 0.0757 0.661 0.573 0.199 0.686
## 0.0564 0.0588 0.635 0.542 0.170 0.661
## survival127 survival128 survival129 survival130 survival131 survival132
## 0.9846 0.991 0.998 0.998 0.998 0.9858
## 0.9693 0.982 0.995 0.996 0.996 0.9718
## 0.9540 0.973 0.993 0.995 0.994 0.9577
## 0.9390 0.963 0.991 0.993 0.992 0.9439
## 0.9240 0.954 0.988 0.991 0.990 0.9301
## 0.9091 0.945 0.986 0.989 0.988 0.9163
## 0.8942 0.936 0.983 0.987 0.986 0.9025
## 0.8794 0.927 0.981 0.985 0.984 0.8887
## 0.8646 0.918 0.978 0.983 0.982 0.8751
## 0.8499 0.908 0.976 0.981 0.980 0.8614
## 0.8355 0.899 0.973 0.979 0.978 0.8480
## 0.8211 0.890 0.971 0.977 0.976 0.8346
## 0.8069 0.881 0.968 0.975 0.974 0.8213
## 0.7785 0.862 0.963 0.971 0.969 0.7947
## 0.7645 0.853 0.961 0.969 0.967 0.7816
## 0.7499 0.843 0.958 0.967 0.965 0.7680
## 0.7355 0.834 0.955 0.965 0.963 0.7544
## 0.7212 0.824 0.952 0.963 0.960 0.7409
## 0.7070 0.815 0.949 0.960 0.958 0.7276
## 0.6931 0.805 0.947 0.958 0.956 0.7144
## 0.6793 0.796 0.944 0.956 0.953 0.7014
## 0.6656 0.786 0.941 0.954 0.951 0.6884
## 0.6520 0.776 0.938 0.951 0.948 0.6755
## 0.6385 0.767 0.935 0.949 0.946 0.6626
## 0.6250 0.757 0.932 0.947 0.943 0.6497
## 0.6111 0.747 0.929 0.944 0.941 0.6364
## 0.5973 0.737 0.926 0.942 0.938 0.6233
## 0.5839 0.727 0.923 0.939 0.936 0.6104
## 0.5703 0.717 0.919 0.937 0.933 0.5974
## 0.5567 0.707 0.916 0.934 0.930 0.5843
## 0.5427 0.697 0.913 0.931 0.927 0.5708
## 0.5290 0.686 0.909 0.928 0.924 0.5575
## 0.5154 0.676 0.906 0.926 0.921 0.5444
## 0.5022 0.665 0.902 0.923 0.918 0.5316
## 0.4890 0.655 0.898 0.920 0.915 0.5188
## 0.4757 0.644 0.895 0.917 0.912 0.5058
## 0.4619 0.633 0.891 0.914 0.909 0.4923
## 0.4480 0.622 0.887 0.910 0.905 0.4787
## 0.4344 0.611 0.883 0.907 0.902 0.4653
## 0.4209 0.599 0.879 0.904 0.898 0.4521
## 0.4078 0.588 0.874 0.901 0.895 0.4392
## 0.3950 0.577 0.870 0.897 0.891 0.4265
## 0.3824 0.566 0.866 0.894 0.888 0.4140
## 0.3700 0.555 0.862 0.890 0.884 0.4016
## 0.3575 0.544 0.857 0.887 0.880 0.3892
## 0.3453 0.533 0.853 0.883 0.877 0.3770
## 0.3334 0.522 0.848 0.880 0.873 0.3650
## 0.3218 0.511 0.844 0.876 0.869 0.3534
## 0.3105 0.501 0.839 0.872 0.865 0.3420
## 0.2994 0.490 0.835 0.869 0.861 0.3307
## 0.2886 0.479 0.830 0.865 0.857 0.3198
## 0.2777 0.469 0.825 0.861 0.853 0.3087
## 0.2668 0.458 0.821 0.857 0.849 0.2975
## 0.2561 0.447 0.816 0.853 0.845 0.2865
## 0.2356 0.425 0.805 0.845 0.836 0.2655
## 0.2252 0.414 0.800 0.840 0.832 0.2547
## 0.2150 0.403 0.794 0.836 0.827 0.2441
## 0.2043 0.391 0.788 0.831 0.822 0.2329
## 0.1936 0.379 0.782 0.825 0.816 0.2217
## 0.1831 0.366 0.776 0.820 0.811 0.2107
## 0.1730 0.354 0.769 0.815 0.805 0.2000
## 0.1634 0.342 0.762 0.809 0.799 0.1897
## 0.1541 0.331 0.756 0.804 0.793 0.1798
## 0.1448 0.319 0.749 0.798 0.787 0.1698
## 0.1355 0.306 0.741 0.792 0.781 0.1598
## 0.1260 0.294 0.733 0.785 0.774 0.1495
## 0.1163 0.280 0.725 0.778 0.766 0.1390
## 0.1061 0.265 0.715 0.769 0.758 0.1277
## 0.0965 0.251 0.705 0.761 0.749 0.1170
## 0.0876 0.237 0.695 0.752 0.740 0.1071
## 0.0793 0.223 0.684 0.744 0.731 0.0977
## 0.0716 0.210 0.674 0.735 0.722 0.0890
## 0.0644 0.197 0.663 0.726 0.712 0.0808
## 0.0567 0.183 0.651 0.715 0.701 0.0718
## 0.0492 0.168 0.637 0.703 0.689 0.0631
## 0.0425 0.154 0.623 0.691 0.676 0.0552
## 0.0355 0.139 0.607 0.677 0.662 0.0468
## 0.0256 0.114 0.578 0.652 0.635 0.0347
## survival133 survival134 survival135 survival136 survival137 survival138
## 0.995 0.997 0.995 0.9876 0.999 0.999
## 0.990 0.993 0.990 0.9753 0.998 0.997
## 0.984 0.990 0.985 0.9629 0.996 0.996
## 0.979 0.986 0.979 0.9507 0.995 0.995
## 0.974 0.983 0.974 0.9386 0.994 0.994
## 0.968 0.979 0.969 0.9264 0.993 0.992
## 0.963 0.976 0.964 0.9142 0.992 0.991
## 0.958 0.972 0.958 0.9020 0.990 0.990
## 0.952 0.969 0.953 0.8899 0.989 0.988
## 0.947 0.965 0.948 0.8777 0.988 0.987
## 0.941 0.961 0.942 0.8658 0.987 0.985
## 0.936 0.958 0.937 0.8538 0.985 0.984
## 0.930 0.954 0.932 0.8419 0.984 0.983
## 0.919 0.947 0.921 0.8180 0.981 0.980
## 0.913 0.943 0.915 0.8062 0.980 0.978
## 0.908 0.939 0.909 0.7939 0.979 0.977
## 0.902 0.935 0.904 0.7816 0.977 0.975
## 0.896 0.931 0.898 0.7694 0.976 0.974
## 0.890 0.927 0.892 0.7573 0.974 0.972
## 0.884 0.923 0.886 0.7453 0.973 0.971
## 0.878 0.919 0.880 0.7334 0.971 0.969
## 0.872 0.915 0.874 0.7215 0.970 0.967
## 0.866 0.910 0.868 0.7096 0.968 0.966
## 0.860 0.906 0.862 0.6978 0.967 0.964
## 0.853 0.902 0.856 0.6859 0.965 0.962
## 0.847 0.898 0.850 0.6737 0.963 0.961
## 0.841 0.893 0.844 0.6615 0.962 0.959
## 0.834 0.889 0.837 0.6495 0.960 0.957
## 0.827 0.884 0.831 0.6374 0.958 0.955
## 0.821 0.879 0.824 0.6252 0.957 0.953
## 0.814 0.874 0.817 0.6125 0.955 0.951
## 0.807 0.870 0.811 0.6000 0.953 0.949
## 0.800 0.865 0.804 0.5877 0.951 0.947
## 0.793 0.860 0.797 0.5755 0.949 0.945
## 0.786 0.855 0.790 0.5634 0.947 0.943
## 0.778 0.850 0.783 0.5511 0.945 0.941
## 0.771 0.844 0.775 0.5382 0.943 0.939
## 0.763 0.838 0.767 0.5252 0.941 0.937
## 0.755 0.833 0.760 0.5123 0.939 0.934
## 0.747 0.827 0.752 0.4996 0.937 0.932
## 0.739 0.821 0.744 0.4871 0.935 0.930
## 0.731 0.816 0.736 0.4747 0.932 0.927
## 0.723 0.810 0.728 0.4625 0.930 0.925
## 0.715 0.804 0.720 0.4505 0.928 0.922
## 0.707 0.798 0.712 0.4382 0.925 0.920
## 0.699 0.792 0.704 0.4262 0.923 0.917
## 0.690 0.786 0.696 0.4144 0.920 0.914
## 0.682 0.780 0.688 0.4028 0.918 0.912
## 0.674 0.774 0.680 0.3914 0.915 0.909
## 0.666 0.767 0.672 0.3801 0.913 0.906
## 0.658 0.761 0.664 0.3691 0.910 0.904
## 0.649 0.755 0.655 0.3579 0.908 0.901
## 0.640 0.748 0.647 0.3465 0.905 0.898
## 0.632 0.742 0.638 0.3353 0.902 0.895
## 0.614 0.728 0.621 0.3137 0.897 0.889
## 0.605 0.721 0.612 0.3025 0.894 0.886
## 0.595 0.714 0.602 0.2914 0.890 0.882
## 0.585 0.706 0.592 0.2797 0.887 0.879
## 0.575 0.697 0.582 0.2680 0.883 0.875
## 0.564 0.689 0.571 0.2563 0.880 0.871
## 0.553 0.680 0.561 0.2449 0.876 0.867
## 0.543 0.672 0.550 0.2339 0.872 0.863
## 0.532 0.663 0.540 0.2232 0.868 0.859
## 0.521 0.654 0.529 0.2123 0.864 0.854
## 0.510 0.645 0.517 0.2013 0.860 0.850
## 0.497 0.635 0.505 0.1898 0.855 0.845
## 0.484 0.624 0.492 0.1781 0.850 0.839
## 0.469 0.611 0.477 0.1654 0.844 0.833
## 0.455 0.599 0.462 0.1533 0.838 0.827
## 0.440 0.586 0.448 0.1419 0.832 0.820
## 0.425 0.573 0.433 0.1309 0.826 0.813
## 0.411 0.561 0.419 0.1207 0.819 0.807
## 0.397 0.548 0.405 0.1109 0.813 0.800
## 0.380 0.533 0.388 0.1000 0.805 0.792
## 0.362 0.516 0.370 0.0893 0.797 0.782
## 0.345 0.500 0.353 0.0794 0.788 0.773
## 0.325 0.481 0.333 0.0688 0.777 0.762
## 0.291 0.448 0.299 0.0530 0.758 0.742
## survival139 survival140 survival141 survival142 survival143 survival144
## 0.999 0.995 0.998 0.998 0.9852 0.994
## 0.997 0.990 0.996 0.996 0.9705 0.989
## 0.996 0.984 0.994 0.995 0.9559 0.983
## 0.994 0.979 0.992 0.993 0.9414 0.978
## 0.993 0.974 0.990 0.991 0.9270 0.972
## 0.991 0.969 0.988 0.989 0.9127 0.966
## 0.990 0.964 0.986 0.987 0.8983 0.961
## 0.988 0.958 0.984 0.985 0.8840 0.955
## 0.987 0.953 0.981 0.983 0.8698 0.949
## 0.985 0.947 0.979 0.981 0.8557 0.943
## 0.984 0.942 0.977 0.979 0.8417 0.937
## 0.982 0.937 0.975 0.977 0.8279 0.931
## 0.981 0.931 0.973 0.975 0.8141 0.926
## 0.978 0.920 0.968 0.971 0.7866 0.914
## 0.976 0.915 0.966 0.969 0.7730 0.908
## 0.974 0.909 0.963 0.967 0.7589 0.902
## 0.973 0.903 0.961 0.965 0.7449 0.895
## 0.971 0.897 0.959 0.963 0.7310 0.889
## 0.969 0.891 0.956 0.961 0.7172 0.883
## 0.968 0.885 0.954 0.958 0.7037 0.876
## 0.966 0.880 0.951 0.956 0.6903 0.870
## 0.964 0.874 0.949 0.954 0.6770 0.864
## 0.962 0.868 0.946 0.952 0.6637 0.857
## 0.960 0.862 0.944 0.949 0.6504 0.851
## 0.959 0.856 0.941 0.947 0.6373 0.844
## 0.957 0.849 0.938 0.945 0.6236 0.837
## 0.955 0.843 0.936 0.942 0.6102 0.831
## 0.953 0.836 0.933 0.940 0.5970 0.824
## 0.951 0.830 0.930 0.937 0.5837 0.817
## 0.949 0.823 0.927 0.934 0.5704 0.810
## 0.946 0.816 0.924 0.932 0.5566 0.802
## 0.944 0.809 0.921 0.929 0.5431 0.795
## 0.942 0.803 0.918 0.926 0.5298 0.788
## 0.940 0.796 0.915 0.923 0.5167 0.780
## 0.938 0.789 0.912 0.920 0.5037 0.773
## 0.935 0.781 0.908 0.918 0.4906 0.765
## 0.933 0.774 0.905 0.914 0.4769 0.757
## 0.930 0.766 0.901 0.911 0.4631 0.749
## 0.928 0.758 0.898 0.908 0.4496 0.741
## 0.925 0.750 0.894 0.905 0.4363 0.732
## 0.922 0.743 0.890 0.901 0.4233 0.724
## 0.920 0.735 0.887 0.898 0.4104 0.716
## 0.917 0.727 0.883 0.895 0.3979 0.707
## 0.914 0.719 0.879 0.891 0.3855 0.699
## 0.912 0.711 0.875 0.888 0.3730 0.690
## 0.909 0.703 0.872 0.884 0.3609 0.682
## 0.906 0.694 0.868 0.881 0.3489 0.673
## 0.903 0.686 0.864 0.877 0.3372 0.665
## 0.900 0.678 0.860 0.873 0.3259 0.656
## 0.897 0.670 0.856 0.870 0.3147 0.648
## 0.894 0.662 0.852 0.866 0.3038 0.639
## 0.891 0.654 0.847 0.862 0.2928 0.630
## 0.888 0.645 0.843 0.858 0.2817 0.621
## 0.885 0.636 0.838 0.854 0.2709 0.612
## 0.878 0.619 0.830 0.846 0.2502 0.594
## 0.874 0.610 0.825 0.841 0.2395 0.584
## 0.871 0.600 0.820 0.837 0.2291 0.575
## 0.867 0.590 0.814 0.832 0.2181 0.564
## 0.863 0.580 0.809 0.827 0.2072 0.554
## 0.858 0.569 0.803 0.821 0.1964 0.542
## 0.854 0.559 0.797 0.816 0.1861 0.532
## 0.850 0.548 0.791 0.811 0.1761 0.521
## 0.845 0.538 0.785 0.805 0.1665 0.510
## 0.840 0.527 0.779 0.799 0.1569 0.498
## 0.835 0.515 0.772 0.793 0.1472 0.487
## 0.830 0.503 0.765 0.787 0.1372 0.474
## 0.824 0.490 0.757 0.779 0.1272 0.461
## 0.817 0.475 0.748 0.771 0.1164 0.446
## 0.810 0.460 0.739 0.763 0.1063 0.431
## 0.803 0.446 0.730 0.754 0.0969 0.416
## 0.796 0.431 0.720 0.745 0.0880 0.401
## 0.789 0.417 0.711 0.737 0.0799 0.387
## 0.781 0.402 0.701 0.728 0.0722 0.372
## 0.772 0.386 0.690 0.717 0.0638 0.356
## 0.763 0.368 0.677 0.705 0.0557 0.338
## 0.753 0.351 0.665 0.694 0.0484 0.321
## 0.741 0.330 0.649 0.679 0.0408 0.301
## 0.719 0.296 0.623 0.654 0.0298 0.267
## survival145 survival146 survival147 survival148 survival149
## 0.997 0.995 0.991 0.990 0.998
## 0.995 0.989 0.981 0.981 0.997
## 0.992 0.984 0.972 0.971 0.995
## 0.989 0.978 0.963 0.962 0.994
## 0.986 0.973 0.953 0.952 0.992
## 0.983 0.968 0.944 0.943 0.990
## 0.981 0.962 0.935 0.933 0.989
## 0.978 0.956 0.925 0.924 0.987
## 0.975 0.951 0.916 0.914 0.985
## 0.972 0.945 0.906 0.904 0.983
## 0.969 0.940 0.897 0.895 0.982
## 0.966 0.934 0.888 0.885 0.980
## 0.963 0.928 0.878 0.876 0.978
## 0.957 0.917 0.859 0.857 0.975
## 0.954 0.911 0.850 0.847 0.973
## 0.951 0.905 0.840 0.837 0.971
## 0.948 0.899 0.830 0.827 0.969
## 0.944 0.893 0.821 0.817 0.967
## 0.941 0.887 0.811 0.807 0.965
## 0.938 0.881 0.801 0.797 0.963
## 0.934 0.875 0.791 0.787 0.961
## 0.931 0.868 0.782 0.777 0.959
## 0.928 0.862 0.772 0.768 0.957
## 0.924 0.856 0.762 0.758 0.955
## 0.921 0.850 0.753 0.748 0.953
## 0.917 0.843 0.742 0.737 0.950
## 0.914 0.836 0.732 0.727 0.948
## 0.910 0.830 0.722 0.717 0.946
## 0.906 0.823 0.712 0.707 0.944
## 0.902 0.816 0.702 0.696 0.941
## 0.898 0.809 0.691 0.685 0.939
## 0.894 0.802 0.680 0.674 0.936
## 0.890 0.795 0.670 0.664 0.934
## 0.886 0.788 0.659 0.653 0.931
## 0.882 0.780 0.649 0.642 0.929
## 0.878 0.773 0.638 0.632 0.926
## 0.873 0.765 0.627 0.620 0.923
## 0.869 0.757 0.615 0.609 0.921
## 0.864 0.749 0.604 0.597 0.918
## 0.859 0.741 0.593 0.586 0.915
## 0.855 0.733 0.581 0.574 0.912
## 0.850 0.725 0.570 0.563 0.909
## 0.845 0.717 0.559 0.552 0.906
## 0.840 0.708 0.548 0.541 0.903
## 0.835 0.700 0.537 0.529 0.899
## 0.830 0.692 0.526 0.518 0.896
## 0.825 0.683 0.515 0.507 0.893
## 0.820 0.675 0.504 0.496 0.890
## 0.815 0.667 0.493 0.485 0.886
## 0.809 0.658 0.482 0.474 0.883
## 0.804 0.650 0.472 0.464 0.880
## 0.799 0.641 0.461 0.453 0.876
## 0.793 0.632 0.450 0.442 0.873
## 0.788 0.623 0.439 0.431 0.869
## 0.776 0.606 0.417 0.409 0.862
## 0.770 0.596 0.406 0.398 0.857
## 0.764 0.587 0.395 0.386 0.853
## 0.757 0.576 0.383 0.374 0.849
## 0.750 0.566 0.370 0.362 0.844
## 0.743 0.555 0.358 0.350 0.839
## 0.735 0.544 0.346 0.338 0.835
## 0.728 0.534 0.334 0.326 0.830
## 0.721 0.523 0.323 0.314 0.825
## 0.713 0.512 0.311 0.303 0.819
## 0.705 0.500 0.299 0.290 0.814
## 0.696 0.488 0.286 0.278 0.808
## 0.686 0.474 0.272 0.264 0.801
## 0.675 0.459 0.257 0.250 0.793
## 0.664 0.444 0.243 0.235 0.786
## 0.653 0.430 0.229 0.222 0.778
## 0.641 0.415 0.216 0.208 0.770
## 0.630 0.401 0.203 0.196 0.762
## 0.618 0.386 0.190 0.183 0.754
## 0.605 0.370 0.176 0.169 0.744
## 0.590 0.352 0.162 0.155 0.733
## 0.575 0.334 0.148 0.142 0.722
## 0.557 0.314 0.133 0.127 0.709
## 0.526 0.281 0.109 0.104 0.68510.4 GBM Classification modeling
- Let’s run and score our classification GBM model:
require(gbm)
var <- paste(colnames(train_df_classificaiton)[ !(names(train_df_classificaiton) %in%
c("PatientID", 'SurvivalTime' , "ReachedEvent", "Event"))],
collapse ="+")
classification_formula <- formula(paste('ReachedEvent ~ ', var))
classification_formula## ReachedEvent ~ Histology + Mstage + Nstage + SourceDataset +
## Tstage + age + shape_Compactness1 + shape_Compactness2 +
## shape_Maximum3DDiameter + shape_SphericalDisproportion +
## shape_Sphericity + shape_SurfaceArea + shape_SurfaceVolumeRatio +
## shape_VoxelVolume + firstorder_Energy + firstorder_Entropy +
## firstorder_Kurtosis + firstorder_Maximum + firstorder_Mean +
## firstorder_MeanAbsoluteDeviation + firstorder_Median + firstorder_Minimum +
## firstorder_Range + firstorder_RootMeanSquared + firstorder_Skewness +
## firstorder_StandardDeviation + firstorder_Uniformity + firstorder_Variance +
## glcm_Autocorrelation + glcm_ClusterProminence + glcm_ClusterShade +
## glcm_ClusterTendency + glcm_Contrast + glcm_Correlation +
## glcm_DifferenceEntropy + glcm_DifferenceAverage + glcm_JointEnergy +
## glcm_JointEntropy + glcm_Id + glcm_Idm + glcm_Imc1 + glcm_Imc2 +
## glcm_Idmn + glcm_Idn + glcm_InverseVariance + glcm_MaximumProbability +
## glcm_SumAverage + glcm_SumEntropy + glrlm_ShortRunEmphasis +
## glrlm_LongRunEmphasis + glrlm_GrayLevelNonUniformity + glrlm_RunLengthNonUniformity +
## glrlm_RunPercentage + glrlm_LowGrayLevelRunEmphasis + glrlm_HighGrayLevelRunEmphasis +
## glrlm_ShortRunLowGrayLevelEmphasis + glrlm_ShortRunHighGrayLevelEmphasis +
## glrlm_LongRunLowGrayLevelEmphasis + glrlm_LongRunHighGrayLevelEmphasisset.seed(1234)
gbm_model = gbm(classification_formula,
data = train_df_classificaiton,
distribution='bernoulli',
n.trees=2000,
interaction.depth=2,
shrinkage=0.001,
bag.fraction=0.8,
keep.data=FALSE,
cv.folds=5)
nTrees_opt_cv <- gbm.perf(gbm_model, method = "cv")
validate_predictions <- predict(gbm_model,
newdata = validate_df_classification[,feature_names],
type="response", n.trees = nTrees_opt_cv )## gbm(formula = classification_formula, distribution = "bernoulli",
## data = train_df_classificaiton, n.trees = 2000, interaction.depth = 2,
## shrinkage = 0.001, bag.fraction = 0.8, cv.folds = 5, keep.data = FALSE)
## A gradient boosted model with bernoulli loss function.
## 2000 iterations were performed.
## The best cross-validation iteration was 1994.
## There were 59 predictors of which 55 had non-zero influence.
## var
## glrlm_GrayLevelNonUniformity glrlm_GrayLevelNonUniformity
## glcm_Idn glcm_Idn
## glcm_JointEntropy glcm_JointEntropy
## age age
## glcm_Imc2 glcm_Imc2
## shape_Maximum3DDiameter shape_Maximum3DDiameter
## glcm_Idmn glcm_Idmn
## glrlm_LowGrayLevelRunEmphasis glrlm_LowGrayLevelRunEmphasis
## glrlm_LongRunLowGrayLevelEmphasis glrlm_LongRunLowGrayLevelEmphasis
## shape_SurfaceVolumeRatio shape_SurfaceVolumeRatio
## glrlm_ShortRunLowGrayLevelEmphasis glrlm_ShortRunLowGrayLevelEmphasis
## glcm_Imc1 glcm_Imc1
## firstorder_Mean firstorder_Mean
## glcm_MaximumProbability glcm_MaximumProbability
## firstorder_Kurtosis firstorder_Kurtosis
## glrlm_RunLengthNonUniformity glrlm_RunLengthNonUniformity
## glcm_JointEnergy glcm_JointEnergy
## firstorder_Skewness firstorder_Skewness
## glcm_Id glcm_Id
## Nstage Nstage
## firstorder_Median firstorder_Median
## glrlm_ShortRunHighGrayLevelEmphasis glrlm_ShortRunHighGrayLevelEmphasis
## glrlm_HighGrayLevelRunEmphasis glrlm_HighGrayLevelRunEmphasis
## firstorder_Maximum firstorder_Maximum
## shape_VoxelVolume shape_VoxelVolume
## glcm_ClusterShade glcm_ClusterShade
## firstorder_Range firstorder_Range
## shape_Compactness1 shape_Compactness1
## glcm_DifferenceEntropy glcm_DifferenceEntropy
## firstorder_Energy firstorder_Energy
## Histology Histology
## shape_SphericalDisproportion shape_SphericalDisproportion
## glrlm_LongRunEmphasis glrlm_LongRunEmphasis
## glcm_ClusterProminence glcm_ClusterProminence
## glcm_InverseVariance glcm_InverseVariance
## glcm_Autocorrelation glcm_Autocorrelation
## glcm_Correlation glcm_Correlation
## shape_SurfaceArea shape_SurfaceArea
## glcm_Idm glcm_Idm
## firstorder_RootMeanSquared firstorder_RootMeanSquared
## glrlm_ShortRunEmphasis glrlm_ShortRunEmphasis
## glcm_DifferenceAverage glcm_DifferenceAverage
## glcm_SumAverage glcm_SumAverage
## glcm_Contrast glcm_Contrast
## firstorder_Uniformity firstorder_Uniformity
## Tstage Tstage
## SourceDataset SourceDataset
## glrlm_RunPercentage glrlm_RunPercentage
## glrlm_LongRunHighGrayLevelEmphasis glrlm_LongRunHighGrayLevelEmphasis
## firstorder_Minimum firstorder_Minimum
## firstorder_StandardDeviation firstorder_StandardDeviation
## firstorder_Entropy firstorder_Entropy
## glcm_SumEntropy glcm_SumEntropy
## glcm_ClusterTendency glcm_ClusterTendency
## firstorder_MeanAbsoluteDeviation firstorder_MeanAbsoluteDeviation
## Mstage Mstage
## shape_Compactness2 shape_Compactness2
## shape_Sphericity shape_Sphericity
## firstorder_Variance firstorder_Variance
## rel.inf
## glrlm_GrayLevelNonUniformity 10.63462324
## glcm_Idn 10.61853054
## glcm_JointEntropy 7.34880093
## age 7.16466880
## glcm_Imc2 7.09082785
## shape_Maximum3DDiameter 6.66863631
## glcm_Idmn 4.94916942
## glrlm_LowGrayLevelRunEmphasis 4.61427258
## glrlm_LongRunLowGrayLevelEmphasis 3.66596813
## shape_SurfaceVolumeRatio 3.43734812
## glrlm_ShortRunLowGrayLevelEmphasis 3.26310024
## glcm_Imc1 3.09482928
## firstorder_Mean 2.60316846
## glcm_MaximumProbability 2.32348685
## firstorder_Kurtosis 1.94839491
## glrlm_RunLengthNonUniformity 1.84132992
## glcm_JointEnergy 1.67199203
## firstorder_Skewness 1.59994874
## glcm_Id 1.54478172
## Nstage 1.30080560
## firstorder_Median 1.27249826
## glrlm_ShortRunHighGrayLevelEmphasis 1.08582519
## glrlm_HighGrayLevelRunEmphasis 1.07074217
## firstorder_Maximum 1.01513415
## shape_VoxelVolume 0.97911330
## glcm_ClusterShade 0.73995204
## firstorder_Range 0.62164633
## shape_Compactness1 0.47367222
## glcm_DifferenceEntropy 0.46761797
## firstorder_Energy 0.42374941
## Histology 0.41105799
## shape_SphericalDisproportion 0.41084501
## glrlm_LongRunEmphasis 0.40357621
## glcm_ClusterProminence 0.37689143
## glcm_InverseVariance 0.29308109
## glcm_Autocorrelation 0.28275583
## glcm_Correlation 0.28113919
## shape_SurfaceArea 0.25195121
## glcm_Idm 0.20880008
## firstorder_RootMeanSquared 0.20251066
## glrlm_ShortRunEmphasis 0.18809456
## glcm_DifferenceAverage 0.18684395
## glcm_SumAverage 0.17856441
## glcm_Contrast 0.14104611
## firstorder_Uniformity 0.10881107
## Tstage 0.10168454
## SourceDataset 0.07619114
## glrlm_RunPercentage 0.07289271
## glrlm_LongRunHighGrayLevelEmphasis 0.04992584
## firstorder_Minimum 0.04921836
## firstorder_StandardDeviation 0.04621650
## firstorder_Entropy 0.04590268
## glcm_SumEntropy 0.03518750
## glcm_ClusterTendency 0.03181835
## firstorder_MeanAbsoluteDeviation 0.03035885
## Mstage 0.00000000
## shape_Compactness2 0.00000000
## shape_Sphericity 0.00000000
## firstorder_Variance 0.00000000## Setting levels: control = 0, case = 1## Setting direction: controls < cases##
## Call:
## roc.default(response = validate_df_classification$ReachedEvent, predictor = validate_predictions)
##
## Data: validate_predictions in 86 controls (validate_df_classification$ReachedEvent 0) < 63 cases (validate_df_classification$ReachedEvent 1).
## Area under the curve: 0.7123validate_predictions_bin <- as.factor(ifelse(validate_predictions > 0.39,1,0))
validate_df_classification_event <- as.factor(validate_df_classification$Event)
caret::confusionMatrix(validate_predictions_bin, validate_df_classification_event)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 38 27
## 1 29 55
##
## Accuracy : 0.6242
## 95% CI : (0.5412, 0.7021)
## No Information Rate : 0.5503
## P-Value [Acc > NIR] : 0.04122
##
## Kappa : 0.2385
##
## Mcnemar's Test P-Value : 0.89369
##
## Sensitivity : 0.5672
## Specificity : 0.6707
## Pos Pred Value : 0.5846
## Neg Pred Value : 0.6548
## Prevalence : 0.4497
## Detection Rate : 0.2550
## Detection Prevalence : 0.4362
## Balanced Accuracy : 0.6189
##
## 'Positive' Class : 0
## 10.4.1 GBM Classification Prediction
gbm_predictions_test <- predict(gbm_model,
imputed_test[,feature_names],
n.trees = nTrees_opt_cv,
type = "response")PatientID <- imputed_test$PatientID
pred <- data.frame(
PatientID = PatientID,
Event = gbm_predictions_test
)
submission_gbm <- output_test %>%
select(PatientID, SurvivalTime) %>%
left_join(pred, by = "PatientID")
fwrite(submission_gbm, "submission_gbm.csv")
#submission_bin_gbm <- submission_gbm %>%
# mutate(Event = ifelse(Event > 0.39, 1,0))
pred_bin_gbm <- as.factor(ifelse(pred > 0.39, 1, 0))
print("ratio of predicted Events in test dataset: "); table(pred_bin_gbm)## [1] "ratio of predicted Events in test dataset: "## pred_bin_gbm
## 0 1
## 53 197## [1] "ratio of Events in train dataset: "##
## 0 1
## 138 162Now that both models can predict the same period and the probability of reaching the event, we average them together and see how they help each other (straight 50/50 here which may not be the best mix)
10.5 Blend both models (Survival and Classification) together
roc(predictor = (validate_predictions + (1 - suvival_predictions$survival[,
which(suvival_predictions$unique.death.times==period_choice)]))/2,
response = validate_df_classification$ReachedEvent)## Setting levels: control = 0, case = 1## Setting direction: controls < cases##
## Call:
## roc.default(response = validate_df_classification$ReachedEvent, predictor = (validate_predictions + (1 - suvival_predictions$survival[, which(suvival_predictions$unique.death.times == period_choice)]))/2)
##
## Data: (validate_predictions + (1 - suvival_predictions$survival[, which(suvival_predictions$unique.death.times == period_choice)]))/2 in 86 controls (validate_df_classification$ReachedEvent 0) < 63 cases (validate_df_classification$ReachedEvent 1).
## Area under the curve: 0.7154