SA analysis for expression data from 290 primary colorectal cancers
Abdu-Allah Bekhit, Mohammed Ali, Sami Emad
November 14, 2017
Overview
This document explains a variety of survival analysis methods that performed on Expression data from 290 primary colorectal cancers
Setup
This section aims to load needed libs to perform survival analysis functionalties.
Load survival library
suppressMessages(library(survival))Load graphics library
suppressMessages(library(ggfortify))## Warning: package 'ggplot2' was built under R version 3.4.2## Warning: namespace 'DBI' is not available and has been replaced
## by .GlobalEnv when processing object 'call.'
## Warning: namespace 'DBI' is not available and has been replaced
## by .GlobalEnv when processing object 'call.'Load the dataset
load("D:/moh/DSTI/Courses/Survival Analysis using R -S17/CRC_226_GSE14333.RData")Dataset Exploration
This section aims to explore dataset data and metadate before performing any kind of analysis.
Metadata
clinical_metadata## variable_name description
## 1 location tumor location
## 2 dukes_stage cancer stage (Duke's classification)
## 3 age_diag age at diagnosis
## 4 gender gender
## 5 dfs_time Disease Free Survival (DFS) time, in months
## 6 dfs_event DFS event: 1=event time, 0=censoring time
## 7 adjXRT adjuvant radiation therapy
## 8 adjCTX adjuvant chemotherapyStructure
str(clinical_data)## 'data.frame': 226 obs. of 9 variables:
## $ sampleID : chr "GSM358341" "GSM358342" "GSM358343" "GSM358344" ...
## $ location : Factor w/ 4 levels "Rectum","Colon",..: 4 1 3 3 3 4 3 3 4 4 ...
## $ dukes_stage: Factor w/ 3 levels "A","B","C": 1 1 1 1 1 1 1 1 1 1 ...
## $ age_diag : num 78 53 80 58 81 57 63 51 86 76 ...
## $ gender : Factor w/ 2 levels "F","M": 2 1 1 2 2 2 1 2 1 2 ...
## $ dfs_time : num 3.64 14.53 16.47 19.75 20.02 ...
## $ dfs_event : num 1 0 1 1 1 1 0 1 1 1 ...
## $ adjXRT : Factor w/ 2 levels "N","Y": 1 1 1 1 1 1 1 1 1 1 ...
## $ adjCTX : Factor w/ 2 levels "N","Y": 1 1 1 1 1 1 1 2 1 1 ...Sample Data
head(clinical_data)## sampleID location dukes_stage age_diag gender dfs_time dfs_event adjXRT
## 1 GSM358341 Right A 78 M 3.64 1 N
## 2 GSM358342 Rectum A 53 F 14.53 0 N
## 3 GSM358343 Left A 80 F 16.47 1 N
## 4 GSM358344 Left A 58 M 19.75 1 N
## 5 GSM358345 Left A 81 M 20.02 1 N
## 6 GSM358346 Right A 57 M 23.96 1 N
## adjCTX
## 1 N
## 2 N
## 3 N
## 4 N
## 5 N
## 6 NFull statistics
summary(clinical_data)## sampleID location dukes_stage age_diag gender
## Length:226 Rectum: 30 A:41 Min. :26.00 F:106
## Class :character Colon : 2 B:94 1st Qu.:58.00 M:120
## Mode :character Left : 93 C:91 Median :67.00
## Right :101 Mean :66.03
## 3rd Qu.:75.00
## Max. :92.00
## dfs_time dfs_event adjXRT adjCTX
## Min. : 0.92 Min. :0.0000 N:204 N:139
## 1st Qu.: 22.28 1st Qu.:1.0000 Y: 22 Y: 87
## Median : 38.46 Median :1.0000
## Mean : 43.52 Mean :0.7788
## 3rd Qu.: 59.50 3rd Qu.:1.0000
## Max. :142.55 Max. :1.0000Basic Non-Parametric
Here we are performing basic analysis using Kaplan-Meier and Fleming-Harrington methods using different time units in Months which is the default and in Years. The rest of analysis will use the default time unitin Months
In months
Kaplan-Meier non-parametric
kmsurvival_month <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ 1)
summary(kmsurvival_month)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## 1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 226 1 0.99558 0.00441 0.98696 1.0000
## 1.80 224 1 0.99113 0.00624 0.97897 1.0000
## 2.26 223 1 0.98669 0.00764 0.97183 1.0000
## 3.64 221 1 0.98222 0.00881 0.96511 0.9996
## 4.10 220 1 0.97776 0.00984 0.95867 0.9972
## 4.24 219 1 0.97329 0.01076 0.95244 0.9946
## 5.20 216 1 0.96879 0.01161 0.94629 0.9918
## 5.22 215 1 0.96428 0.01240 0.94028 0.9889
## 10.20 205 1 0.95958 0.01320 0.93404 0.9858
## 11.60 203 1 0.95485 0.01396 0.92788 0.9826
## 12.10 201 1 0.95010 0.01468 0.92177 0.9793
## 13.50 200 1 0.94535 0.01535 0.91573 0.9759
## 14.40 195 1 0.94050 0.01602 0.90962 0.9724
## 15.00 192 1 0.93560 0.01667 0.90350 0.9688
## 15.05 191 1 0.93070 0.01729 0.89743 0.9652
## 15.71 189 1 0.92578 0.01788 0.89138 0.9615
## 16.47 187 1 0.92083 0.01846 0.88535 0.9577
## 16.90 186 1 0.91588 0.01901 0.87936 0.9539
## 17.95 185 1 0.91093 0.01954 0.87342 0.9500
## 18.18 183 1 0.90595 0.02006 0.86747 0.9461
## 18.70 182 1 0.90097 0.02056 0.86156 0.9422
## 18.80 181 1 0.89599 0.02104 0.85569 0.9382
## 18.96 179 1 0.89099 0.02151 0.84981 0.9342
## 19.75 177 1 0.88595 0.02197 0.84393 0.9301
## 19.98 176 1 0.88092 0.02241 0.83807 0.9260
## 20.02 175 1 0.87589 0.02284 0.83224 0.9218
## 20.44 174 1 0.87085 0.02326 0.82644 0.9177
## 22.02 171 1 0.86576 0.02368 0.82058 0.9134
## 22.25 170 1 0.86067 0.02408 0.81475 0.9092
## 22.80 167 1 0.85551 0.02448 0.80886 0.9049
## 23.96 165 1 0.85033 0.02487 0.80295 0.9005
## 24.00 164 1 0.84514 0.02526 0.79706 0.8961
## 24.19 162 1 0.83993 0.02563 0.79116 0.8917
## 24.20 161 1 0.83471 0.02600 0.78528 0.8873
## 25.24 158 1 0.82943 0.02637 0.77933 0.8827
## 25.61 157 1 0.82414 0.02672 0.77340 0.8782
## 26.26 156 1 0.81886 0.02707 0.76749 0.8737
## 26.53 155 1 0.81358 0.02740 0.76160 0.8691
## 26.66 154 1 0.80830 0.02773 0.75573 0.8645
## 26.82 153 1 0.80301 0.02805 0.74988 0.8599
## 26.92 152 1 0.79773 0.02836 0.74404 0.8553
## 27.15 150 1 0.79241 0.02866 0.73818 0.8506
## 28.50 146 1 0.78698 0.02898 0.73219 0.8459
## 28.63 145 1 0.78156 0.02928 0.72623 0.8411
## 28.86 144 1 0.77613 0.02957 0.72027 0.8363
## 28.96 143 1 0.77070 0.02986 0.71434 0.8315
## 29.22 142 1 0.76527 0.03014 0.70842 0.8267
## 29.60 140 1 0.75981 0.03042 0.70247 0.8218
## 30.00 139 1 0.75434 0.03069 0.69653 0.8169
## 30.90 138 1 0.74888 0.03095 0.69061 0.8121
## 31.06 137 1 0.74341 0.03120 0.68471 0.8071
## 31.30 136 1 0.73794 0.03145 0.67881 0.8022
## 31.36 135 1 0.73248 0.03168 0.67294 0.7973
## 31.60 134 1 0.72701 0.03192 0.66707 0.7923
## 31.92 133 1 0.72154 0.03214 0.66122 0.7874
## 33.20 131 1 0.71604 0.03236 0.65533 0.7824
## 33.69 130 1 0.71053 0.03258 0.64946 0.7773
## 33.80 129 1 0.70502 0.03279 0.64360 0.7723
## 33.90 128 1 0.69951 0.03299 0.63775 0.7673
## 35.90 126 1 0.69396 0.03319 0.63186 0.7622
## 36.20 125 1 0.68841 0.03339 0.62598 0.7571
## 36.30 124 1 0.68286 0.03358 0.62012 0.7519
## 36.75 123 1 0.67731 0.03376 0.61426 0.7468
## 36.92 122 1 0.67175 0.03394 0.60842 0.7417
## 37.00 120 1 0.66616 0.03411 0.60254 0.7365
## 37.31 119 1 0.66056 0.03428 0.59667 0.7313
## 38.00 117 1 0.65491 0.03445 0.59075 0.7260
## 38.07 116 1 0.64927 0.03462 0.58485 0.7208
## 38.20 114 1 0.64357 0.03478 0.57889 0.7155
## 38.72 113 1 0.63788 0.03493 0.57296 0.7102
## 39.25 112 1 0.63218 0.03508 0.56703 0.7048
## 40.00 111 1 0.62648 0.03522 0.56111 0.6995
## 40.40 109 2 0.61499 0.03550 0.54920 0.6887
## 42.00 106 1 0.60919 0.03564 0.54319 0.6832
## 42.90 105 1 0.60339 0.03577 0.53720 0.6777
## 43.79 104 1 0.59758 0.03589 0.53122 0.6722
## 43.90 103 1 0.59178 0.03601 0.52525 0.6667
## 44.20 102 1 0.58598 0.03612 0.51929 0.6612
## 44.40 101 1 0.58018 0.03623 0.51335 0.6557
## 44.67 100 1 0.57438 0.03633 0.50741 0.6502
## 44.74 99 1 0.56858 0.03642 0.50149 0.6446
## 44.80 98 1 0.56277 0.03651 0.49558 0.6391
## 44.97 97 1 0.55697 0.03659 0.48968 0.6335
## 45.30 96 1 0.55117 0.03667 0.48380 0.6279
## 45.40 95 1 0.54537 0.03674 0.47792 0.6223
## 46.71 94 1 0.53957 0.03680 0.47205 0.6167
## 47.40 93 1 0.53376 0.03686 0.46620 0.6111
## 47.70 92 1 0.52796 0.03691 0.46035 0.6055
## 47.80 91 1 0.52216 0.03696 0.45452 0.5999
## 47.86 90 1 0.51636 0.03700 0.44870 0.5942
## 49.11 89 1 0.51056 0.03704 0.44289 0.5886
## 49.60 88 1 0.50476 0.03707 0.43709 0.5829
## 49.84 87 1 0.49895 0.03709 0.43130 0.5772
## 50.43 86 1 0.49315 0.03711 0.42552 0.5715
## 50.59 85 1 0.48735 0.03713 0.41975 0.5658
## 50.90 84 1 0.48155 0.03714 0.41400 0.5601
## 52.10 83 1 0.47575 0.03714 0.40825 0.5544
## 52.14 82 1 0.46994 0.03714 0.40252 0.5487
## 52.24 81 1 0.46414 0.03713 0.39679 0.5429
## 52.50 80 1 0.45834 0.03711 0.39108 0.5372
## 52.80 79 1 0.45254 0.03710 0.38537 0.5314
## 52.86 78 1 0.44674 0.03707 0.37968 0.5256
## 54.40 77 1 0.44094 0.03704 0.37400 0.5199
## 54.90 76 1 0.43513 0.03700 0.36833 0.5141
## 55.13 75 1 0.42933 0.03696 0.36267 0.5083
## 55.33 74 1 0.42353 0.03692 0.35702 0.5024
## 55.70 73 1 0.41773 0.03686 0.35138 0.4966
## 55.90 72 1 0.41193 0.03681 0.34575 0.4908
## 55.92 71 1 0.40613 0.03674 0.34014 0.4849
## 56.30 70 1 0.40032 0.03667 0.33453 0.4791
## 56.50 69 1 0.39452 0.03660 0.32894 0.4732
## 56.80 68 1 0.38872 0.03652 0.32335 0.4673
## 57.00 67 1 0.38292 0.03643 0.31778 0.4614
## 57.79 66 1 0.37712 0.03634 0.31222 0.4555
## 57.80 65 1 0.37131 0.03624 0.30667 0.4496
## 58.02 64 1 0.36551 0.03613 0.30113 0.4437
## 58.40 63 1 0.35971 0.03602 0.29561 0.4377
## 58.45 62 1 0.35391 0.03590 0.29009 0.4318
## 59.07 61 1 0.34811 0.03578 0.28459 0.4258
## 59.20 60 1 0.34231 0.03565 0.27910 0.4198
## 59.34 59 1 0.33650 0.03552 0.27362 0.4138
## 59.50 58 2 0.32490 0.03523 0.26270 0.4018
## 59.53 56 1 0.31910 0.03507 0.25726 0.3958
## 59.60 55 1 0.31330 0.03491 0.25183 0.3898
## 59.96 54 1 0.30749 0.03474 0.24641 0.3837
## 61.40 53 1 0.30169 0.03457 0.24101 0.3777
## 63.25 52 1 0.29589 0.03439 0.23562 0.3716
## 64.10 51 1 0.29009 0.03420 0.23024 0.3655
## 64.33 50 1 0.28429 0.03400 0.22488 0.3594
## 64.37 49 1 0.27849 0.03380 0.21953 0.3533
## 64.50 48 1 0.27268 0.03359 0.21419 0.3472
## 64.86 47 1 0.26688 0.03337 0.20887 0.3410
## 64.93 46 1 0.26108 0.03315 0.20356 0.3349
## 65.55 45 1 0.25528 0.03292 0.19827 0.3287
## 65.88 44 1 0.24948 0.03268 0.19299 0.3225
## 67.19 43 1 0.24368 0.03243 0.18773 0.3163
## 67.82 42 1 0.23787 0.03217 0.18249 0.3101
## 68.10 41 1 0.23207 0.03190 0.17726 0.3038
## 68.51 40 1 0.22627 0.03163 0.17204 0.2976
## 68.70 39 1 0.22047 0.03135 0.16685 0.2913
## 69.10 38 1 0.21467 0.03105 0.16167 0.2850
## 70.65 37 1 0.20886 0.03075 0.15651 0.2787
## 70.80 36 1 0.20306 0.03044 0.15137 0.2724
## 72.09 35 1 0.19726 0.03012 0.14624 0.2661
## 74.20 33 1 0.19128 0.02979 0.14096 0.2596
## 74.36 32 1 0.18531 0.02945 0.13570 0.2530
## 74.53 31 1 0.17933 0.02910 0.13047 0.2465
## 76.04 30 1 0.17335 0.02874 0.12525 0.2399
## 76.07 29 1 0.16737 0.02837 0.12007 0.2333
## 79.13 28 1 0.16140 0.02798 0.11491 0.2267
## 80.25 26 1 0.15519 0.02758 0.10954 0.2199
## 80.80 25 1 0.14898 0.02717 0.10421 0.2130
## 82.29 24 1 0.14277 0.02673 0.09891 0.2061
## 83.60 23 1 0.13657 0.02628 0.09365 0.1991
## 83.73 22 1 0.13036 0.02581 0.08843 0.1922
## 84.13 21 1 0.12415 0.02532 0.08325 0.1852
## 84.70 20 1 0.11794 0.02480 0.07811 0.1781
## 84.90 19 1 0.11174 0.02426 0.07301 0.1710
## 85.28 18 1 0.10553 0.02369 0.06796 0.1639
## 85.61 17 1 0.09932 0.02310 0.06296 0.1567
## 86.43 15 1 0.09270 0.02249 0.05762 0.1491
## 88.99 14 1 0.08608 0.02183 0.05236 0.1415
## 89.62 13 1 0.07946 0.02113 0.04718 0.1338
## 95.07 11 1 0.07223 0.02041 0.04152 0.1257
## 99.51 10 1 0.06501 0.01961 0.03600 0.1174
## 105.17 9 1 0.05779 0.01871 0.03063 0.1090
## 106.94 8 1 0.05056 0.01771 0.02545 0.1005
## 109.21 7 1 0.04334 0.01659 0.02047 0.0918
## 110.79 6 1 0.03612 0.01532 0.01573 0.0829
## 112.33 5 1 0.02889 0.01385 0.01129 0.0739
## 118.58 4 1 0.02167 0.01213 0.00724 0.0649
## 119.21 3 1 0.01445 0.01001 0.00372 0.0562
## 122.72 2 1 0.00722 0.00715 0.00104 0.0503
## 142.55 1 1 0.00000 NaN NA NAautoplot(kmsurvival_month, xlab="Time in Month", ylab="Survival Probability", surv.linetype = 'dashed', surv.colour = 'blue',
conf.int.fill = 'dodgerblue3', conf.int.alpha = 0.5)
Fleming-Harrington non-parametric analysis
fhsurvival_month <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ 1, type="fleming-harrington")
summary(fhsurvival_month)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## 1, type = "fleming-harrington")
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 226 1 0.99558 0.00442 0.98697 1.0000
## 1.80 224 1 0.99115 0.00624 0.97899 1.0000
## 2.26 223 1 0.98672 0.00764 0.97186 1.0000
## 3.64 221 1 0.98226 0.00881 0.96514 0.9997
## 4.10 220 1 0.97781 0.00984 0.95872 0.9973
## 4.24 219 1 0.97335 0.01076 0.95249 0.9947
## 5.20 216 1 0.96886 0.01161 0.94636 0.9919
## 5.22 215 1 0.96436 0.01240 0.94035 0.9890
## 10.20 205 1 0.95967 0.01320 0.93413 0.9859
## 11.60 203 1 0.95495 0.01396 0.92798 0.9827
## 12.10 201 1 0.95021 0.01468 0.92188 0.9794
## 13.50 200 1 0.94547 0.01535 0.91585 0.9761
## 14.40 195 1 0.94064 0.01602 0.90975 0.9726
## 15.00 192 1 0.93575 0.01667 0.90364 0.9690
## 15.05 191 1 0.93086 0.01729 0.89759 0.9654
## 15.71 189 1 0.92595 0.01789 0.89155 0.9617
## 16.47 187 1 0.92101 0.01846 0.88553 0.9579
## 16.90 186 1 0.91607 0.01902 0.87955 0.9541
## 17.95 185 1 0.91114 0.01955 0.87362 0.9503
## 18.18 183 1 0.90617 0.02007 0.86768 0.9464
## 18.70 182 1 0.90121 0.02056 0.86179 0.9424
## 18.80 181 1 0.89624 0.02105 0.85593 0.9385
## 18.96 179 1 0.89125 0.02152 0.85006 0.9344
## 19.75 177 1 0.88623 0.02198 0.84419 0.9304
## 19.98 176 1 0.88121 0.02242 0.83834 0.9263
## 20.02 175 1 0.87618 0.02285 0.83252 0.9221
## 20.44 174 1 0.87116 0.02327 0.82673 0.9180
## 22.02 171 1 0.86608 0.02368 0.82089 0.9138
## 22.25 170 1 0.86100 0.02409 0.81507 0.9095
## 22.80 167 1 0.85586 0.02449 0.80919 0.9052
## 23.96 165 1 0.85069 0.02488 0.80329 0.9009
## 24.00 164 1 0.84552 0.02527 0.79742 0.8965
## 24.19 162 1 0.84032 0.02565 0.79153 0.8921
## 24.20 161 1 0.83511 0.02601 0.78566 0.8877
## 25.24 158 1 0.82985 0.02638 0.77972 0.8832
## 25.61 157 1 0.82458 0.02674 0.77380 0.8787
## 26.26 156 1 0.81931 0.02708 0.76791 0.8741
## 26.53 155 1 0.81404 0.02742 0.76203 0.8696
## 26.66 154 1 0.80877 0.02775 0.75617 0.8650
## 26.82 153 1 0.80350 0.02807 0.75033 0.8604
## 26.92 152 1 0.79823 0.02837 0.74451 0.8558
## 27.15 150 1 0.79293 0.02868 0.73866 0.8512
## 28.50 146 1 0.78752 0.02900 0.73269 0.8464
## 28.63 145 1 0.78210 0.02930 0.72673 0.8417
## 28.86 144 1 0.77669 0.02960 0.72080 0.8369
## 28.96 143 1 0.77128 0.02988 0.71488 0.8321
## 29.22 142 1 0.76587 0.03016 0.70897 0.8273
## 29.60 140 1 0.76042 0.03044 0.70303 0.8225
## 30.00 139 1 0.75496 0.03071 0.69711 0.8176
## 30.90 138 1 0.74951 0.03097 0.69120 0.8127
## 31.06 137 1 0.74406 0.03123 0.68531 0.8079
## 31.30 136 1 0.73861 0.03147 0.67943 0.8029
## 31.36 135 1 0.73316 0.03171 0.67357 0.7980
## 31.60 134 1 0.72771 0.03195 0.66771 0.7931
## 31.92 133 1 0.72226 0.03217 0.66188 0.7881
## 33.20 131 1 0.71677 0.03240 0.65600 0.7832
## 33.69 130 1 0.71127 0.03261 0.65014 0.7782
## 33.80 129 1 0.70578 0.03282 0.64429 0.7731
## 33.90 128 1 0.70029 0.03303 0.63845 0.7681
## 35.90 126 1 0.69475 0.03323 0.63258 0.7630
## 36.20 125 1 0.68922 0.03343 0.62671 0.7580
## 36.30 124 1 0.68368 0.03362 0.62086 0.7529
## 36.75 123 1 0.67815 0.03380 0.61502 0.7477
## 36.92 122 1 0.67261 0.03398 0.60920 0.7426
## 37.00 120 1 0.66703 0.03416 0.60333 0.7375
## 37.31 119 1 0.66145 0.03433 0.59747 0.7323
## 38.00 117 1 0.65582 0.03450 0.59157 0.7270
## 38.07 116 1 0.65019 0.03466 0.58568 0.7218
## 38.20 114 1 0.64451 0.03483 0.57974 0.7165
## 38.72 113 1 0.63883 0.03498 0.57381 0.7112
## 39.25 112 1 0.63315 0.03514 0.56790 0.7059
## 40.00 111 1 0.62747 0.03528 0.56200 0.7006
## 40.40 109 2 0.61607 0.03557 0.55016 0.6899
## 42.00 106 1 0.61028 0.03570 0.54417 0.6844
## 42.90 105 1 0.60450 0.03584 0.53819 0.6790
## 43.79 104 1 0.59871 0.03596 0.53222 0.6735
## 43.90 103 1 0.59293 0.03608 0.52627 0.6680
## 44.20 102 1 0.58714 0.03619 0.52032 0.6625
## 44.40 101 1 0.58136 0.03630 0.51439 0.6570
## 44.67 100 1 0.57557 0.03640 0.50847 0.6515
## 44.74 99 1 0.56979 0.03650 0.50256 0.6460
## 44.80 98 1 0.56400 0.03659 0.49667 0.6405
## 44.97 97 1 0.55822 0.03667 0.49078 0.6349
## 45.30 96 1 0.55243 0.03675 0.48491 0.6294
## 45.40 95 1 0.54665 0.03682 0.47904 0.6238
## 46.71 94 1 0.54087 0.03689 0.47319 0.6182
## 47.40 93 1 0.53508 0.03695 0.46735 0.6126
## 47.70 92 1 0.52930 0.03701 0.46152 0.6070
## 47.80 91 1 0.52351 0.03705 0.45570 0.6014
## 47.86 90 1 0.51773 0.03710 0.44989 0.5958
## 49.11 89 1 0.51194 0.03714 0.44409 0.5902
## 49.60 88 1 0.50616 0.03717 0.43830 0.5845
## 49.84 87 1 0.50037 0.03720 0.43253 0.5789
## 50.43 86 1 0.49459 0.03722 0.42676 0.5732
## 50.59 85 1 0.48880 0.03724 0.42101 0.5675
## 50.90 84 1 0.48302 0.03725 0.41526 0.5618
## 52.10 83 1 0.47723 0.03725 0.40953 0.5561
## 52.14 82 1 0.47145 0.03726 0.40380 0.5504
## 52.24 81 1 0.46567 0.03725 0.39809 0.5447
## 52.50 80 1 0.45988 0.03724 0.39239 0.5390
## 52.80 79 1 0.45410 0.03722 0.38670 0.5332
## 52.86 78 1 0.44831 0.03720 0.38102 0.5275
## 54.40 77 1 0.44253 0.03717 0.37535 0.5217
## 54.90 76 1 0.43674 0.03714 0.36969 0.5160
## 55.13 75 1 0.43096 0.03710 0.36404 0.5102
## 55.33 74 1 0.42517 0.03706 0.35840 0.5044
## 55.70 73 1 0.41939 0.03701 0.35278 0.4986
## 55.90 72 1 0.41360 0.03696 0.34716 0.4928
## 55.92 71 1 0.40782 0.03689 0.34156 0.4869
## 56.30 70 1 0.40204 0.03683 0.33596 0.4811
## 56.50 69 1 0.39625 0.03676 0.33038 0.4753
## 56.80 68 1 0.39047 0.03668 0.32481 0.4694
## 57.00 67 1 0.38468 0.03660 0.31924 0.4635
## 57.79 66 1 0.37890 0.03651 0.31369 0.4577
## 57.80 65 1 0.37311 0.03641 0.30816 0.4518
## 58.02 64 1 0.36733 0.03631 0.30263 0.4459
## 58.40 63 1 0.36154 0.03620 0.29711 0.4399
## 58.45 62 1 0.35576 0.03609 0.29161 0.4340
## 59.07 61 1 0.34997 0.03597 0.28612 0.4281
## 59.20 60 1 0.34419 0.03585 0.28063 0.4221
## 59.34 59 1 0.33840 0.03572 0.27517 0.4162
## 59.50 58 2 0.32693 0.03545 0.26434 0.4043
## 59.53 56 1 0.32115 0.03530 0.25891 0.3983
## 59.60 55 1 0.31536 0.03514 0.25349 0.3923
## 59.96 54 1 0.30958 0.03498 0.24808 0.3863
## 61.40 53 1 0.30379 0.03481 0.24268 0.3803
## 63.25 52 1 0.29800 0.03463 0.23730 0.3742
## 64.10 51 1 0.29222 0.03445 0.23193 0.3682
## 64.33 50 1 0.28643 0.03426 0.22657 0.3621
## 64.37 49 1 0.28064 0.03406 0.22123 0.3560
## 64.50 48 1 0.27486 0.03386 0.21590 0.3499
## 64.86 47 1 0.26907 0.03365 0.21058 0.3438
## 64.93 46 1 0.26329 0.03343 0.20528 0.3377
## 65.55 45 1 0.25750 0.03320 0.20000 0.3315
## 65.88 44 1 0.25171 0.03297 0.19472 0.3254
## 67.19 43 1 0.24593 0.03273 0.18947 0.3192
## 67.82 42 1 0.24014 0.03248 0.18423 0.3130
## 68.10 41 1 0.23435 0.03222 0.17900 0.3068
## 68.51 40 1 0.22857 0.03195 0.17379 0.3006
## 68.70 39 1 0.22278 0.03167 0.16860 0.2944
## 69.10 38 1 0.21700 0.03139 0.16342 0.2881
## 70.65 37 1 0.21121 0.03110 0.15827 0.2819
## 70.80 36 1 0.20542 0.03079 0.15313 0.2756
## 72.09 35 1 0.19964 0.03048 0.14801 0.2693
## 74.20 33 1 0.19368 0.03017 0.14273 0.2628
## 74.36 32 1 0.18772 0.02984 0.13747 0.2563
## 74.53 31 1 0.18176 0.02950 0.13224 0.2498
## 76.04 30 1 0.17580 0.02915 0.12703 0.2433
## 76.07 29 1 0.16984 0.02878 0.12184 0.2368
## 79.13 28 1 0.16388 0.02841 0.11668 0.2302
## 80.25 26 1 0.15770 0.02803 0.11132 0.2234
## 80.80 25 1 0.15152 0.02763 0.10599 0.2166
## 82.29 24 1 0.14533 0.02721 0.10069 0.2098
## 83.60 23 1 0.13915 0.02678 0.09543 0.2029
## 83.73 22 1 0.13297 0.02633 0.09020 0.1960
## 84.13 21 1 0.12678 0.02585 0.08501 0.1891
## 84.70 20 1 0.12060 0.02536 0.07987 0.1821
## 84.90 19 1 0.11442 0.02484 0.07476 0.1751
## 85.28 18 1 0.10823 0.02430 0.06970 0.1681
## 85.61 17 1 0.10205 0.02373 0.06469 0.1610
## 86.43 15 1 0.09547 0.02316 0.05934 0.1536
## 88.99 14 1 0.08889 0.02255 0.05407 0.1461
## 89.62 13 1 0.08231 0.02189 0.04887 0.1386
## 95.07 11 1 0.07515 0.02124 0.04320 0.1308
## 99.51 10 1 0.06800 0.02051 0.03765 0.1228
## 105.17 9 1 0.06085 0.01970 0.03226 0.1148
## 106.94 8 1 0.05370 0.01881 0.02703 0.1067
## 109.21 7 1 0.04655 0.01782 0.02199 0.0986
## 110.79 6 1 0.03941 0.01671 0.01716 0.0905
## 112.33 5 1 0.03226 0.01547 0.01261 0.0826
## 118.58 4 1 0.02513 0.01406 0.00839 0.0752
## 119.21 3 1 0.01800 0.01247 0.00463 0.0700
## 122.72 2 1 0.01092 0.01081 0.00157 0.0760
## 142.55 1 1 0.00402 Inf 0.00000 1.0000autoplot(fhsurvival_month, xlab="Time in Month", ylab="Survival Probability", surv.linetype = 'dashed', surv.colour = 'blue',
conf.int.fill = 'dodgerblue3', conf.int.alpha = 0.5)
In years
Kaplan-Meier non-parametric
kmsurvival_year <- survfit(Surv(clinical_data$dfs_time/12, clinical_data$dfs_event) ~ 1)
summary(kmsurvival_year)## Call: survfit(formula = Surv(clinical_data$dfs_time/12, clinical_data$dfs_event) ~
## 1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.0767 226 1 0.99558 0.00441 0.98696 1.0000
## 0.1500 224 1 0.99113 0.00624 0.97897 1.0000
## 0.1883 223 1 0.98669 0.00764 0.97183 1.0000
## 0.3033 221 1 0.98222 0.00881 0.96511 0.9996
## 0.3417 220 1 0.97776 0.00984 0.95867 0.9972
## 0.3533 219 1 0.97329 0.01076 0.95244 0.9946
## 0.4333 216 1 0.96879 0.01161 0.94629 0.9918
## 0.4350 215 1 0.96428 0.01240 0.94028 0.9889
## 0.8500 205 1 0.95958 0.01320 0.93404 0.9858
## 0.9667 203 1 0.95485 0.01396 0.92788 0.9826
## 1.0083 201 1 0.95010 0.01468 0.92177 0.9793
## 1.1250 200 1 0.94535 0.01535 0.91573 0.9759
## 1.2000 195 1 0.94050 0.01602 0.90962 0.9724
## 1.2500 192 1 0.93560 0.01667 0.90350 0.9688
## 1.2542 191 1 0.93070 0.01729 0.89743 0.9652
## 1.3092 189 1 0.92578 0.01788 0.89138 0.9615
## 1.3725 187 1 0.92083 0.01846 0.88535 0.9577
## 1.4083 186 1 0.91588 0.01901 0.87936 0.9539
## 1.4958 185 1 0.91093 0.01954 0.87342 0.9500
## 1.5150 183 1 0.90595 0.02006 0.86747 0.9461
## 1.5583 182 1 0.90097 0.02056 0.86156 0.9422
## 1.5667 181 1 0.89599 0.02104 0.85569 0.9382
## 1.5800 179 1 0.89099 0.02151 0.84981 0.9342
## 1.6458 177 1 0.88595 0.02197 0.84393 0.9301
## 1.6650 176 1 0.88092 0.02241 0.83807 0.9260
## 1.6683 175 1 0.87589 0.02284 0.83224 0.9218
## 1.7033 174 1 0.87085 0.02326 0.82644 0.9177
## 1.8350 171 1 0.86576 0.02368 0.82058 0.9134
## 1.8542 170 1 0.86067 0.02408 0.81475 0.9092
## 1.9000 167 1 0.85551 0.02448 0.80886 0.9049
## 1.9967 165 1 0.85033 0.02487 0.80295 0.9005
## 2.0000 164 1 0.84514 0.02526 0.79706 0.8961
## 2.0158 162 1 0.83993 0.02563 0.79116 0.8917
## 2.0167 161 1 0.83471 0.02600 0.78528 0.8873
## 2.1033 158 1 0.82943 0.02637 0.77933 0.8827
## 2.1342 157 1 0.82414 0.02672 0.77340 0.8782
## 2.1883 156 1 0.81886 0.02707 0.76749 0.8737
## 2.2108 155 1 0.81358 0.02740 0.76160 0.8691
## 2.2217 154 1 0.80830 0.02773 0.75573 0.8645
## 2.2350 153 1 0.80301 0.02805 0.74988 0.8599
## 2.2433 152 1 0.79773 0.02836 0.74404 0.8553
## 2.2625 150 1 0.79241 0.02866 0.73818 0.8506
## 2.3750 146 1 0.78698 0.02898 0.73219 0.8459
## 2.3858 145 1 0.78156 0.02928 0.72623 0.8411
## 2.4050 144 1 0.77613 0.02957 0.72027 0.8363
## 2.4133 143 1 0.77070 0.02986 0.71434 0.8315
## 2.4350 142 1 0.76527 0.03014 0.70842 0.8267
## 2.4667 140 1 0.75981 0.03042 0.70247 0.8218
## 2.5000 139 1 0.75434 0.03069 0.69653 0.8169
## 2.5750 138 1 0.74888 0.03095 0.69061 0.8121
## 2.5883 137 1 0.74341 0.03120 0.68471 0.8071
## 2.6083 136 1 0.73794 0.03145 0.67881 0.8022
## 2.6133 135 1 0.73248 0.03168 0.67294 0.7973
## 2.6333 134 1 0.72701 0.03192 0.66707 0.7923
## 2.6600 133 1 0.72154 0.03214 0.66122 0.7874
## 2.7667 131 1 0.71604 0.03236 0.65533 0.7824
## 2.8075 130 1 0.71053 0.03258 0.64946 0.7773
## 2.8167 129 1 0.70502 0.03279 0.64360 0.7723
## 2.8250 128 1 0.69951 0.03299 0.63775 0.7673
## 2.9917 126 1 0.69396 0.03319 0.63186 0.7622
## 3.0167 125 1 0.68841 0.03339 0.62598 0.7571
## 3.0250 124 1 0.68286 0.03358 0.62012 0.7519
## 3.0625 123 1 0.67731 0.03376 0.61426 0.7468
## 3.0767 122 1 0.67175 0.03394 0.60842 0.7417
## 3.0833 120 1 0.66616 0.03411 0.60254 0.7365
## 3.1092 119 1 0.66056 0.03428 0.59667 0.7313
## 3.1667 117 1 0.65491 0.03445 0.59075 0.7260
## 3.1725 116 1 0.64927 0.03462 0.58485 0.7208
## 3.1833 114 1 0.64357 0.03478 0.57889 0.7155
## 3.2267 113 1 0.63788 0.03493 0.57296 0.7102
## 3.2708 112 1 0.63218 0.03508 0.56703 0.7048
## 3.3333 111 1 0.62648 0.03522 0.56111 0.6995
## 3.3667 109 2 0.61499 0.03550 0.54920 0.6887
## 3.5000 106 1 0.60919 0.03564 0.54319 0.6832
## 3.5750 105 1 0.60339 0.03577 0.53720 0.6777
## 3.6492 104 1 0.59758 0.03589 0.53122 0.6722
## 3.6583 103 1 0.59178 0.03601 0.52525 0.6667
## 3.6833 102 1 0.58598 0.03612 0.51929 0.6612
## 3.7000 101 1 0.58018 0.03623 0.51335 0.6557
## 3.7225 100 1 0.57438 0.03633 0.50741 0.6502
## 3.7283 99 1 0.56858 0.03642 0.50149 0.6446
## 3.7333 98 1 0.56277 0.03651 0.49558 0.6391
## 3.7475 97 1 0.55697 0.03659 0.48968 0.6335
## 3.7750 96 1 0.55117 0.03667 0.48380 0.6279
## 3.7833 95 1 0.54537 0.03674 0.47792 0.6223
## 3.8925 94 1 0.53957 0.03680 0.47205 0.6167
## 3.9500 93 1 0.53376 0.03686 0.46620 0.6111
## 3.9750 92 1 0.52796 0.03691 0.46035 0.6055
## 3.9833 91 1 0.52216 0.03696 0.45452 0.5999
## 3.9883 90 1 0.51636 0.03700 0.44870 0.5942
## 4.0925 89 1 0.51056 0.03704 0.44289 0.5886
## 4.1333 88 1 0.50476 0.03707 0.43709 0.5829
## 4.1533 87 1 0.49895 0.03709 0.43130 0.5772
## 4.2025 86 1 0.49315 0.03711 0.42552 0.5715
## 4.2158 85 1 0.48735 0.03713 0.41975 0.5658
## 4.2417 84 1 0.48155 0.03714 0.41400 0.5601
## 4.3417 83 1 0.47575 0.03714 0.40825 0.5544
## 4.3450 82 1 0.46994 0.03714 0.40252 0.5487
## 4.3533 81 1 0.46414 0.03713 0.39679 0.5429
## 4.3750 80 1 0.45834 0.03711 0.39108 0.5372
## 4.4000 79 1 0.45254 0.03710 0.38537 0.5314
## 4.4050 78 1 0.44674 0.03707 0.37968 0.5256
## 4.5333 77 1 0.44094 0.03704 0.37400 0.5199
## 4.5750 76 1 0.43513 0.03700 0.36833 0.5141
## 4.5942 75 1 0.42933 0.03696 0.36267 0.5083
## 4.6108 74 1 0.42353 0.03692 0.35702 0.5024
## 4.6417 73 1 0.41773 0.03686 0.35138 0.4966
## 4.6583 72 1 0.41193 0.03681 0.34575 0.4908
## 4.6600 71 1 0.40613 0.03674 0.34014 0.4849
## 4.6917 70 1 0.40032 0.03667 0.33453 0.4791
## 4.7083 69 1 0.39452 0.03660 0.32894 0.4732
## 4.7333 68 1 0.38872 0.03652 0.32335 0.4673
## 4.7500 67 1 0.38292 0.03643 0.31778 0.4614
## 4.8158 66 1 0.37712 0.03634 0.31222 0.4555
## 4.8167 65 1 0.37131 0.03624 0.30667 0.4496
## 4.8350 64 1 0.36551 0.03613 0.30113 0.4437
## 4.8667 63 1 0.35971 0.03602 0.29561 0.4377
## 4.8708 62 1 0.35391 0.03590 0.29009 0.4318
## 4.9225 61 1 0.34811 0.03578 0.28459 0.4258
## 4.9333 60 1 0.34231 0.03565 0.27910 0.4198
## 4.9450 59 1 0.33650 0.03552 0.27362 0.4138
## 4.9583 58 2 0.32490 0.03523 0.26270 0.4018
## 4.9608 56 1 0.31910 0.03507 0.25726 0.3958
## 4.9667 55 1 0.31330 0.03491 0.25183 0.3898
## 4.9967 54 1 0.30749 0.03474 0.24641 0.3837
## 5.1167 53 1 0.30169 0.03457 0.24101 0.3777
## 5.2708 52 1 0.29589 0.03439 0.23562 0.3716
## 5.3417 51 1 0.29009 0.03420 0.23024 0.3655
## 5.3608 50 1 0.28429 0.03400 0.22488 0.3594
## 5.3642 49 1 0.27849 0.03380 0.21953 0.3533
## 5.3750 48 1 0.27268 0.03359 0.21419 0.3472
## 5.4050 47 1 0.26688 0.03337 0.20887 0.3410
## 5.4108 46 1 0.26108 0.03315 0.20356 0.3349
## 5.4625 45 1 0.25528 0.03292 0.19827 0.3287
## 5.4900 44 1 0.24948 0.03268 0.19299 0.3225
## 5.5992 43 1 0.24368 0.03243 0.18773 0.3163
## 5.6517 42 1 0.23787 0.03217 0.18249 0.3101
## 5.6750 41 1 0.23207 0.03190 0.17726 0.3038
## 5.7092 40 1 0.22627 0.03163 0.17204 0.2976
## 5.7250 39 1 0.22047 0.03135 0.16685 0.2913
## 5.7583 38 1 0.21467 0.03105 0.16167 0.2850
## 5.8875 37 1 0.20886 0.03075 0.15651 0.2787
## 5.9000 36 1 0.20306 0.03044 0.15137 0.2724
## 6.0075 35 1 0.19726 0.03012 0.14624 0.2661
## 6.1833 33 1 0.19128 0.02979 0.14096 0.2596
## 6.1967 32 1 0.18531 0.02945 0.13570 0.2530
## 6.2108 31 1 0.17933 0.02910 0.13047 0.2465
## 6.3367 30 1 0.17335 0.02874 0.12525 0.2399
## 6.3392 29 1 0.16737 0.02837 0.12007 0.2333
## 6.5942 28 1 0.16140 0.02798 0.11491 0.2267
## 6.6875 26 1 0.15519 0.02758 0.10954 0.2199
## 6.7333 25 1 0.14898 0.02717 0.10421 0.2130
## 6.8575 24 1 0.14277 0.02673 0.09891 0.2061
## 6.9667 23 1 0.13657 0.02628 0.09365 0.1991
## 6.9775 22 1 0.13036 0.02581 0.08843 0.1922
## 7.0108 21 1 0.12415 0.02532 0.08325 0.1852
## 7.0583 20 1 0.11794 0.02480 0.07811 0.1781
## 7.0750 19 1 0.11174 0.02426 0.07301 0.1710
## 7.1067 18 1 0.10553 0.02369 0.06796 0.1639
## 7.1342 17 1 0.09932 0.02310 0.06296 0.1567
## 7.2025 15 1 0.09270 0.02249 0.05762 0.1491
## 7.4158 14 1 0.08608 0.02183 0.05236 0.1415
## 7.4683 13 1 0.07946 0.02113 0.04718 0.1338
## 7.9225 11 1 0.07223 0.02041 0.04152 0.1257
## 8.2925 10 1 0.06501 0.01961 0.03600 0.1174
## 8.7642 9 1 0.05779 0.01871 0.03063 0.1090
## 8.9117 8 1 0.05056 0.01771 0.02545 0.1005
## 9.1008 7 1 0.04334 0.01659 0.02047 0.0918
## 9.2325 6 1 0.03612 0.01532 0.01573 0.0829
## 9.3608 5 1 0.02889 0.01385 0.01129 0.0739
## 9.8817 4 1 0.02167 0.01213 0.00724 0.0649
## 9.9342 3 1 0.01445 0.01001 0.00372 0.0562
## 10.2267 2 1 0.00722 0.00715 0.00104 0.0503
## 11.8792 1 1 0.00000 NaN NA NAautoplot(kmsurvival_year, xlab="Time in Years", ylab="Survival Probability", surv.linetype = 'dashed', surv.colour = 'blue',
conf.int.fill = 'dodgerblue3', conf.int.alpha = 0.5)
Fleming-Harrington non-parametric analysis
fhsurvival_year <- survfit(Surv(clinical_data$dfs_time/12, clinical_data$dfs_event) ~ 1, type="fleming-harrington")
summary(fhsurvival_year)## Call: survfit(formula = Surv(clinical_data$dfs_time/12, clinical_data$dfs_event) ~
## 1, type = "fleming-harrington")
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.0767 226 1 0.99558 0.00442 0.98697 1.0000
## 0.1500 224 1 0.99115 0.00624 0.97899 1.0000
## 0.1883 223 1 0.98672 0.00764 0.97186 1.0000
## 0.3033 221 1 0.98226 0.00881 0.96514 0.9997
## 0.3417 220 1 0.97781 0.00984 0.95872 0.9973
## 0.3533 219 1 0.97335 0.01076 0.95249 0.9947
## 0.4333 216 1 0.96886 0.01161 0.94636 0.9919
## 0.4350 215 1 0.96436 0.01240 0.94035 0.9890
## 0.8500 205 1 0.95967 0.01320 0.93413 0.9859
## 0.9667 203 1 0.95495 0.01396 0.92798 0.9827
## 1.0083 201 1 0.95021 0.01468 0.92188 0.9794
## 1.1250 200 1 0.94547 0.01535 0.91585 0.9761
## 1.2000 195 1 0.94064 0.01602 0.90975 0.9726
## 1.2500 192 1 0.93575 0.01667 0.90364 0.9690
## 1.2542 191 1 0.93086 0.01729 0.89759 0.9654
## 1.3092 189 1 0.92595 0.01789 0.89155 0.9617
## 1.3725 187 1 0.92101 0.01846 0.88553 0.9579
## 1.4083 186 1 0.91607 0.01902 0.87955 0.9541
## 1.4958 185 1 0.91114 0.01955 0.87362 0.9503
## 1.5150 183 1 0.90617 0.02007 0.86768 0.9464
## 1.5583 182 1 0.90121 0.02056 0.86179 0.9424
## 1.5667 181 1 0.89624 0.02105 0.85593 0.9385
## 1.5800 179 1 0.89125 0.02152 0.85006 0.9344
## 1.6458 177 1 0.88623 0.02198 0.84419 0.9304
## 1.6650 176 1 0.88121 0.02242 0.83834 0.9263
## 1.6683 175 1 0.87618 0.02285 0.83252 0.9221
## 1.7033 174 1 0.87116 0.02327 0.82673 0.9180
## 1.8350 171 1 0.86608 0.02368 0.82089 0.9138
## 1.8542 170 1 0.86100 0.02409 0.81507 0.9095
## 1.9000 167 1 0.85586 0.02449 0.80919 0.9052
## 1.9967 165 1 0.85069 0.02488 0.80329 0.9009
## 2.0000 164 1 0.84552 0.02527 0.79742 0.8965
## 2.0158 162 1 0.84032 0.02565 0.79153 0.8921
## 2.0167 161 1 0.83511 0.02601 0.78566 0.8877
## 2.1033 158 1 0.82985 0.02638 0.77972 0.8832
## 2.1342 157 1 0.82458 0.02674 0.77380 0.8787
## 2.1883 156 1 0.81931 0.02708 0.76791 0.8741
## 2.2108 155 1 0.81404 0.02742 0.76203 0.8696
## 2.2217 154 1 0.80877 0.02775 0.75617 0.8650
## 2.2350 153 1 0.80350 0.02807 0.75033 0.8604
## 2.2433 152 1 0.79823 0.02837 0.74451 0.8558
## 2.2625 150 1 0.79293 0.02868 0.73866 0.8512
## 2.3750 146 1 0.78752 0.02900 0.73269 0.8464
## 2.3858 145 1 0.78210 0.02930 0.72673 0.8417
## 2.4050 144 1 0.77669 0.02960 0.72080 0.8369
## 2.4133 143 1 0.77128 0.02988 0.71488 0.8321
## 2.4350 142 1 0.76587 0.03016 0.70897 0.8273
## 2.4667 140 1 0.76042 0.03044 0.70303 0.8225
## 2.5000 139 1 0.75496 0.03071 0.69711 0.8176
## 2.5750 138 1 0.74951 0.03097 0.69120 0.8127
## 2.5883 137 1 0.74406 0.03123 0.68531 0.8079
## 2.6083 136 1 0.73861 0.03147 0.67943 0.8029
## 2.6133 135 1 0.73316 0.03171 0.67357 0.7980
## 2.6333 134 1 0.72771 0.03195 0.66771 0.7931
## 2.6600 133 1 0.72226 0.03217 0.66188 0.7881
## 2.7667 131 1 0.71677 0.03240 0.65600 0.7832
## 2.8075 130 1 0.71127 0.03261 0.65014 0.7782
## 2.8167 129 1 0.70578 0.03282 0.64429 0.7731
## 2.8250 128 1 0.70029 0.03303 0.63845 0.7681
## 2.9917 126 1 0.69475 0.03323 0.63258 0.7630
## 3.0167 125 1 0.68922 0.03343 0.62671 0.7580
## 3.0250 124 1 0.68368 0.03362 0.62086 0.7529
## 3.0625 123 1 0.67815 0.03380 0.61502 0.7477
## 3.0767 122 1 0.67261 0.03398 0.60920 0.7426
## 3.0833 120 1 0.66703 0.03416 0.60333 0.7375
## 3.1092 119 1 0.66145 0.03433 0.59747 0.7323
## 3.1667 117 1 0.65582 0.03450 0.59157 0.7270
## 3.1725 116 1 0.65019 0.03466 0.58568 0.7218
## 3.1833 114 1 0.64451 0.03483 0.57974 0.7165
## 3.2267 113 1 0.63883 0.03498 0.57381 0.7112
## 3.2708 112 1 0.63315 0.03514 0.56790 0.7059
## 3.3333 111 1 0.62747 0.03528 0.56200 0.7006
## 3.3667 109 2 0.61607 0.03557 0.55016 0.6899
## 3.5000 106 1 0.61028 0.03570 0.54417 0.6844
## 3.5750 105 1 0.60450 0.03584 0.53819 0.6790
## 3.6492 104 1 0.59871 0.03596 0.53222 0.6735
## 3.6583 103 1 0.59293 0.03608 0.52627 0.6680
## 3.6833 102 1 0.58714 0.03619 0.52032 0.6625
## 3.7000 101 1 0.58136 0.03630 0.51439 0.6570
## 3.7225 100 1 0.57557 0.03640 0.50847 0.6515
## 3.7283 99 1 0.56979 0.03650 0.50256 0.6460
## 3.7333 98 1 0.56400 0.03659 0.49667 0.6405
## 3.7475 97 1 0.55822 0.03667 0.49078 0.6349
## 3.7750 96 1 0.55243 0.03675 0.48491 0.6294
## 3.7833 95 1 0.54665 0.03682 0.47904 0.6238
## 3.8925 94 1 0.54087 0.03689 0.47319 0.6182
## 3.9500 93 1 0.53508 0.03695 0.46735 0.6126
## 3.9750 92 1 0.52930 0.03701 0.46152 0.6070
## 3.9833 91 1 0.52351 0.03705 0.45570 0.6014
## 3.9883 90 1 0.51773 0.03710 0.44989 0.5958
## 4.0925 89 1 0.51194 0.03714 0.44409 0.5902
## 4.1333 88 1 0.50616 0.03717 0.43830 0.5845
## 4.1533 87 1 0.50037 0.03720 0.43253 0.5789
## 4.2025 86 1 0.49459 0.03722 0.42676 0.5732
## 4.2158 85 1 0.48880 0.03724 0.42101 0.5675
## 4.2417 84 1 0.48302 0.03725 0.41526 0.5618
## 4.3417 83 1 0.47723 0.03725 0.40953 0.5561
## 4.3450 82 1 0.47145 0.03726 0.40380 0.5504
## 4.3533 81 1 0.46567 0.03725 0.39809 0.5447
## 4.3750 80 1 0.45988 0.03724 0.39239 0.5390
## 4.4000 79 1 0.45410 0.03722 0.38670 0.5332
## 4.4050 78 1 0.44831 0.03720 0.38102 0.5275
## 4.5333 77 1 0.44253 0.03717 0.37535 0.5217
## 4.5750 76 1 0.43674 0.03714 0.36969 0.5160
## 4.5942 75 1 0.43096 0.03710 0.36404 0.5102
## 4.6108 74 1 0.42517 0.03706 0.35840 0.5044
## 4.6417 73 1 0.41939 0.03701 0.35278 0.4986
## 4.6583 72 1 0.41360 0.03696 0.34716 0.4928
## 4.6600 71 1 0.40782 0.03689 0.34156 0.4869
## 4.6917 70 1 0.40204 0.03683 0.33596 0.4811
## 4.7083 69 1 0.39625 0.03676 0.33038 0.4753
## 4.7333 68 1 0.39047 0.03668 0.32481 0.4694
## 4.7500 67 1 0.38468 0.03660 0.31924 0.4635
## 4.8158 66 1 0.37890 0.03651 0.31369 0.4577
## 4.8167 65 1 0.37311 0.03641 0.30816 0.4518
## 4.8350 64 1 0.36733 0.03631 0.30263 0.4459
## 4.8667 63 1 0.36154 0.03620 0.29711 0.4399
## 4.8708 62 1 0.35576 0.03609 0.29161 0.4340
## 4.9225 61 1 0.34997 0.03597 0.28612 0.4281
## 4.9333 60 1 0.34419 0.03585 0.28063 0.4221
## 4.9450 59 1 0.33840 0.03572 0.27517 0.4162
## 4.9583 58 2 0.32693 0.03545 0.26434 0.4043
## 4.9608 56 1 0.32115 0.03530 0.25891 0.3983
## 4.9667 55 1 0.31536 0.03514 0.25349 0.3923
## 4.9967 54 1 0.30958 0.03498 0.24808 0.3863
## 5.1167 53 1 0.30379 0.03481 0.24268 0.3803
## 5.2708 52 1 0.29800 0.03463 0.23730 0.3742
## 5.3417 51 1 0.29222 0.03445 0.23193 0.3682
## 5.3608 50 1 0.28643 0.03426 0.22657 0.3621
## 5.3642 49 1 0.28064 0.03406 0.22123 0.3560
## 5.3750 48 1 0.27486 0.03386 0.21590 0.3499
## 5.4050 47 1 0.26907 0.03365 0.21058 0.3438
## 5.4108 46 1 0.26329 0.03343 0.20528 0.3377
## 5.4625 45 1 0.25750 0.03320 0.20000 0.3315
## 5.4900 44 1 0.25171 0.03297 0.19472 0.3254
## 5.5992 43 1 0.24593 0.03273 0.18947 0.3192
## 5.6517 42 1 0.24014 0.03248 0.18423 0.3130
## 5.6750 41 1 0.23435 0.03222 0.17900 0.3068
## 5.7092 40 1 0.22857 0.03195 0.17379 0.3006
## 5.7250 39 1 0.22278 0.03167 0.16860 0.2944
## 5.7583 38 1 0.21700 0.03139 0.16342 0.2881
## 5.8875 37 1 0.21121 0.03110 0.15827 0.2819
## 5.9000 36 1 0.20542 0.03079 0.15313 0.2756
## 6.0075 35 1 0.19964 0.03048 0.14801 0.2693
## 6.1833 33 1 0.19368 0.03017 0.14273 0.2628
## 6.1967 32 1 0.18772 0.02984 0.13747 0.2563
## 6.2108 31 1 0.18176 0.02950 0.13224 0.2498
## 6.3367 30 1 0.17580 0.02915 0.12703 0.2433
## 6.3392 29 1 0.16984 0.02878 0.12184 0.2368
## 6.5942 28 1 0.16388 0.02841 0.11668 0.2302
## 6.6875 26 1 0.15770 0.02803 0.11132 0.2234
## 6.7333 25 1 0.15152 0.02763 0.10599 0.2166
## 6.8575 24 1 0.14533 0.02721 0.10069 0.2098
## 6.9667 23 1 0.13915 0.02678 0.09543 0.2029
## 6.9775 22 1 0.13297 0.02633 0.09020 0.1960
## 7.0108 21 1 0.12678 0.02585 0.08501 0.1891
## 7.0583 20 1 0.12060 0.02536 0.07987 0.1821
## 7.0750 19 1 0.11442 0.02484 0.07476 0.1751
## 7.1067 18 1 0.10823 0.02430 0.06970 0.1681
## 7.1342 17 1 0.10205 0.02373 0.06469 0.1610
## 7.2025 15 1 0.09547 0.02316 0.05934 0.1536
## 7.4158 14 1 0.08889 0.02255 0.05407 0.1461
## 7.4683 13 1 0.08231 0.02189 0.04887 0.1386
## 7.9225 11 1 0.07515 0.02124 0.04320 0.1308
## 8.2925 10 1 0.06800 0.02051 0.03765 0.1228
## 8.7642 9 1 0.06085 0.01970 0.03226 0.1148
## 8.9117 8 1 0.05370 0.01881 0.02703 0.1067
## 9.1008 7 1 0.04655 0.01782 0.02199 0.0986
## 9.2325 6 1 0.03941 0.01671 0.01716 0.0905
## 9.3608 5 1 0.03226 0.01547 0.01261 0.0826
## 9.8817 4 1 0.02513 0.01406 0.00839 0.0752
## 9.9342 3 1 0.01800 0.01247 0.00463 0.0700
## 10.2267 2 1 0.01092 0.01081 0.00157 0.0760
## 11.8792 1 1 0.00402 Inf 0.00000 1.0000autoplot(fhsurvival_year, xlab="Time in Years", ylab="Survival Probability", surv.linetype = 'dashed', surv.colour = 'blue',
conf.int.fill = 'dodgerblue3', conf.int.alpha = 0.5)
Non-Parametric Groups Analysis
This section aims to perform different group analysis on the dataset.
Gender Analysis
It seems from the analysis that males are living longer than females
Kaplan-Meier non-parametric
kmsurvival1_gender <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$gender)
summary(kmsurvival1_gender)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$gender)
##
## clinical_data$gender=F
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2.26 105 1 0.9905 0.00948 0.97207 1.000
## 4.24 103 1 0.9809 0.01340 0.95494 1.000
## 5.22 100 1 0.9711 0.01647 0.93930 1.000
## 12.10 96 1 0.9609 0.01916 0.92411 0.999
## 14.40 94 1 0.9507 0.02151 0.90948 0.994
## 15.00 92 1 0.9404 0.02363 0.89519 0.988
## 16.47 90 1 0.9299 0.02557 0.88114 0.981
## 16.90 89 1 0.9195 0.02733 0.86744 0.975
## 17.95 88 1 0.9090 0.02895 0.85402 0.968
## 18.80 87 1 0.8986 0.03045 0.84085 0.960
## 18.96 85 1 0.8880 0.03187 0.82769 0.953
## 19.98 84 1 0.8774 0.03320 0.81473 0.945
## 22.02 83 1 0.8669 0.03444 0.80193 0.937
## 22.25 82 1 0.8563 0.03561 0.78928 0.929
## 22.80 79 1 0.8455 0.03677 0.77638 0.921
## 24.00 78 1 0.8346 0.03786 0.76362 0.912
## 24.19 76 1 0.8236 0.03892 0.75078 0.904
## 24.20 75 1 0.8127 0.03992 0.73806 0.895
## 26.26 73 1 0.8015 0.04090 0.72524 0.886
## 26.53 72 1 0.7904 0.04182 0.71254 0.877
## 26.92 71 1 0.7793 0.04269 0.69993 0.868
## 27.15 69 1 0.7680 0.04354 0.68721 0.858
## 28.63 66 1 0.7563 0.04440 0.67412 0.849
## 28.86 65 1 0.7447 0.04522 0.66114 0.839
## 29.22 64 1 0.7331 0.04599 0.64825 0.829
## 29.60 63 1 0.7214 0.04670 0.63545 0.819
## 30.00 62 1 0.7098 0.04738 0.62274 0.809
## 31.06 61 1 0.6982 0.04801 0.61012 0.799
## 31.36 60 1 0.6865 0.04860 0.59758 0.789
## 31.92 59 1 0.6749 0.04915 0.58511 0.778
## 33.80 57 1 0.6630 0.04969 0.57246 0.768
## 33.90 56 1 0.6512 0.05020 0.55989 0.757
## 36.20 55 1 0.6394 0.05066 0.54739 0.747
## 36.75 54 1 0.6275 0.05109 0.53497 0.736
## 38.07 51 1 0.6152 0.05155 0.52205 0.725
## 38.72 50 1 0.6029 0.05196 0.50920 0.714
## 39.25 49 1 0.5906 0.05234 0.49644 0.703
## 42.00 48 1 0.5783 0.05267 0.48375 0.691
## 42.90 47 1 0.5660 0.05297 0.47114 0.680
## 43.79 46 1 0.5537 0.05323 0.45861 0.668
## 43.90 45 1 0.5414 0.05345 0.44614 0.657
## 44.40 44 1 0.5291 0.05363 0.43375 0.645
## 45.30 43 1 0.5168 0.05378 0.42143 0.634
## 45.40 42 1 0.5045 0.05389 0.40918 0.622
## 46.71 41 1 0.4922 0.05396 0.39700 0.610
## 49.11 40 1 0.4799 0.05399 0.38490 0.598
## 50.59 39 1 0.4676 0.05399 0.37286 0.586
## 52.10 38 1 0.4553 0.05396 0.36089 0.574
## 52.14 37 1 0.4430 0.05388 0.34899 0.562
## 52.50 36 1 0.4307 0.05377 0.33716 0.550
## 54.90 35 1 0.4183 0.05363 0.32541 0.538
## 55.13 34 1 0.4060 0.05344 0.31372 0.526
## 55.33 33 1 0.3937 0.05322 0.30210 0.513
## 55.90 32 1 0.3814 0.05296 0.29056 0.501
## 55.92 31 1 0.3691 0.05266 0.27909 0.488
## 56.50 30 1 0.3568 0.05232 0.26769 0.476
## 57.80 29 1 0.3445 0.05195 0.25637 0.463
## 58.40 28 1 0.3322 0.05153 0.24513 0.450
## 58.45 27 1 0.3199 0.05107 0.23397 0.437
## 59.20 26 1 0.3076 0.05056 0.22288 0.425
## 59.50 25 1 0.2953 0.05002 0.21188 0.412
## 59.60 24 1 0.2830 0.04942 0.20097 0.399
## 64.10 23 1 0.2707 0.04878 0.19015 0.385
## 64.37 22 1 0.2584 0.04809 0.17941 0.372
## 64.50 21 1 0.2461 0.04735 0.16878 0.359
## 65.55 20 1 0.2338 0.04655 0.15824 0.345
## 67.19 19 1 0.2215 0.04570 0.14781 0.332
## 67.82 18 1 0.2092 0.04479 0.13748 0.318
## 68.70 17 1 0.1969 0.04381 0.12728 0.305
## 70.65 16 1 0.1846 0.04276 0.11720 0.291
## 74.20 14 1 0.1714 0.04169 0.10639 0.276
## 74.36 13 1 0.1582 0.04052 0.09576 0.261
## 79.13 12 1 0.1450 0.03923 0.08534 0.246
## 80.25 11 1 0.1318 0.03781 0.07514 0.231
## 80.80 10 1 0.1186 0.03625 0.06519 0.216
## 85.28 9 1 0.1055 0.03454 0.05551 0.200
## 85.61 8 1 0.0923 0.03264 0.04614 0.185
## 86.43 7 1 0.0791 0.03052 0.03713 0.169
## 95.07 6 1 0.0659 0.02814 0.02855 0.152
## 99.51 5 1 0.0527 0.02541 0.02050 0.136
## 110.79 4 1 0.0395 0.02222 0.01315 0.119
## 112.33 3 1 0.0264 0.01831 0.00676 0.103
## 118.58 2 1 0.0132 0.01307 0.00189 0.092
## 119.21 1 1 0.0000 NaN NA NA
##
## clinical_data$gender=M
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 120 1 0.9917 0.0083 0.97553 1.000
## 1.80 119 1 0.9833 0.0117 0.96069 1.000
## 3.64 118 1 0.9750 0.0143 0.94746 1.000
## 4.10 117 1 0.9667 0.0164 0.93508 0.999
## 5.20 116 1 0.9583 0.0182 0.92324 0.995
## 10.20 109 1 0.9495 0.0201 0.91099 0.990
## 11.60 107 1 0.9407 0.0218 0.89896 0.984
## 13.50 105 1 0.9317 0.0233 0.88709 0.979
## 15.05 100 1 0.9224 0.0249 0.87488 0.972
## 15.71 98 1 0.9130 0.0264 0.86276 0.966
## 18.18 96 1 0.9035 0.0277 0.85070 0.960
## 18.70 95 1 0.8940 0.0290 0.83883 0.953
## 19.75 93 1 0.8843 0.0303 0.82696 0.946
## 20.02 92 1 0.8747 0.0314 0.81525 0.939
## 20.44 91 1 0.8651 0.0325 0.80367 0.931
## 23.96 87 1 0.8552 0.0336 0.79173 0.924
## 25.24 85 1 0.8451 0.0347 0.77975 0.916
## 25.61 84 1 0.8351 0.0357 0.76789 0.908
## 26.66 83 1 0.8250 0.0367 0.75614 0.900
## 26.82 82 1 0.8149 0.0376 0.74449 0.892
## 28.50 80 1 0.8047 0.0385 0.73276 0.884
## 28.96 79 1 0.7946 0.0393 0.72112 0.875
## 30.90 77 1 0.7842 0.0401 0.70939 0.867
## 31.30 76 1 0.7739 0.0409 0.69775 0.858
## 31.60 75 1 0.7636 0.0416 0.68618 0.850
## 33.20 74 1 0.7533 0.0423 0.67470 0.841
## 33.69 73 1 0.7430 0.0430 0.66328 0.832
## 35.90 71 1 0.7325 0.0437 0.65175 0.823
## 36.30 70 1 0.7220 0.0443 0.64029 0.814
## 36.92 69 1 0.7116 0.0448 0.62889 0.805
## 37.00 68 1 0.7011 0.0454 0.61756 0.796
## 37.31 67 1 0.6906 0.0459 0.60629 0.787
## 38.00 66 1 0.6802 0.0464 0.59508 0.777
## 38.20 64 1 0.6696 0.0469 0.58373 0.768
## 40.00 63 1 0.6589 0.0473 0.57243 0.758
## 40.40 61 2 0.6373 0.0482 0.54959 0.739
## 44.20 58 1 0.6263 0.0486 0.53802 0.729
## 44.67 57 1 0.6153 0.0489 0.52652 0.719
## 44.74 56 1 0.6044 0.0493 0.51508 0.709
## 44.80 55 1 0.5934 0.0496 0.50370 0.699
## 44.97 54 1 0.5824 0.0499 0.49238 0.689
## 47.40 53 1 0.5714 0.0501 0.48111 0.679
## 47.70 52 1 0.5604 0.0504 0.46990 0.668
## 47.80 51 1 0.5494 0.0506 0.45874 0.658
## 47.86 50 1 0.5384 0.0507 0.44764 0.648
## 49.60 49 1 0.5274 0.0509 0.43659 0.637
## 49.84 48 1 0.5164 0.0510 0.42560 0.627
## 50.43 47 1 0.5055 0.0511 0.41466 0.616
## 50.90 46 1 0.4945 0.0511 0.40377 0.606
## 52.24 45 1 0.4835 0.0512 0.39293 0.595
## 52.80 44 1 0.4725 0.0512 0.38215 0.584
## 52.86 43 1 0.4615 0.0511 0.37142 0.573
## 54.40 42 1 0.4505 0.0511 0.36074 0.563
## 55.70 41 1 0.4395 0.0510 0.35011 0.552
## 56.30 40 1 0.4285 0.0509 0.33954 0.541
## 56.80 39 1 0.4176 0.0508 0.32901 0.530
## 57.00 38 1 0.4066 0.0506 0.31855 0.519
## 57.79 37 1 0.3956 0.0504 0.30813 0.508
## 58.02 36 1 0.3846 0.0502 0.29777 0.497
## 59.07 35 1 0.3736 0.0500 0.28747 0.486
## 59.34 34 1 0.3626 0.0497 0.27722 0.474
## 59.50 33 1 0.3516 0.0494 0.26702 0.463
## 59.53 32 1 0.3406 0.0490 0.25689 0.452
## 59.96 31 1 0.3296 0.0487 0.24681 0.440
## 61.40 30 1 0.3187 0.0483 0.23680 0.429
## 63.25 29 1 0.3077 0.0478 0.22684 0.417
## 64.33 28 1 0.2967 0.0474 0.21695 0.406
## 64.86 27 1 0.2857 0.0469 0.20712 0.394
## 64.93 26 1 0.2747 0.0464 0.19736 0.382
## 65.88 25 1 0.2637 0.0458 0.18766 0.371
## 68.10 24 1 0.2527 0.0452 0.17804 0.359
## 68.51 23 1 0.2417 0.0445 0.16849 0.347
## 69.10 22 1 0.2308 0.0438 0.15902 0.335
## 70.80 21 1 0.2198 0.0431 0.14963 0.323
## 72.09 20 1 0.2088 0.0423 0.14032 0.311
## 74.53 19 1 0.1978 0.0415 0.13110 0.298
## 76.04 18 1 0.1868 0.0406 0.12197 0.286
## 76.07 17 1 0.1758 0.0397 0.11295 0.274
## 82.29 15 1 0.1641 0.0387 0.10331 0.261
## 83.60 14 1 0.1524 0.0377 0.09382 0.247
## 83.73 13 1 0.1406 0.0366 0.08448 0.234
## 84.13 12 1 0.1289 0.0354 0.07532 0.221
## 84.70 11 1 0.1172 0.0340 0.06635 0.207
## 84.90 10 1 0.1055 0.0326 0.05758 0.193
## 88.99 8 1 0.0923 0.0311 0.04772 0.179
## 89.62 7 1 0.0791 0.0293 0.03829 0.163
## 105.17 5 1 0.0633 0.0274 0.02711 0.148
## 106.94 4 1 0.0475 0.0247 0.01713 0.132
## 109.21 3 1 0.0316 0.0209 0.00866 0.116
## 122.72 2 1 0.0158 0.0153 0.00237 0.106
## 142.55 1 1 0.0000 NaN NA NAautoplot(kmsurvival1_gender,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Fleming-Harrington non-parametric analysis
fhsurvival1_gender <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$gender, type="fleming-harrington")
summary(fhsurvival1_gender)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$gender, type = "fleming-harrington")
##
## clinical_data$gender=F
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2.26 105 1 0.99052 0.00948 0.97212 1.000
## 4.24 103 1 0.98095 0.01341 0.95503 1.000
## 5.22 100 1 0.97119 0.01648 0.93943 1.000
## 12.10 96 1 0.96113 0.01916 0.92430 0.999
## 14.40 94 1 0.95096 0.02151 0.90971 0.994
## 15.00 92 1 0.94068 0.02363 0.89548 0.988
## 16.47 90 1 0.93028 0.02558 0.88147 0.982
## 16.90 89 1 0.91989 0.02735 0.86782 0.975
## 17.95 88 1 0.90949 0.02897 0.85445 0.968
## 18.80 87 1 0.89910 0.03046 0.84133 0.961
## 18.96 85 1 0.88858 0.03189 0.82823 0.953
## 19.98 84 1 0.87807 0.03322 0.81531 0.946
## 22.02 83 1 0.86755 0.03447 0.80256 0.938
## 22.25 82 1 0.85704 0.03564 0.78996 0.930
## 22.80 79 1 0.84626 0.03680 0.77711 0.922
## 24.00 78 1 0.83548 0.03790 0.76440 0.913
## 24.19 76 1 0.82455 0.03897 0.75161 0.905
## 24.20 75 1 0.81363 0.03997 0.73895 0.896
## 26.26 73 1 0.80256 0.04095 0.72618 0.887
## 26.53 72 1 0.79149 0.04188 0.71353 0.878
## 26.92 71 1 0.78042 0.04275 0.70098 0.869
## 27.15 69 1 0.76920 0.04360 0.68831 0.860
## 28.63 66 1 0.75763 0.04448 0.67528 0.850
## 28.86 65 1 0.74606 0.04530 0.66235 0.840
## 29.22 64 1 0.73450 0.04608 0.64952 0.831
## 29.60 63 1 0.72293 0.04680 0.63678 0.821
## 30.00 62 1 0.71136 0.04748 0.62413 0.811
## 31.06 61 1 0.69980 0.04812 0.61156 0.801
## 31.36 60 1 0.68823 0.04872 0.59907 0.791
## 31.92 59 1 0.67666 0.04928 0.58666 0.780
## 33.80 57 1 0.66490 0.04983 0.57406 0.770
## 33.90 56 1 0.65313 0.05034 0.56155 0.760
## 36.20 55 1 0.64136 0.05082 0.54911 0.749
## 36.75 54 1 0.62959 0.05126 0.53674 0.739
## 38.07 51 1 0.61737 0.05173 0.52387 0.728
## 38.72 50 1 0.60514 0.05215 0.51109 0.717
## 39.25 49 1 0.59292 0.05254 0.49838 0.705
## 42.00 48 1 0.58069 0.05289 0.48575 0.694
## 42.90 47 1 0.56847 0.05320 0.47320 0.683
## 43.79 46 1 0.55624 0.05347 0.46072 0.672
## 43.90 45 1 0.54402 0.05371 0.44831 0.660
## 44.40 44 1 0.53179 0.05391 0.43597 0.649
## 45.30 43 1 0.51957 0.05407 0.42371 0.637
## 45.40 42 1 0.50735 0.05419 0.41151 0.625
## 46.71 41 1 0.49512 0.05428 0.39938 0.614
## 49.11 40 1 0.48290 0.05434 0.38733 0.602
## 50.59 39 1 0.47067 0.05435 0.37534 0.590
## 52.10 38 1 0.45845 0.05433 0.36342 0.578
## 52.14 37 1 0.44622 0.05428 0.35157 0.566
## 52.50 36 1 0.43400 0.05419 0.33978 0.554
## 54.90 35 1 0.42177 0.05407 0.32807 0.542
## 55.13 34 1 0.40955 0.05390 0.31643 0.530
## 55.33 33 1 0.39732 0.05370 0.30485 0.518
## 55.90 32 1 0.38510 0.05347 0.29335 0.506
## 55.92 31 1 0.37288 0.05320 0.28192 0.493
## 56.50 30 1 0.36065 0.05288 0.27056 0.481
## 57.80 29 1 0.34843 0.05254 0.25928 0.468
## 58.40 28 1 0.33620 0.05215 0.24807 0.456
## 58.45 27 1 0.32398 0.05172 0.23694 0.443
## 59.20 26 1 0.31175 0.05125 0.22589 0.430
## 59.50 25 1 0.29953 0.05073 0.21492 0.417
## 59.60 24 1 0.28731 0.05017 0.20403 0.405
## 64.10 23 1 0.27508 0.04957 0.19323 0.392
## 64.37 22 1 0.26286 0.04892 0.18252 0.379
## 64.50 21 1 0.25064 0.04822 0.17190 0.365
## 65.55 20 1 0.23841 0.04747 0.16137 0.352
## 67.19 19 1 0.22619 0.04667 0.15095 0.339
## 67.82 18 1 0.21396 0.04581 0.14063 0.326
## 68.70 17 1 0.20174 0.04489 0.13043 0.312
## 70.65 16 1 0.18952 0.04391 0.12034 0.298
## 74.20 14 1 0.17645 0.04293 0.10954 0.284
## 74.36 13 1 0.16339 0.04185 0.09891 0.270
## 79.13 12 1 0.15033 0.04066 0.08847 0.255
## 80.25 11 1 0.13726 0.03937 0.07824 0.241
## 80.80 10 1 0.12420 0.03795 0.06824 0.226
## 85.28 9 1 0.11114 0.03640 0.05849 0.211
## 85.61 8 1 0.09808 0.03469 0.04903 0.196
## 86.43 7 1 0.08502 0.03281 0.03991 0.181
## 95.07 6 1 0.07197 0.03073 0.03117 0.166
## 99.51 5 1 0.05892 0.02840 0.02291 0.152
## 110.79 4 1 0.04589 0.02578 0.01526 0.138
## 112.33 3 1 0.03288 0.02283 0.00843 0.128
## 118.58 2 1 0.01994 0.01977 0.00286 0.139
## 119.21 1 1 0.00734 Inf 0.00000 1.000
##
## clinical_data$gender=M
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 120 1 0.99170 0.0083 0.97557 1.000
## 1.80 119 1 0.98340 0.0117 0.96076 1.000
## 3.64 118 1 0.97510 0.0143 0.94756 1.000
## 4.10 117 1 0.96681 0.0164 0.93521 0.999
## 5.20 116 1 0.95851 0.0182 0.92341 0.995
## 10.20 109 1 0.94975 0.0201 0.91119 0.990
## 11.60 107 1 0.94092 0.0218 0.89920 0.985
## 13.50 105 1 0.93200 0.0233 0.88736 0.979
## 15.05 100 1 0.92273 0.0249 0.87520 0.973
## 15.71 98 1 0.91336 0.0264 0.86312 0.967
## 18.18 96 1 0.90389 0.0278 0.85110 0.960
## 18.70 95 1 0.89443 0.0290 0.83927 0.953
## 19.75 93 1 0.88486 0.0303 0.82744 0.946
## 20.02 92 1 0.87530 0.0315 0.81577 0.939
## 20.44 91 1 0.86573 0.0325 0.80424 0.932
## 23.96 87 1 0.85584 0.0337 0.79234 0.924
## 25.24 85 1 0.84583 0.0347 0.78041 0.917
## 25.61 84 1 0.83582 0.0358 0.76859 0.909
## 26.66 83 1 0.82581 0.0367 0.75688 0.901
## 26.82 82 1 0.81580 0.0376 0.74528 0.893
## 28.50 80 1 0.80566 0.0385 0.73359 0.885
## 28.96 79 1 0.79553 0.0394 0.72200 0.877
## 30.90 77 1 0.78527 0.0402 0.71032 0.868
## 31.30 76 1 0.77500 0.0410 0.69872 0.860
## 31.60 75 1 0.76474 0.0417 0.68720 0.851
## 33.20 74 1 0.75447 0.0424 0.67576 0.842
## 33.69 73 1 0.74421 0.0431 0.66439 0.834
## 35.90 71 1 0.73380 0.0437 0.65290 0.825
## 36.30 70 1 0.72339 0.0443 0.64149 0.816
## 36.92 69 1 0.71298 0.0449 0.63014 0.807
## 37.00 68 1 0.70257 0.0455 0.61885 0.798
## 37.31 67 1 0.69216 0.0460 0.60763 0.788
## 38.00 66 1 0.68176 0.0465 0.59646 0.779
## 38.20 64 1 0.67119 0.0470 0.58515 0.770
## 40.00 63 1 0.66062 0.0474 0.57390 0.760
## 40.40 61 2 0.63931 0.0483 0.55130 0.741
## 44.20 58 1 0.62838 0.0487 0.53978 0.732
## 44.67 57 1 0.61745 0.0491 0.52833 0.722
## 44.74 56 1 0.60652 0.0495 0.51693 0.712
## 44.80 55 1 0.59560 0.0498 0.50559 0.702
## 44.97 54 1 0.58467 0.0501 0.49431 0.692
## 47.40 53 1 0.57374 0.0503 0.48309 0.681
## 47.70 52 1 0.56281 0.0506 0.47192 0.671
## 47.80 51 1 0.55188 0.0508 0.46080 0.661
## 47.86 50 1 0.54096 0.0510 0.44974 0.651
## 49.60 49 1 0.53003 0.0511 0.43874 0.640
## 49.84 48 1 0.51910 0.0512 0.42778 0.630
## 50.43 47 1 0.50817 0.0513 0.41688 0.619
## 50.90 46 1 0.49724 0.0514 0.40603 0.609
## 52.24 45 1 0.48632 0.0515 0.39523 0.598
## 52.80 44 1 0.47539 0.0515 0.38449 0.588
## 52.86 43 1 0.46446 0.0515 0.37379 0.577
## 54.40 42 1 0.45353 0.0514 0.36315 0.566
## 55.70 41 1 0.44260 0.0514 0.35256 0.556
## 56.30 40 1 0.43168 0.0513 0.34202 0.545
## 56.80 39 1 0.42075 0.0512 0.33153 0.534
## 57.00 38 1 0.40982 0.0510 0.32110 0.523
## 57.79 37 1 0.39889 0.0508 0.31071 0.512
## 58.02 36 1 0.38796 0.0506 0.30038 0.501
## 59.07 35 1 0.37704 0.0504 0.29011 0.490
## 59.34 34 1 0.36611 0.0502 0.27989 0.479
## 59.50 33 1 0.35518 0.0499 0.26973 0.468
## 59.53 32 1 0.34425 0.0496 0.25962 0.456
## 59.96 31 1 0.33333 0.0492 0.24957 0.445
## 61.40 30 1 0.32240 0.0488 0.23957 0.434
## 63.25 29 1 0.31147 0.0484 0.22964 0.422
## 64.33 28 1 0.30054 0.0480 0.21977 0.411
## 64.86 27 1 0.28962 0.0475 0.20996 0.399
## 64.93 26 1 0.27869 0.0470 0.20022 0.388
## 65.88 25 1 0.26776 0.0465 0.19054 0.376
## 68.10 24 1 0.25683 0.0459 0.18093 0.365
## 68.51 23 1 0.24591 0.0453 0.17139 0.353
## 69.10 22 1 0.23498 0.0446 0.16193 0.341
## 70.80 21 1 0.22405 0.0439 0.15254 0.329
## 72.09 20 1 0.21312 0.0432 0.14324 0.317
## 74.53 19 1 0.20220 0.0424 0.13402 0.305
## 76.04 18 1 0.19127 0.0416 0.12489 0.293
## 76.07 17 1 0.18034 0.0407 0.11586 0.281
## 82.29 15 1 0.16871 0.0398 0.10622 0.268
## 83.60 14 1 0.15708 0.0389 0.09672 0.255
## 83.73 13 1 0.14545 0.0378 0.08737 0.242
## 84.13 12 1 0.13382 0.0367 0.07818 0.229
## 84.70 11 1 0.12219 0.0355 0.06917 0.216
## 84.90 10 1 0.11056 0.0342 0.06035 0.203
## 88.99 8 1 0.09757 0.0328 0.05045 0.189
## 89.62 7 1 0.08458 0.0313 0.04094 0.175
## 105.17 5 1 0.06925 0.0300 0.02967 0.162
## 106.94 4 1 0.05393 0.0280 0.01946 0.149
## 109.21 3 1 0.03864 0.0255 0.01058 0.141
## 122.72 2 1 0.02344 0.0227 0.00352 0.156
## 142.55 1 1 0.00862 Inf 0.00000 1.000autoplot(fhsurvival1_gender,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Tumor Location
It seems from the analysis that Colon cancer is the most dengraous cancer location.
Kaplan-Meier non-parametric
kmsurvival1_location <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$location)
summary(kmsurvival1_location)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$location)
##
## clinical_data$location=Rectum
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 10.2 29 1 0.9655 0.0339 0.9013 1.000
## 11.6 28 1 0.9310 0.0471 0.8432 1.000
## 16.9 24 1 0.8922 0.0590 0.7839 1.000
## 18.8 23 1 0.8534 0.0680 0.7301 0.998
## 22.8 21 1 0.8128 0.0759 0.6768 0.976
## 30.9 20 1 0.7722 0.0823 0.6266 0.952
## 37.0 19 1 0.7315 0.0874 0.5788 0.925
## 38.2 17 1 0.6885 0.0923 0.5295 0.895
## 40.4 16 1 0.6455 0.0960 0.4822 0.864
## 44.8 15 1 0.6024 0.0988 0.4369 0.831
## 54.4 14 1 0.5594 0.1007 0.3932 0.796
## 55.7 13 1 0.5164 0.1017 0.3510 0.760
## 57.0 12 1 0.4733 0.1019 0.3104 0.722
## 59.2 11 1 0.4303 0.1013 0.2712 0.683
## 61.4 10 1 0.3873 0.0999 0.2336 0.642
## 67.8 9 1 0.3442 0.0976 0.1974 0.600
## 68.5 8 1 0.3012 0.0944 0.1629 0.557
## 74.4 7 1 0.2582 0.0902 0.1302 0.512
## 80.8 6 1 0.2152 0.0848 0.0993 0.466
## 83.7 5 1 0.1721 0.0780 0.0708 0.418
## 84.1 4 1 0.1291 0.0694 0.0450 0.370
## 85.6 3 1 0.0861 0.0581 0.0229 0.323
## 118.6 1 1 0.0000 NaN NA NA
##
## clinical_data$location=Colon
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 45.4 2 1 0.5 0.354 0.125 1
## 52.1 1 1 0.0 NaN NA NA
##
## clinical_data$location=Left
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2.26 93 1 0.9892 0.0107 0.96851 1.000
## 5.20 92 1 0.9785 0.0150 0.94945 1.000
## 14.40 85 1 0.9670 0.0188 0.93090 1.000
## 15.05 84 1 0.9555 0.0218 0.91372 0.999
## 15.71 82 1 0.9438 0.0244 0.89712 0.993
## 16.47 80 1 0.9320 0.0268 0.88089 0.986
## 18.70 79 1 0.9202 0.0290 0.86517 0.979
## 18.96 78 1 0.9084 0.0309 0.84983 0.971
## 19.75 76 1 0.8965 0.0327 0.83457 0.963
## 20.02 75 1 0.8845 0.0344 0.81959 0.955
## 24.00 69 1 0.8717 0.0362 0.80353 0.946
## 24.20 67 1 0.8587 0.0379 0.78746 0.936
## 25.61 64 1 0.8453 0.0396 0.77103 0.927
## 26.53 63 1 0.8319 0.0412 0.75485 0.917
## 28.86 58 1 0.8175 0.0429 0.73754 0.906
## 28.96 57 1 0.8032 0.0445 0.72049 0.895
## 31.92 55 1 0.7886 0.0460 0.70330 0.884
## 33.20 54 1 0.7740 0.0474 0.68634 0.873
## 33.80 53 1 0.7594 0.0487 0.66959 0.861
## 35.90 52 1 0.7448 0.0499 0.65302 0.849
## 36.30 51 1 0.7302 0.0511 0.63664 0.837
## 36.92 50 1 0.7156 0.0521 0.62042 0.825
## 37.31 49 1 0.7009 0.0530 0.60435 0.813
## 38.00 48 1 0.6863 0.0539 0.58844 0.801
## 43.90 46 1 0.6714 0.0548 0.57225 0.788
## 44.20 45 1 0.6565 0.0555 0.55621 0.775
## 44.40 44 1 0.6416 0.0562 0.54031 0.762
## 44.67 43 1 0.6267 0.0569 0.52454 0.749
## 44.74 42 1 0.6117 0.0574 0.50891 0.735
## 44.97 41 1 0.5968 0.0579 0.49340 0.722
## 46.71 40 1 0.5819 0.0584 0.47801 0.708
## 47.70 39 1 0.5670 0.0588 0.46274 0.695
## 47.80 38 1 0.5521 0.0591 0.44760 0.681
## 47.86 37 1 0.5371 0.0593 0.43256 0.667
## 50.43 36 1 0.5222 0.0595 0.41764 0.653
## 50.90 35 1 0.5073 0.0597 0.40284 0.639
## 52.14 34 1 0.4924 0.0598 0.38814 0.625
## 52.80 33 1 0.4775 0.0598 0.37356 0.610
## 52.86 32 1 0.4625 0.0597 0.35908 0.596
## 54.90 31 1 0.4476 0.0597 0.34472 0.581
## 55.92 30 1 0.4327 0.0595 0.33047 0.567
## 56.80 29 1 0.4178 0.0593 0.31633 0.552
## 58.02 28 1 0.4029 0.0590 0.30230 0.537
## 58.45 27 1 0.3879 0.0587 0.28839 0.522
## 59.50 26 1 0.3730 0.0583 0.27459 0.507
## 59.53 25 1 0.3581 0.0578 0.26091 0.491
## 63.25 24 1 0.3432 0.0573 0.24735 0.476
## 64.33 23 1 0.3283 0.0567 0.23392 0.461
## 64.37 22 1 0.3133 0.0561 0.22061 0.445
## 64.93 21 1 0.2984 0.0554 0.20743 0.429
## 65.55 20 1 0.2835 0.0546 0.19439 0.413
## 67.19 19 1 0.2686 0.0537 0.18149 0.397
## 68.10 18 1 0.2536 0.0528 0.16874 0.381
## 69.10 17 1 0.2387 0.0517 0.15614 0.365
## 70.65 16 1 0.2238 0.0506 0.14370 0.349
## 70.80 15 1 0.2089 0.0494 0.13144 0.332
## 74.53 13 1 0.1928 0.0481 0.11824 0.314
## 76.04 12 1 0.1768 0.0467 0.10530 0.297
## 82.29 10 1 0.1591 0.0453 0.09108 0.278
## 85.28 9 1 0.1414 0.0435 0.07732 0.259
## 86.43 8 1 0.1237 0.0415 0.06408 0.239
## 89.62 7 1 0.1061 0.0392 0.05141 0.219
## 105.17 6 1 0.0884 0.0364 0.03940 0.198
## 106.94 5 1 0.0707 0.0331 0.02820 0.177
## 109.21 4 1 0.0530 0.0292 0.01802 0.156
## 110.79 3 1 0.0354 0.0242 0.00922 0.135
## 119.21 2 1 0.0177 0.0174 0.00257 0.122
## 122.72 1 1 0.0000 NaN NA NA
##
## clinical_data$location=Right
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 101 1 0.9901 0.00985 0.97098 1.000
## 1.80 99 1 0.9801 0.01393 0.95317 1.000
## 3.64 97 1 0.9700 0.01706 0.93712 1.000
## 4.10 96 1 0.9599 0.01965 0.92214 0.999
## 4.24 95 1 0.9498 0.02189 0.90784 0.994
## 5.22 92 1 0.9395 0.02396 0.89365 0.988
## 12.10 87 1 0.9287 0.02601 0.87907 0.981
## 13.50 86 1 0.9179 0.02786 0.86486 0.974
## 15.00 82 1 0.9067 0.02968 0.85033 0.967
## 17.95 81 1 0.8955 0.03135 0.83609 0.959
## 18.18 79 1 0.8841 0.03294 0.82188 0.951
## 19.98 78 1 0.8728 0.03441 0.80790 0.943
## 20.44 77 1 0.8615 0.03579 0.79411 0.935
## 22.02 76 1 0.8501 0.03707 0.78051 0.926
## 22.25 75 1 0.8388 0.03827 0.76706 0.917
## 23.96 74 1 0.8275 0.03939 0.75375 0.908
## 24.19 73 1 0.8161 0.04045 0.74058 0.899
## 25.24 72 1 0.8048 0.04145 0.72753 0.890
## 26.26 71 1 0.7935 0.04238 0.71459 0.881
## 26.66 70 1 0.7821 0.04327 0.70176 0.872
## 26.82 69 1 0.7708 0.04410 0.68903 0.862
## 26.92 68 1 0.7595 0.04489 0.67639 0.853
## 27.15 67 1 0.7481 0.04562 0.66384 0.843
## 28.50 66 1 0.7368 0.04632 0.65137 0.833
## 28.63 65 1 0.7255 0.04697 0.63899 0.824
## 29.22 64 1 0.7141 0.04759 0.62668 0.814
## 29.60 63 1 0.7028 0.04816 0.61445 0.804
## 30.00 62 1 0.6914 0.04870 0.60229 0.794
## 31.06 61 1 0.6801 0.04920 0.59020 0.784
## 31.30 60 1 0.6688 0.04967 0.57817 0.774
## 31.36 59 1 0.6574 0.05011 0.56621 0.763
## 31.60 58 1 0.6461 0.05051 0.55432 0.753
## 33.69 56 1 0.6346 0.05091 0.54224 0.743
## 33.90 55 1 0.6230 0.05127 0.53022 0.732
## 36.20 53 1 0.6113 0.05164 0.51800 0.721
## 36.75 52 1 0.5995 0.05196 0.50585 0.711
## 38.07 49 1 0.5873 0.05232 0.49319 0.699
## 38.72 48 1 0.5750 0.05265 0.48059 0.688
## 39.25 47 1 0.5628 0.05293 0.46808 0.677
## 40.00 46 1 0.5506 0.05317 0.45563 0.665
## 40.40 44 1 0.5381 0.05342 0.44293 0.654
## 42.00 43 1 0.5256 0.05362 0.43030 0.642
## 42.90 42 1 0.5130 0.05378 0.41775 0.630
## 43.79 41 1 0.5005 0.05391 0.40528 0.618
## 45.30 40 1 0.4880 0.05399 0.39288 0.606
## 47.40 39 1 0.4755 0.05404 0.38055 0.594
## 49.11 38 1 0.4630 0.05405 0.36830 0.582
## 49.60 37 1 0.4505 0.05401 0.35613 0.570
## 49.84 36 1 0.4380 0.05394 0.34403 0.558
## 50.59 35 1 0.4254 0.05383 0.33200 0.545
## 52.24 34 1 0.4129 0.05369 0.32005 0.533
## 52.50 33 1 0.4004 0.05350 0.30817 0.520
## 55.13 32 1 0.3879 0.05327 0.29637 0.508
## 55.33 31 1 0.3754 0.05300 0.28465 0.495
## 55.90 30 1 0.3629 0.05269 0.27301 0.482
## 56.30 29 1 0.3504 0.05234 0.26144 0.470
## 56.50 28 1 0.3379 0.05194 0.24996 0.457
## 57.79 27 1 0.3253 0.05150 0.23856 0.444
## 57.80 26 1 0.3128 0.05102 0.22724 0.431
## 58.40 25 1 0.3003 0.05049 0.21601 0.418
## 59.07 24 1 0.2878 0.04991 0.20487 0.404
## 59.34 23 1 0.2753 0.04929 0.19382 0.391
## 59.50 22 1 0.2628 0.04861 0.18286 0.378
## 59.60 21 1 0.2503 0.04788 0.17201 0.364
## 59.96 20 1 0.2377 0.04709 0.16126 0.351
## 64.10 19 1 0.2252 0.04624 0.15062 0.337
## 64.50 18 1 0.2127 0.04534 0.14009 0.323
## 64.86 17 1 0.2002 0.04436 0.12968 0.309
## 65.88 16 1 0.1877 0.04332 0.11940 0.295
## 68.70 15 1 0.1752 0.04220 0.10926 0.281
## 72.09 14 1 0.1627 0.04100 0.09926 0.267
## 74.20 13 1 0.1502 0.03971 0.08942 0.252
## 76.07 12 1 0.1376 0.03832 0.07976 0.238
## 79.13 11 1 0.1251 0.03682 0.07029 0.223
## 80.25 10 1 0.1126 0.03520 0.06103 0.208
## 83.60 9 1 0.1001 0.03344 0.05201 0.193
## 84.70 8 1 0.0876 0.03152 0.04327 0.177
## 84.90 7 1 0.0751 0.02939 0.03486 0.162
## 88.99 5 1 0.0601 0.02708 0.02482 0.145
## 95.07 4 1 0.0450 0.02412 0.01578 0.129
## 99.51 3 1 0.0300 0.02022 0.00803 0.112
## 112.33 2 1 0.0150 0.01466 0.00222 0.102
## 142.55 1 1 0.0000 NaN NA NAautoplot(kmsurvival1_location,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Fleming-Harrington non-parametric analysis
fhsurvival1_location <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$location, type="fleming-harrington")
summary(fhsurvival1_location)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$location, type = "fleming-harrington")
##
## clinical_data$location=Rectum
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 10.2 29 1 0.966 0.0339 0.9019 1.000
## 11.6 28 1 0.932 0.0471 0.8443 1.000
## 16.9 24 1 0.894 0.0591 0.7856 1.000
## 18.8 23 1 0.856 0.0682 0.7324 1.000
## 22.8 21 1 0.816 0.0762 0.6798 0.980
## 30.9 20 1 0.776 0.0827 0.6301 0.957
## 37.0 19 1 0.737 0.0880 0.5829 0.931
## 38.2 17 1 0.695 0.0931 0.5342 0.903
## 40.4 16 1 0.653 0.0971 0.4875 0.873
## 44.8 15 1 0.610 0.1001 0.4427 0.842
## 54.4 14 1 0.568 0.1023 0.3994 0.809
## 55.7 13 1 0.526 0.1036 0.3577 0.774
## 57.0 12 1 0.484 0.1043 0.3175 0.738
## 59.2 11 1 0.442 0.1041 0.2787 0.701
## 61.4 10 1 0.400 0.1032 0.2413 0.663
## 67.8 9 1 0.358 0.1015 0.2053 0.624
## 68.5 8 1 0.316 0.0991 0.1709 0.584
## 74.4 7 1 0.274 0.0957 0.1381 0.543
## 80.8 6 1 0.232 0.0914 0.1070 0.502
## 83.7 5 1 0.190 0.0860 0.0781 0.461
## 84.1 4 1 0.148 0.0794 0.0516 0.424
## 85.6 3 1 0.106 0.0715 0.0282 0.398
## 118.6 1 1 0.039 Inf 0.0000 1.000
##
## clinical_data$location=Colon
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 45.4 2 1 0.607 0.429 0.152 1
## 52.1 1 1 0.223 Inf 0.000 1
##
## clinical_data$location=Left
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2.26 93 1 0.98930 0.0107 0.96856 1.000
## 5.20 92 1 0.97861 0.0150 0.94956 1.000
## 14.40 85 1 0.96716 0.0188 0.93108 1.000
## 15.05 84 1 0.95572 0.0218 0.91395 0.999
## 15.71 82 1 0.94413 0.0244 0.89742 0.993
## 16.47 80 1 0.93241 0.0268 0.88126 0.987
## 18.70 79 1 0.92068 0.0290 0.86559 0.979
## 18.96 78 1 0.90895 0.0309 0.85032 0.972
## 19.75 76 1 0.89707 0.0327 0.83512 0.964
## 20.02 75 1 0.88519 0.0344 0.82021 0.955
## 24.00 69 1 0.87245 0.0362 0.80422 0.946
## 24.20 67 1 0.85953 0.0380 0.78822 0.937
## 25.61 64 1 0.84620 0.0397 0.77187 0.928
## 26.53 63 1 0.83287 0.0413 0.75578 0.918
## 28.86 58 1 0.81864 0.0430 0.73856 0.907
## 28.96 57 1 0.80440 0.0446 0.72159 0.897
## 31.92 55 1 0.78991 0.0461 0.70450 0.886
## 33.20 54 1 0.77541 0.0475 0.68762 0.874
## 33.80 53 1 0.76092 0.0488 0.67096 0.863
## 35.90 52 1 0.74643 0.0501 0.65448 0.851
## 36.30 51 1 0.73193 0.0512 0.63819 0.839
## 36.92 50 1 0.71744 0.0522 0.62205 0.827
## 37.31 49 1 0.70295 0.0532 0.60607 0.815
## 38.00 48 1 0.68845 0.0541 0.59024 0.803
## 43.90 46 1 0.67365 0.0549 0.57414 0.790
## 44.20 45 1 0.65884 0.0557 0.55819 0.778
## 44.40 44 1 0.64404 0.0565 0.54238 0.765
## 44.67 43 1 0.62923 0.0571 0.52669 0.752
## 44.74 42 1 0.61443 0.0577 0.51114 0.739
## 44.97 41 1 0.59963 0.0582 0.49571 0.725
## 46.71 40 1 0.58482 0.0587 0.48041 0.712
## 47.70 39 1 0.57002 0.0591 0.46522 0.698
## 47.80 38 1 0.55521 0.0594 0.45015 0.685
## 47.86 37 1 0.54041 0.0597 0.43519 0.671
## 50.43 36 1 0.52560 0.0599 0.42035 0.657
## 50.90 35 1 0.51080 0.0601 0.40561 0.643
## 52.14 34 1 0.49599 0.0602 0.39099 0.629
## 52.80 33 1 0.48119 0.0602 0.37647 0.615
## 52.86 32 1 0.46638 0.0602 0.36207 0.601
## 54.90 31 1 0.45158 0.0602 0.34777 0.586
## 55.92 30 1 0.43677 0.0601 0.33358 0.572
## 56.80 29 1 0.42197 0.0599 0.31950 0.557
## 58.02 28 1 0.40716 0.0597 0.30554 0.543
## 58.45 27 1 0.39236 0.0594 0.29168 0.528
## 59.50 26 1 0.37756 0.0590 0.27794 0.513
## 59.53 25 1 0.36275 0.0586 0.26431 0.498
## 63.25 24 1 0.34795 0.0581 0.25080 0.483
## 64.33 23 1 0.33314 0.0576 0.23740 0.467
## 64.37 22 1 0.31834 0.0570 0.22414 0.452
## 64.93 21 1 0.30354 0.0563 0.21100 0.437
## 65.55 20 1 0.28873 0.0556 0.19799 0.421
## 67.19 19 1 0.27393 0.0548 0.18511 0.405
## 68.10 18 1 0.25913 0.0539 0.17238 0.390
## 69.10 17 1 0.24432 0.0529 0.15980 0.374
## 70.65 16 1 0.22952 0.0519 0.14737 0.357
## 70.80 15 1 0.21472 0.0507 0.13511 0.341
## 74.53 13 1 0.19882 0.0496 0.12192 0.324
## 76.04 12 1 0.18292 0.0483 0.10897 0.307
## 82.29 10 1 0.16552 0.0471 0.09477 0.289
## 85.28 9 1 0.14811 0.0456 0.08099 0.271
## 86.43 8 1 0.13071 0.0439 0.06769 0.252
## 89.62 7 1 0.11331 0.0419 0.05492 0.234
## 105.17 6 1 0.09591 0.0395 0.04276 0.215
## 106.94 5 1 0.07853 0.0368 0.03133 0.197
## 109.21 4 1 0.06116 0.0337 0.02079 0.180
## 110.79 3 1 0.04382 0.0300 0.01143 0.168
## 119.21 2 1 0.02658 0.0262 0.00386 0.183
## 122.72 1 1 0.00978 Inf 0.00000 1.000
##
## clinical_data$location=Right
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 101 1 0.99015 0.00985 0.97102 1.000
## 1.80 99 1 0.98020 0.01393 0.95326 1.000
## 3.64 97 1 0.97014 0.01707 0.93726 1.000
## 4.10 96 1 0.96009 0.01966 0.92233 0.999
## 4.24 95 1 0.95004 0.02189 0.90808 0.994
## 5.22 92 1 0.93977 0.02397 0.89394 0.988
## 12.10 87 1 0.92903 0.02602 0.87941 0.981
## 13.50 86 1 0.91829 0.02787 0.86526 0.975
## 15.00 82 1 0.90716 0.02970 0.85078 0.967
## 17.95 81 1 0.89603 0.03137 0.83660 0.960
## 18.18 79 1 0.88475 0.03296 0.82245 0.952
## 19.98 78 1 0.87348 0.03444 0.80852 0.944
## 20.44 77 1 0.86221 0.03582 0.79480 0.935
## 22.02 76 1 0.85094 0.03710 0.78125 0.927
## 22.25 75 1 0.83967 0.03831 0.76785 0.918
## 23.96 74 1 0.82840 0.03944 0.75460 0.909
## 24.19 73 1 0.81713 0.04050 0.74149 0.900
## 25.24 72 1 0.80586 0.04150 0.72849 0.891
## 26.26 71 1 0.79459 0.04244 0.71561 0.882
## 26.66 70 1 0.78332 0.04333 0.70283 0.873
## 26.82 69 1 0.77205 0.04417 0.69015 0.864
## 26.92 68 1 0.76078 0.04496 0.67756 0.854
## 27.15 67 1 0.74951 0.04571 0.66507 0.845
## 28.50 66 1 0.73824 0.04641 0.65265 0.835
## 28.63 65 1 0.72697 0.04707 0.64032 0.825
## 29.22 64 1 0.71570 0.04769 0.62807 0.816
## 29.60 63 1 0.70443 0.04828 0.61589 0.806
## 30.00 62 1 0.69315 0.04882 0.60378 0.796
## 31.06 61 1 0.68188 0.04933 0.59174 0.786
## 31.30 60 1 0.67061 0.04981 0.57976 0.776
## 31.36 59 1 0.65934 0.05025 0.56785 0.766
## 31.60 58 1 0.64807 0.05066 0.55601 0.755
## 33.69 56 1 0.63660 0.05107 0.54398 0.745
## 33.90 55 1 0.62513 0.05145 0.53201 0.735
## 36.20 53 1 0.61345 0.05182 0.51985 0.724
## 36.75 52 1 0.60176 0.05216 0.50775 0.713
## 38.07 49 1 0.58961 0.05253 0.49514 0.702
## 38.72 48 1 0.57745 0.05287 0.48260 0.691
## 39.25 47 1 0.56529 0.05316 0.47014 0.680
## 40.00 46 1 0.55314 0.05342 0.45775 0.668
## 40.40 44 1 0.54071 0.05368 0.44510 0.657
## 42.00 43 1 0.52828 0.05390 0.43253 0.645
## 42.90 42 1 0.51585 0.05408 0.42004 0.634
## 43.79 41 1 0.50342 0.05422 0.40762 0.622
## 45.30 40 1 0.49099 0.05432 0.39527 0.610
## 47.40 39 1 0.47856 0.05439 0.38300 0.598
## 49.11 38 1 0.46613 0.05441 0.37080 0.586
## 49.60 37 1 0.45370 0.05440 0.35868 0.574
## 49.84 36 1 0.44127 0.05435 0.34663 0.562
## 50.59 35 1 0.42884 0.05426 0.33465 0.550
## 52.24 34 1 0.41641 0.05414 0.32275 0.537
## 52.50 33 1 0.40398 0.05397 0.31092 0.525
## 55.13 32 1 0.39156 0.05377 0.29916 0.512
## 55.33 31 1 0.37913 0.05353 0.28748 0.500
## 55.90 30 1 0.36670 0.05324 0.27588 0.487
## 56.30 29 1 0.35427 0.05292 0.26435 0.475
## 56.50 28 1 0.34184 0.05255 0.25290 0.462
## 57.79 27 1 0.32941 0.05215 0.24154 0.449
## 57.80 26 1 0.31698 0.05170 0.23025 0.436
## 58.40 25 1 0.30455 0.05120 0.21905 0.423
## 59.07 24 1 0.29212 0.05066 0.20794 0.410
## 59.34 23 1 0.27969 0.05008 0.19692 0.397
## 59.50 22 1 0.26726 0.04944 0.18599 0.384
## 59.60 21 1 0.25484 0.04875 0.17515 0.371
## 59.96 20 1 0.24241 0.04801 0.16442 0.357
## 64.10 19 1 0.22998 0.04722 0.15379 0.344
## 64.50 18 1 0.21755 0.04637 0.14327 0.330
## 64.86 17 1 0.20512 0.04545 0.13286 0.317
## 65.88 16 1 0.19270 0.04447 0.12258 0.303
## 68.70 15 1 0.18027 0.04342 0.11243 0.289
## 72.09 14 1 0.16784 0.04230 0.10241 0.275
## 74.20 13 1 0.15541 0.04110 0.09255 0.261
## 76.07 12 1 0.14299 0.03981 0.08286 0.247
## 79.13 11 1 0.13056 0.03842 0.07334 0.232
## 80.25 10 1 0.11814 0.03693 0.06402 0.218
## 83.60 9 1 0.10571 0.03532 0.05493 0.203
## 84.70 8 1 0.09329 0.03357 0.04609 0.189
## 84.90 7 1 0.08087 0.03166 0.03755 0.174
## 88.99 5 1 0.06621 0.02985 0.02736 0.160
## 95.07 4 1 0.05157 0.02761 0.01806 0.147
## 99.51 3 1 0.03695 0.02488 0.00987 0.138
## 112.33 2 1 0.02241 0.02188 0.00331 0.152
## 142.55 1 1 0.00824 Inf 0.00000 1.000autoplot(fhsurvival1_location,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Cancer Stage
As expected, stage A is with the least death rate.
Kaplan-Meier non-parametric
kmsurvival1_stage <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$dukes_stage)
summary(kmsurvival1_stage)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$dukes_stage)
##
## clinical_data$dukes_stage=A
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 1.80 41 1 0.9756 0.0241 0.92952 1.000
## 3.64 40 1 0.9512 0.0336 0.88752 1.000
## 14.40 39 1 0.9268 0.0407 0.85045 1.000
## 16.47 37 1 0.9018 0.0467 0.81483 0.998
## 19.75 36 1 0.8767 0.0516 0.78113 0.984
## 20.02 35 1 0.8517 0.0559 0.74885 0.969
## 22.80 34 1 0.8266 0.0596 0.71767 0.952
## 23.96 33 1 0.8016 0.0629 0.68739 0.935
## 28.96 31 1 0.7757 0.0659 0.65669 0.916
## 30.00 30 1 0.7499 0.0686 0.62675 0.897
## 36.30 29 1 0.7240 0.0710 0.59748 0.877
## 42.00 28 1 0.6982 0.0730 0.56881 0.857
## 43.79 27 1 0.6723 0.0747 0.54070 0.836
## 43.90 26 1 0.6464 0.0762 0.51310 0.814
## 44.20 25 1 0.6206 0.0774 0.48599 0.792
## 52.10 24 1 0.5947 0.0784 0.45934 0.770
## 52.24 23 1 0.5689 0.0791 0.43313 0.747
## 54.40 22 1 0.5430 0.0796 0.40735 0.724
## 55.13 21 1 0.5171 0.0799 0.38199 0.700
## 56.50 20 1 0.4913 0.0800 0.35704 0.676
## 57.79 19 1 0.4654 0.0799 0.33250 0.652
## 59.53 18 1 0.4396 0.0795 0.30837 0.627
## 64.10 17 1 0.4137 0.0789 0.28466 0.601
## 64.37 16 1 0.3879 0.0781 0.26137 0.576
## 64.50 15 1 0.3620 0.0771 0.23851 0.549
## 65.88 14 1 0.3361 0.0758 0.21610 0.523
## 67.19 13 1 0.3103 0.0742 0.19415 0.496
## 67.82 12 1 0.2844 0.0724 0.17270 0.468
## 68.51 11 1 0.2586 0.0703 0.15178 0.441
## 76.07 10 1 0.2327 0.0678 0.13142 0.412
## 80.80 9 1 0.2069 0.0651 0.11169 0.383
## 82.29 8 1 0.1810 0.0618 0.09265 0.354
## 83.60 7 1 0.1551 0.0582 0.07441 0.323
## 83.73 6 1 0.1293 0.0539 0.05710 0.293
## 84.13 5 1 0.1034 0.0489 0.04092 0.261
## 109.21 4 1 0.0776 0.0430 0.02618 0.230
## 119.21 3 1 0.0517 0.0356 0.01342 0.199
## 122.72 2 1 0.0259 0.0255 0.00374 0.179
## 142.55 1 1 0.0000 NaN NA NA
##
## clinical_data$dukes_stage=B
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2.26 94 1 0.9894 0.0106 0.96884 1.000
## 4.10 93 1 0.9787 0.0149 0.94998 1.000
## 5.20 92 1 0.9681 0.0181 0.93320 1.000
## 11.60 89 1 0.9572 0.0209 0.91704 0.999
## 12.10 88 1 0.9463 0.0234 0.90165 0.993
## 13.50 87 1 0.9355 0.0255 0.88680 0.987
## 15.05 82 1 0.9240 0.0276 0.87147 0.980
## 15.71 81 1 0.9126 0.0295 0.85654 0.972
## 17.95 80 1 0.9012 0.0313 0.84193 0.965
## 18.18 79 1 0.8898 0.0329 0.82760 0.957
## 22.02 77 1 0.8783 0.0345 0.81327 0.948
## 24.19 74 1 0.8664 0.0360 0.79868 0.940
## 25.24 72 1 0.8544 0.0374 0.78406 0.931
## 25.61 71 1 0.8423 0.0388 0.76963 0.922
## 26.53 70 1 0.8303 0.0401 0.75538 0.913
## 26.66 69 1 0.8183 0.0412 0.74128 0.903
## 26.82 68 1 0.8062 0.0424 0.72734 0.894
## 27.15 67 1 0.7942 0.0434 0.71353 0.884
## 28.50 65 1 0.7820 0.0444 0.69958 0.874
## 28.63 64 1 0.7698 0.0454 0.68577 0.864
## 28.86 63 1 0.7575 0.0463 0.67207 0.854
## 29.22 62 1 0.7453 0.0471 0.65848 0.844
## 29.60 61 1 0.7331 0.0479 0.64499 0.833
## 31.06 60 1 0.7209 0.0486 0.63160 0.823
## 31.30 59 1 0.7087 0.0493 0.61831 0.812
## 33.20 57 1 0.6962 0.0500 0.60483 0.801
## 33.69 56 1 0.6838 0.0506 0.59144 0.791
## 33.80 55 1 0.6714 0.0512 0.57814 0.780
## 33.90 54 1 0.6589 0.0517 0.56493 0.769
## 35.90 53 1 0.6465 0.0522 0.55180 0.757
## 36.20 52 1 0.6341 0.0527 0.53876 0.746
## 36.75 51 1 0.6216 0.0531 0.52579 0.735
## 37.00 50 1 0.6092 0.0535 0.51290 0.724
## 37.31 49 1 0.5968 0.0538 0.50009 0.712
## 38.00 47 1 0.5841 0.0542 0.48703 0.700
## 38.20 46 1 0.5714 0.0544 0.47405 0.689
## 39.25 45 1 0.5587 0.0547 0.46114 0.677
## 40.00 44 1 0.5460 0.0549 0.44832 0.665
## 40.40 43 1 0.5333 0.0551 0.43556 0.653
## 42.90 42 1 0.5206 0.0552 0.42289 0.641
## 44.40 41 1 0.5079 0.0553 0.41029 0.629
## 44.80 40 1 0.4952 0.0554 0.39776 0.616
## 44.97 39 1 0.4825 0.0554 0.38530 0.604
## 45.30 38 1 0.4698 0.0554 0.37292 0.592
## 45.40 37 1 0.4571 0.0553 0.36061 0.579
## 46.71 36 1 0.4444 0.0552 0.34838 0.567
## 47.40 35 1 0.4317 0.0551 0.33622 0.554
## 47.70 34 1 0.4190 0.0549 0.32413 0.542
## 47.86 33 1 0.4063 0.0547 0.31212 0.529
## 49.84 32 1 0.3936 0.0544 0.30019 0.516
## 50.90 31 1 0.3809 0.0541 0.28833 0.503
## 52.14 30 1 0.3682 0.0538 0.27655 0.490
## 52.50 29 1 0.3555 0.0534 0.26484 0.477
## 52.80 28 1 0.3428 0.0530 0.25322 0.464
## 55.33 27 1 0.3301 0.0525 0.24168 0.451
## 55.70 26 1 0.3174 0.0520 0.23023 0.438
## 55.90 25 1 0.3047 0.0515 0.21886 0.424
## 55.92 24 1 0.2920 0.0509 0.20758 0.411
## 56.30 23 1 0.2793 0.0502 0.19639 0.397
## 56.80 22 1 0.2666 0.0495 0.18530 0.384
## 57.00 21 1 0.2539 0.0488 0.17431 0.370
## 58.02 20 1 0.2412 0.0479 0.16342 0.356
## 58.40 19 1 0.2286 0.0471 0.15265 0.342
## 59.50 18 1 0.2159 0.0461 0.14198 0.328
## 59.60 17 1 0.2032 0.0451 0.13144 0.314
## 59.96 16 1 0.1905 0.0441 0.12103 0.300
## 63.25 15 1 0.1778 0.0429 0.11075 0.285
## 64.86 14 1 0.1651 0.0417 0.10062 0.271
## 70.65 13 1 0.1524 0.0404 0.09065 0.256
## 74.20 12 1 0.1397 0.0389 0.08086 0.241
## 76.04 11 1 0.1270 0.0374 0.07126 0.226
## 79.13 10 1 0.1143 0.0358 0.06188 0.211
## 80.25 9 1 0.1016 0.0340 0.05274 0.196
## 84.90 8 1 0.0889 0.0320 0.04388 0.180
## 85.28 7 1 0.0762 0.0299 0.03535 0.164
## 86.43 6 1 0.0635 0.0274 0.02721 0.148
## 88.99 5 1 0.0508 0.0247 0.01957 0.132
## 106.94 3 1 0.0339 0.0215 0.00975 0.118
## 110.79 2 1 0.0169 0.0161 0.00263 0.109
## 118.58 1 1 0.0000 NaN NA NA
##
## clinical_data$dukes_stage=C
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 91 1 0.9890 0.0109 0.96782 1.000
## 4.24 88 1 0.9778 0.0155 0.94778 1.000
## 5.22 85 1 0.9663 0.0191 0.92946 1.000
## 10.20 77 1 0.9537 0.0226 0.91036 0.999
## 15.00 73 1 0.9407 0.0258 0.89137 0.993
## 16.90 70 1 0.9272 0.0287 0.87256 0.985
## 18.70 68 1 0.9136 0.0314 0.85409 0.977
## 18.80 67 1 0.8999 0.0338 0.83617 0.969
## 18.96 65 1 0.8861 0.0360 0.81835 0.959
## 19.98 64 1 0.8723 0.0380 0.80092 0.950
## 20.44 63 1 0.8584 0.0398 0.78382 0.940
## 22.25 60 1 0.8441 0.0416 0.76631 0.930
## 24.00 58 1 0.8296 0.0434 0.74872 0.919
## 24.20 56 1 0.8147 0.0451 0.73101 0.908
## 26.26 54 1 0.7996 0.0467 0.71317 0.897
## 26.92 53 1 0.7846 0.0482 0.69557 0.885
## 30.90 49 1 0.7685 0.0498 0.67689 0.873
## 31.36 48 1 0.7525 0.0513 0.65847 0.860
## 31.60 47 1 0.7365 0.0526 0.64029 0.847
## 31.92 46 1 0.7205 0.0539 0.62233 0.834
## 36.92 44 1 0.7041 0.0551 0.60408 0.821
## 38.07 42 1 0.6874 0.0562 0.58552 0.807
## 38.72 40 1 0.6702 0.0574 0.56661 0.793
## 40.40 38 1 0.6526 0.0585 0.54733 0.778
## 44.67 36 1 0.6344 0.0597 0.52764 0.763
## 44.74 35 1 0.6163 0.0606 0.50820 0.747
## 47.80 34 1 0.5982 0.0615 0.48899 0.732
## 49.11 33 1 0.5800 0.0623 0.47000 0.716
## 49.60 32 1 0.5619 0.0629 0.45123 0.700
## 50.43 31 1 0.5438 0.0634 0.43267 0.683
## 50.59 30 1 0.5257 0.0638 0.41431 0.667
## 52.86 29 1 0.5075 0.0642 0.39614 0.650
## 54.90 28 1 0.4894 0.0644 0.37818 0.633
## 57.80 27 1 0.4713 0.0645 0.36040 0.616
## 58.45 26 1 0.4532 0.0645 0.34282 0.599
## 59.07 25 1 0.4350 0.0644 0.32543 0.582
## 59.20 24 1 0.4169 0.0642 0.30822 0.564
## 59.34 23 1 0.3988 0.0640 0.29121 0.546
## 59.50 22 1 0.3807 0.0636 0.27440 0.528
## 61.40 21 1 0.3625 0.0631 0.25778 0.510
## 64.33 20 1 0.3444 0.0625 0.24136 0.491
## 64.93 19 1 0.3263 0.0618 0.22515 0.473
## 65.55 18 1 0.3082 0.0609 0.20915 0.454
## 68.10 17 1 0.2900 0.0600 0.19337 0.435
## 68.70 16 1 0.2719 0.0589 0.17782 0.416
## 69.10 15 1 0.2538 0.0577 0.16252 0.396
## 70.80 14 1 0.2356 0.0564 0.14747 0.377
## 72.09 13 1 0.2175 0.0549 0.13269 0.357
## 74.36 11 1 0.1977 0.0533 0.11657 0.335
## 74.53 10 1 0.1780 0.0515 0.10091 0.314
## 84.70 8 1 0.1557 0.0497 0.08336 0.291
## 85.61 7 1 0.1335 0.0473 0.06666 0.267
## 89.62 5 1 0.1068 0.0447 0.04698 0.243
## 95.07 4 1 0.0801 0.0407 0.02955 0.217
## 99.51 3 1 0.0534 0.0348 0.01487 0.192
## 105.17 2 1 0.0267 0.0257 0.00405 0.176
## 112.33 1 1 0.0000 NaN NA NAautoplot(kmsurvival1_stage,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Fleming-Harrington non-parametric analysis
fhsurvival1_stage <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$dukes_stage, type="fleming-harrington")
summary(fhsurvival1_stage)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$dukes_stage, type = "fleming-harrington")
##
## clinical_data$dukes_stage=A
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 1.80 41 1 0.9759 0.0241 0.92980 1.000
## 3.64 40 1 0.9518 0.0337 0.88807 1.000
## 14.40 39 1 0.9277 0.0407 0.85126 1.000
## 16.47 37 1 0.9030 0.0467 0.81591 0.999
## 19.75 36 1 0.8782 0.0517 0.78248 0.986
## 20.02 35 1 0.8535 0.0560 0.75045 0.971
## 22.80 34 1 0.8288 0.0598 0.71952 0.955
## 23.96 33 1 0.8040 0.0630 0.68949 0.938
## 28.96 31 1 0.7785 0.0662 0.65905 0.920
## 30.00 30 1 0.7530 0.0689 0.62935 0.901
## 36.30 29 1 0.7275 0.0713 0.60033 0.882
## 42.00 28 1 0.7019 0.0734 0.57190 0.862
## 43.79 27 1 0.6764 0.0752 0.54402 0.841
## 43.90 26 1 0.6509 0.0767 0.51664 0.820
## 44.20 25 1 0.6254 0.0780 0.48974 0.799
## 52.10 24 1 0.5998 0.0791 0.46330 0.777
## 52.24 23 1 0.5743 0.0799 0.43729 0.754
## 54.40 22 1 0.5488 0.0805 0.41170 0.732
## 55.13 21 1 0.5233 0.0809 0.38652 0.708
## 56.50 20 1 0.4978 0.0811 0.36174 0.685
## 57.79 19 1 0.4722 0.0810 0.33737 0.661
## 59.53 18 1 0.4467 0.0808 0.31339 0.637
## 64.10 17 1 0.4212 0.0804 0.28981 0.612
## 64.37 16 1 0.3957 0.0797 0.26664 0.587
## 64.50 15 1 0.3702 0.0788 0.24389 0.562
## 65.88 14 1 0.3446 0.0777 0.22156 0.536
## 67.19 13 1 0.3191 0.0763 0.19969 0.510
## 67.82 12 1 0.2936 0.0747 0.17828 0.484
## 68.51 11 1 0.2681 0.0729 0.15737 0.457
## 76.07 10 1 0.2426 0.0707 0.13699 0.430
## 80.80 9 1 0.2171 0.0683 0.11720 0.402
## 82.29 8 1 0.1916 0.0655 0.09806 0.374
## 83.60 7 1 0.1661 0.0623 0.07964 0.346
## 83.73 6 1 0.1406 0.0586 0.06208 0.318
## 84.13 5 1 0.1151 0.0545 0.04553 0.291
## 109.21 4 1 0.0896 0.0497 0.03025 0.266
## 119.21 3 1 0.0642 0.0442 0.01666 0.248
## 122.72 2 1 0.0390 0.0384 0.00563 0.270
## 142.55 1 1 0.0143 Inf 0.00000 1.000
##
## clinical_data$dukes_stage=B
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2.26 94 1 0.98942 0.0106 0.96889 1.000
## 4.10 93 1 0.97884 0.0149 0.95009 1.000
## 5.20 92 1 0.96825 0.0181 0.93336 1.000
## 11.60 89 1 0.95744 0.0209 0.91726 0.999
## 12.10 88 1 0.94662 0.0234 0.90192 0.994
## 13.50 87 1 0.93580 0.0255 0.88713 0.987
## 15.05 82 1 0.92446 0.0276 0.87186 0.980
## 15.71 81 1 0.91311 0.0296 0.85699 0.973
## 17.95 80 1 0.90177 0.0313 0.84244 0.965
## 18.18 79 1 0.89043 0.0329 0.82816 0.957
## 22.02 77 1 0.87894 0.0345 0.81389 0.949
## 24.19 74 1 0.86714 0.0360 0.79937 0.941
## 25.24 72 1 0.85518 0.0375 0.78481 0.932
## 25.61 71 1 0.84322 0.0388 0.77044 0.923
## 26.53 70 1 0.83126 0.0401 0.75625 0.914
## 26.66 69 1 0.81930 0.0413 0.74222 0.904
## 26.82 68 1 0.80734 0.0424 0.72834 0.895
## 27.15 67 1 0.79538 0.0435 0.71459 0.885
## 28.50 65 1 0.78324 0.0445 0.70071 0.875
## 28.63 64 1 0.77109 0.0455 0.68696 0.866
## 28.86 63 1 0.75895 0.0464 0.67332 0.855
## 29.22 62 1 0.74681 0.0472 0.65979 0.845
## 29.60 61 1 0.73466 0.0480 0.64636 0.835
## 31.06 60 1 0.72252 0.0487 0.63303 0.825
## 31.30 59 1 0.71038 0.0494 0.61980 0.814
## 33.20 57 1 0.69802 0.0501 0.60638 0.804
## 33.69 56 1 0.68567 0.0508 0.59306 0.793
## 33.80 55 1 0.67332 0.0514 0.57982 0.782
## 33.90 54 1 0.66096 0.0519 0.56667 0.771
## 35.90 53 1 0.64861 0.0524 0.55360 0.760
## 36.20 52 1 0.63625 0.0529 0.54061 0.749
## 36.75 51 1 0.62390 0.0533 0.52770 0.738
## 37.00 50 1 0.61155 0.0537 0.51487 0.726
## 37.31 49 1 0.59919 0.0540 0.50211 0.715
## 38.00 47 1 0.58658 0.0544 0.48911 0.703
## 38.20 46 1 0.57396 0.0547 0.47619 0.692
## 39.25 45 1 0.56135 0.0550 0.46334 0.680
## 40.00 44 1 0.54874 0.0552 0.45057 0.668
## 40.40 43 1 0.53612 0.0554 0.43788 0.656
## 42.90 42 1 0.52351 0.0555 0.42526 0.644
## 44.40 41 1 0.51089 0.0556 0.41271 0.632
## 44.80 40 1 0.49828 0.0557 0.40024 0.620
## 44.97 39 1 0.48567 0.0557 0.38783 0.608
## 45.30 38 1 0.47305 0.0557 0.37550 0.596
## 45.40 37 1 0.46044 0.0557 0.36324 0.584
## 46.71 36 1 0.44782 0.0556 0.35106 0.571
## 47.40 35 1 0.43521 0.0555 0.33895 0.559
## 47.70 34 1 0.42260 0.0554 0.32691 0.546
## 47.86 33 1 0.40998 0.0552 0.31494 0.534
## 49.84 32 1 0.39737 0.0549 0.30305 0.521
## 50.90 31 1 0.38475 0.0547 0.29123 0.508
## 52.14 30 1 0.37214 0.0544 0.27949 0.496
## 52.50 29 1 0.35953 0.0540 0.26782 0.483
## 52.80 28 1 0.34691 0.0536 0.25624 0.470
## 55.33 27 1 0.33430 0.0532 0.24473 0.457
## 55.70 26 1 0.32169 0.0527 0.23331 0.444
## 55.90 25 1 0.30907 0.0522 0.22197 0.430
## 55.92 24 1 0.29646 0.0516 0.21072 0.417
## 56.30 23 1 0.28385 0.0510 0.19956 0.404
## 56.80 22 1 0.27123 0.0504 0.18849 0.390
## 57.00 21 1 0.25862 0.0496 0.17752 0.377
## 58.02 20 1 0.24601 0.0489 0.16665 0.363
## 58.40 19 1 0.23339 0.0481 0.15588 0.349
## 59.50 18 1 0.22078 0.0472 0.14522 0.336
## 59.60 17 1 0.20817 0.0462 0.13468 0.322
## 59.96 16 1 0.19556 0.0452 0.12426 0.308
## 63.25 15 1 0.18294 0.0442 0.11398 0.294
## 64.86 14 1 0.17033 0.0430 0.10383 0.279
## 70.65 13 1 0.15772 0.0418 0.09384 0.265
## 74.20 12 1 0.14511 0.0405 0.08401 0.251
## 76.04 11 1 0.13250 0.0390 0.07436 0.236
## 79.13 10 1 0.11989 0.0375 0.06492 0.221
## 80.25 9 1 0.10728 0.0359 0.05570 0.207
## 84.90 8 1 0.09468 0.0341 0.04674 0.192
## 85.28 7 1 0.08207 0.0322 0.03808 0.177
## 86.43 6 1 0.06947 0.0300 0.02978 0.162
## 88.99 5 1 0.05688 0.0277 0.02191 0.148
## 106.94 3 1 0.04076 0.0259 0.01174 0.142
## 110.79 2 1 0.02472 0.0235 0.00384 0.159
## 118.58 1 1 0.00909 Inf 0.00000 1.000
##
## clinical_data$dukes_stage=C
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 91 1 0.9891 0.0109 0.96788 1.000
## 4.24 88 1 0.9779 0.0155 0.94790 1.000
## 5.22 85 1 0.9665 0.0192 0.92964 1.000
## 10.20 77 1 0.9540 0.0226 0.91061 0.999
## 15.00 73 1 0.9410 0.0258 0.89171 0.993
## 16.90 70 1 0.9277 0.0288 0.87298 0.986
## 18.70 68 1 0.9141 0.0314 0.85459 0.978
## 18.80 67 1 0.9006 0.0338 0.83675 0.969
## 18.96 65 1 0.8868 0.0360 0.81902 0.960
## 19.98 64 1 0.8731 0.0380 0.80168 0.951
## 20.44 63 1 0.8593 0.0399 0.78466 0.941
## 22.25 60 1 0.8451 0.0417 0.76724 0.931
## 24.00 58 1 0.8307 0.0434 0.74974 0.920
## 24.20 56 1 0.8160 0.0451 0.73213 0.909
## 26.26 54 1 0.8010 0.0468 0.71438 0.898
## 26.92 53 1 0.7860 0.0483 0.69688 0.887
## 30.90 49 1 0.7702 0.0499 0.67831 0.874
## 31.36 48 1 0.7543 0.0514 0.66000 0.862
## 31.60 47 1 0.7384 0.0528 0.64192 0.849
## 31.92 46 1 0.7225 0.0540 0.62406 0.837
## 36.92 44 1 0.7063 0.0552 0.60592 0.823
## 38.07 42 1 0.6897 0.0564 0.58747 0.810
## 38.72 40 1 0.6726 0.0576 0.56868 0.796
## 40.40 38 1 0.6552 0.0588 0.54953 0.781
## 44.67 36 1 0.6372 0.0599 0.52997 0.766
## 44.74 35 1 0.6193 0.0609 0.51065 0.751
## 47.80 34 1 0.6013 0.0618 0.49156 0.736
## 49.11 33 1 0.5834 0.0626 0.47270 0.720
## 49.60 32 1 0.5654 0.0633 0.45404 0.704
## 50.43 31 1 0.5475 0.0639 0.43560 0.688
## 50.59 30 1 0.5295 0.0643 0.41735 0.672
## 52.86 29 1 0.5116 0.0647 0.39930 0.655
## 54.90 28 1 0.4936 0.0649 0.38143 0.639
## 57.80 27 1 0.4757 0.0651 0.36376 0.622
## 58.45 26 1 0.4577 0.0652 0.34628 0.605
## 59.07 25 1 0.4398 0.0651 0.32898 0.588
## 59.20 24 1 0.4218 0.0650 0.31187 0.571
## 59.34 23 1 0.4039 0.0648 0.29494 0.553
## 59.50 22 1 0.3859 0.0645 0.27821 0.535
## 61.40 21 1 0.3680 0.0640 0.26167 0.518
## 64.33 20 1 0.3500 0.0635 0.24532 0.499
## 64.93 19 1 0.3321 0.0629 0.22917 0.481
## 65.55 18 1 0.3142 0.0621 0.21323 0.463
## 68.10 17 1 0.2962 0.0613 0.19750 0.444
## 68.70 16 1 0.2783 0.0603 0.18199 0.425
## 69.10 15 1 0.2603 0.0592 0.16671 0.406
## 70.80 14 1 0.2424 0.0580 0.15167 0.387
## 72.09 13 1 0.2244 0.0566 0.13690 0.368
## 74.36 11 1 0.2049 0.0553 0.12081 0.348
## 74.53 10 1 0.1854 0.0537 0.10513 0.327
## 84.70 8 1 0.1636 0.0522 0.08759 0.306
## 85.61 7 1 0.1419 0.0502 0.07085 0.284
## 89.62 5 1 0.1161 0.0486 0.05110 0.264
## 95.07 4 1 0.0904 0.0460 0.03337 0.245
## 99.51 3 1 0.0648 0.0423 0.01805 0.233
## 105.17 2 1 0.0393 0.0378 0.00597 0.259
## 112.33 1 1 0.0145 Inf 0.00000 1.000autoplot(fhsurvival1_stage,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Adjuvant Radiation Therapy
It seems that who had the thetapy had a better chance to live.
Kaplan-Meier non-parametric analysis
kmsurvival1_adjXRT <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$adjXRT)
summary(kmsurvival1_adjXRT)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$adjXRT)
##
## clinical_data$adjXRT=N
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 204 1 0.99510 0.00489 0.98556 1.0000
## 1.80 202 1 0.99017 0.00692 0.97671 1.0000
## 2.26 201 1 0.98525 0.00846 0.96881 1.0000
## 3.64 199 1 0.98029 0.00976 0.96136 0.9996
## 4.10 198 1 0.97534 0.01089 0.95423 0.9969
## 4.24 197 1 0.97039 0.01191 0.94733 0.9940
## 5.20 194 1 0.96539 0.01285 0.94052 0.9909
## 5.22 193 1 0.96039 0.01373 0.93386 0.9877
## 10.20 186 1 0.95523 0.01459 0.92705 0.9843
## 11.60 184 1 0.95003 0.01541 0.92031 0.9807
## 12.10 183 1 0.94484 0.01617 0.91367 0.9771
## 13.50 182 1 0.93965 0.01690 0.90711 0.9734
## 14.40 178 1 0.93437 0.01761 0.90049 0.9695
## 15.00 175 1 0.92903 0.01830 0.89385 0.9656
## 15.05 174 1 0.92369 0.01896 0.88728 0.9616
## 15.71 172 1 0.91832 0.01959 0.88071 0.9575
## 16.47 170 1 0.91292 0.02021 0.87416 0.9534
## 16.90 169 1 0.90752 0.02080 0.86766 0.9492
## 17.95 168 1 0.90212 0.02136 0.86120 0.9450
## 18.18 166 1 0.89668 0.02192 0.85474 0.9407
## 18.70 165 1 0.89125 0.02245 0.84832 0.9363
## 18.80 164 1 0.88581 0.02296 0.84194 0.9320
## 19.75 161 1 0.88031 0.02347 0.83550 0.9275
## 19.98 160 1 0.87481 0.02396 0.82910 0.9230
## 20.02 159 1 0.86931 0.02443 0.82272 0.9185
## 20.44 158 1 0.86381 0.02489 0.81638 0.9140
## 22.02 155 1 0.85823 0.02534 0.80997 0.9094
## 22.25 154 1 0.85266 0.02578 0.80360 0.9047
## 22.80 153 1 0.84709 0.02621 0.79724 0.9000
## 23.96 151 1 0.84148 0.02663 0.79087 0.8953
## 24.00 150 1 0.83587 0.02704 0.78452 0.8906
## 24.19 148 1 0.83022 0.02744 0.77815 0.8858
## 24.20 147 1 0.82457 0.02783 0.77180 0.8810
## 25.24 145 1 0.81889 0.02821 0.76542 0.8761
## 26.26 144 1 0.81320 0.02858 0.75907 0.8712
## 26.53 143 1 0.80751 0.02894 0.75274 0.8663
## 26.66 142 1 0.80183 0.02929 0.74642 0.8613
## 26.82 141 1 0.79614 0.02963 0.74013 0.8564
## 26.92 140 1 0.79045 0.02996 0.73386 0.8514
## 27.15 138 1 0.78472 0.03028 0.72756 0.8464
## 28.50 136 1 0.77895 0.03061 0.72122 0.8413
## 28.63 135 1 0.77318 0.03092 0.71490 0.8362
## 28.86 134 1 0.76741 0.03122 0.70860 0.8311
## 28.96 133 1 0.76164 0.03152 0.70231 0.8260
## 29.22 132 1 0.75587 0.03180 0.69605 0.8208
## 29.60 131 1 0.75010 0.03208 0.68980 0.8157
## 30.00 130 1 0.74433 0.03235 0.68356 0.8105
## 30.90 129 1 0.73856 0.03261 0.67735 0.8053
## 31.06 128 1 0.73279 0.03286 0.67114 0.8001
## 31.30 127 1 0.72702 0.03310 0.66496 0.7949
## 31.36 126 1 0.72125 0.03334 0.65879 0.7896
## 31.60 125 1 0.71548 0.03357 0.65263 0.7844
## 31.92 124 1 0.70971 0.03379 0.64649 0.7791
## 33.20 122 1 0.70390 0.03401 0.64030 0.7738
## 33.69 121 1 0.69808 0.03422 0.63413 0.7685
## 33.80 120 1 0.69226 0.03443 0.62797 0.7631
## 33.90 119 1 0.68644 0.03463 0.62183 0.7578
## 35.90 118 1 0.68063 0.03482 0.61570 0.7524
## 36.20 117 1 0.67481 0.03500 0.60958 0.7470
## 36.30 116 1 0.66899 0.03518 0.60347 0.7416
## 36.75 115 1 0.66318 0.03535 0.59738 0.7362
## 36.92 114 1 0.65736 0.03552 0.59130 0.7308
## 37.00 112 1 0.65149 0.03568 0.58518 0.7253
## 37.31 111 1 0.64562 0.03584 0.57906 0.7198
## 38.00 109 1 0.63970 0.03600 0.57289 0.7143
## 38.07 108 1 0.63377 0.03615 0.56674 0.7087
## 38.20 106 1 0.62779 0.03630 0.56053 0.7031
## 38.72 105 1 0.62182 0.03644 0.55434 0.6975
## 39.25 104 1 0.61584 0.03658 0.54816 0.6919
## 40.00 103 1 0.60986 0.03671 0.54199 0.6862
## 40.40 101 2 0.59778 0.03696 0.52955 0.6748
## 42.00 99 1 0.59174 0.03708 0.52336 0.6691
## 42.90 98 1 0.58570 0.03719 0.51717 0.6633
## 43.79 97 1 0.57967 0.03729 0.51100 0.6576
## 43.90 96 1 0.57363 0.03739 0.50483 0.6518
## 44.20 95 1 0.56759 0.03748 0.49869 0.6460
## 44.40 94 1 0.56155 0.03756 0.49255 0.6402
## 44.67 93 1 0.55551 0.03764 0.48642 0.6344
## 44.74 92 1 0.54948 0.03771 0.48031 0.6286
## 44.80 91 1 0.54344 0.03778 0.47421 0.6228
## 44.97 90 1 0.53740 0.03784 0.46812 0.6169
## 45.30 89 1 0.53136 0.03789 0.46205 0.6111
## 45.40 88 1 0.52532 0.03794 0.45598 0.6052
## 46.71 87 1 0.51928 0.03798 0.44993 0.5993
## 47.40 86 1 0.51325 0.03802 0.44389 0.5934
## 47.70 85 1 0.50721 0.03805 0.43786 0.5875
## 47.86 84 1 0.50117 0.03807 0.43184 0.5816
## 49.11 83 1 0.49513 0.03809 0.42584 0.5757
## 49.60 82 1 0.48909 0.03810 0.41984 0.5698
## 49.84 81 1 0.48306 0.03810 0.41386 0.5638
## 50.43 80 1 0.47702 0.03810 0.40789 0.5579
## 50.59 79 1 0.47098 0.03810 0.40193 0.5519
## 50.90 78 1 0.46494 0.03808 0.39598 0.5459
## 52.10 77 1 0.45890 0.03806 0.39005 0.5399
## 52.14 76 1 0.45286 0.03804 0.38412 0.5339
## 52.24 75 1 0.44683 0.03801 0.37821 0.5279
## 52.50 74 1 0.44079 0.03797 0.37231 0.5219
## 52.80 73 1 0.43475 0.03793 0.36642 0.5158
## 52.86 72 1 0.42871 0.03788 0.36054 0.5098
## 54.40 71 1 0.42267 0.03782 0.35468 0.5037
## 54.90 70 1 0.41664 0.03776 0.34882 0.4976
## 55.13 69 1 0.41060 0.03769 0.34298 0.4915
## 55.33 68 1 0.40456 0.03762 0.33715 0.4854
## 55.70 67 1 0.39852 0.03754 0.33134 0.4793
## 55.90 66 1 0.39248 0.03745 0.32553 0.4732
## 55.92 65 1 0.38644 0.03736 0.31974 0.4671
## 56.30 64 1 0.38041 0.03726 0.31396 0.4609
## 56.50 63 1 0.37437 0.03716 0.30819 0.4548
## 56.80 62 1 0.36833 0.03705 0.30243 0.4486
## 57.00 61 1 0.36229 0.03693 0.29669 0.4424
## 57.79 60 1 0.35625 0.03680 0.29096 0.4362
## 57.80 59 1 0.35021 0.03667 0.28524 0.4300
## 58.02 58 1 0.34418 0.03653 0.27953 0.4238
## 58.40 57 1 0.33814 0.03639 0.27384 0.4175
## 58.45 56 1 0.33210 0.03623 0.26816 0.4113
## 59.07 55 1 0.32606 0.03607 0.26250 0.4050
## 59.20 54 1 0.32002 0.03591 0.25685 0.3987
## 59.34 53 1 0.31399 0.03573 0.25121 0.3925
## 59.50 52 2 0.30191 0.03537 0.23997 0.3798
## 59.53 50 1 0.29587 0.03517 0.23438 0.3735
## 59.60 49 1 0.28983 0.03497 0.22880 0.3671
## 59.96 48 1 0.28379 0.03476 0.22323 0.3608
## 61.40 47 1 0.27776 0.03454 0.21768 0.3544
## 63.25 46 1 0.27172 0.03431 0.21215 0.3480
## 64.10 45 1 0.26568 0.03407 0.20663 0.3416
## 64.33 44 1 0.25964 0.03383 0.20112 0.3352
## 64.37 43 1 0.25360 0.03358 0.19564 0.3287
## 64.50 42 1 0.24757 0.03332 0.19017 0.3223
## 64.93 41 1 0.24153 0.03305 0.18471 0.3158
## 65.55 40 1 0.23549 0.03277 0.17928 0.3093
## 65.88 39 1 0.22945 0.03248 0.17386 0.3028
## 67.19 38 1 0.22341 0.03218 0.16846 0.2963
## 67.82 37 1 0.21737 0.03187 0.16308 0.2897
## 68.10 36 1 0.21134 0.03155 0.15772 0.2832
## 68.51 35 1 0.20530 0.03123 0.15238 0.2766
## 68.70 34 1 0.19926 0.03089 0.14706 0.2700
## 69.10 33 1 0.19322 0.03053 0.14176 0.2634
## 70.65 32 1 0.18718 0.03017 0.13648 0.2567
## 70.80 31 1 0.18115 0.02980 0.13123 0.2501
## 72.09 30 1 0.17511 0.02941 0.12599 0.2434
## 74.20 28 1 0.16885 0.02902 0.12057 0.2365
## 74.53 27 1 0.16260 0.02861 0.11518 0.2295
## 76.04 26 1 0.15635 0.02818 0.10981 0.2226
## 76.07 25 1 0.15009 0.02774 0.10448 0.2156
## 79.13 24 1 0.14384 0.02728 0.09918 0.2086
## 80.25 22 1 0.13730 0.02681 0.09364 0.2013
## 80.80 21 1 0.13076 0.02632 0.08814 0.1940
## 82.29 20 1 0.12422 0.02580 0.08268 0.1866
## 83.60 19 1 0.11769 0.02526 0.07727 0.1792
## 83.73 18 1 0.11115 0.02469 0.07192 0.1718
## 84.13 17 1 0.10461 0.02409 0.06662 0.1643
## 84.70 16 1 0.09807 0.02345 0.06138 0.1567
## 84.90 15 1 0.09153 0.02278 0.05620 0.1491
## 85.28 14 1 0.08500 0.02207 0.05109 0.1414
## 86.43 13 1 0.07846 0.02132 0.04606 0.1336
## 88.99 12 1 0.07192 0.02052 0.04111 0.1258
## 89.62 11 1 0.06538 0.01967 0.03625 0.1179
## 95.07 9 1 0.05812 0.01878 0.03085 0.1095
## 99.51 8 1 0.05085 0.01778 0.02563 0.1009
## 106.94 7 1 0.04359 0.01666 0.02061 0.0922
## 109.21 6 1 0.03632 0.01538 0.01584 0.0833
## 110.79 5 1 0.02906 0.01392 0.01137 0.0743
## 112.33 4 1 0.02179 0.01219 0.00728 0.0652
## 119.21 3 1 0.01453 0.01006 0.00374 0.0564
## 122.72 2 1 0.00726 0.00719 0.00104 0.0505
## 142.55 1 1 0.00000 NaN NA NA
##
## clinical_data$adjXRT=Y
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 19.0 17 1 0.941 0.0571 0.8357 1.000
## 25.6 13 1 0.869 0.0873 0.7135 1.000
## 47.8 7 1 0.745 0.1371 0.5191 1.000
## 64.9 6 1 0.621 0.1609 0.3733 1.000
## 74.4 5 1 0.496 0.1700 0.2538 0.971
## 85.6 4 1 0.372 0.1667 0.1548 0.896
## 105.2 2 1 0.186 0.1558 0.0361 0.960
## 118.6 1 1 0.000 NaN NA NAautoplot(kmsurvival1_adjXRT,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Fleming-Harrington non-parametric analysis
fhsurvival1_adjXRT <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$adjXRT, type="fleming-harrington")
summary(fhsurvival1_adjXRT)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$adjXRT, type = "fleming-harrington")
##
## clinical_data$adjXRT=N
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 204 1 0.99511 0.00489 0.98557 1.0000
## 1.80 202 1 0.99020 0.00692 0.97673 1.0000
## 2.26 201 1 0.98528 0.00846 0.96885 1.0000
## 3.64 199 1 0.98034 0.00976 0.96141 0.9997
## 4.10 198 1 0.97540 0.01089 0.95429 0.9970
## 4.24 197 1 0.97047 0.01191 0.94740 0.9941
## 5.20 194 1 0.96548 0.01285 0.94061 0.9910
## 5.22 193 1 0.96049 0.01373 0.93395 0.9878
## 10.20 186 1 0.95534 0.01459 0.92716 0.9844
## 11.60 184 1 0.95016 0.01541 0.92043 0.9808
## 12.10 183 1 0.94498 0.01618 0.91380 0.9772
## 13.50 182 1 0.93980 0.01690 0.90725 0.9735
## 14.40 178 1 0.93454 0.01761 0.90065 0.9697
## 15.00 175 1 0.92921 0.01830 0.89402 0.9658
## 15.05 174 1 0.92389 0.01896 0.88746 0.9618
## 15.71 172 1 0.91853 0.01960 0.88091 0.9578
## 16.47 170 1 0.91314 0.02021 0.87437 0.9536
## 16.90 169 1 0.90776 0.02080 0.86788 0.9495
## 17.95 168 1 0.90237 0.02137 0.86144 0.9452
## 18.18 166 1 0.89695 0.02192 0.85500 0.9410
## 18.70 165 1 0.89153 0.02245 0.84859 0.9366
## 18.80 164 1 0.88611 0.02297 0.84222 0.9323
## 19.75 161 1 0.88062 0.02347 0.83580 0.9279
## 19.98 160 1 0.87514 0.02396 0.82941 0.9234
## 20.02 159 1 0.86965 0.02444 0.82305 0.9189
## 20.44 158 1 0.86416 0.02490 0.81672 0.9144
## 22.02 155 1 0.85861 0.02535 0.81033 0.9098
## 22.25 154 1 0.85305 0.02579 0.80396 0.9051
## 22.80 153 1 0.84749 0.02622 0.79763 0.9005
## 23.96 151 1 0.84190 0.02664 0.79127 0.8958
## 24.00 150 1 0.83630 0.02705 0.78493 0.8910
## 24.19 148 1 0.83067 0.02745 0.77857 0.8863
## 24.20 147 1 0.82504 0.02784 0.77224 0.8815
## 25.24 145 1 0.81937 0.02823 0.76588 0.8766
## 26.26 144 1 0.81370 0.02860 0.75954 0.8717
## 26.53 143 1 0.80803 0.02896 0.75322 0.8668
## 26.66 142 1 0.80236 0.02931 0.74692 0.8619
## 26.82 141 1 0.79669 0.02965 0.74064 0.8570
## 26.92 140 1 0.79102 0.02998 0.73439 0.8520
## 27.15 138 1 0.78531 0.03031 0.72810 0.8470
## 28.50 136 1 0.77955 0.03063 0.72177 0.8420
## 28.63 135 1 0.77380 0.03094 0.71547 0.8369
## 28.86 134 1 0.76805 0.03125 0.70918 0.8318
## 28.96 133 1 0.76229 0.03154 0.70291 0.8267
## 29.22 132 1 0.75654 0.03183 0.69666 0.8216
## 29.60 131 1 0.75079 0.03211 0.69043 0.8164
## 30.00 130 1 0.74504 0.03238 0.68421 0.8113
## 30.90 129 1 0.73928 0.03264 0.67800 0.8061
## 31.06 128 1 0.73353 0.03289 0.67182 0.8009
## 31.30 127 1 0.72778 0.03314 0.66565 0.7957
## 31.36 126 1 0.72202 0.03337 0.65949 0.7905
## 31.60 125 1 0.71627 0.03360 0.65335 0.7853
## 31.92 124 1 0.71052 0.03383 0.64722 0.7800
## 33.20 122 1 0.70472 0.03405 0.64105 0.7747
## 33.69 121 1 0.69892 0.03426 0.63489 0.7694
## 33.80 120 1 0.69312 0.03447 0.62875 0.7641
## 33.90 119 1 0.68732 0.03467 0.62262 0.7587
## 35.90 118 1 0.68152 0.03486 0.61650 0.7534
## 36.20 117 1 0.67572 0.03505 0.61040 0.7480
## 36.30 116 1 0.66992 0.03523 0.60431 0.7426
## 36.75 115 1 0.66412 0.03540 0.59823 0.7373
## 36.92 114 1 0.65832 0.03557 0.59217 0.7319
## 37.00 112 1 0.65246 0.03574 0.58605 0.7264
## 37.31 111 1 0.64661 0.03590 0.57995 0.7209
## 38.00 109 1 0.64071 0.03605 0.57380 0.7154
## 38.07 108 1 0.63480 0.03621 0.56766 0.7099
## 38.20 106 1 0.62884 0.03636 0.56147 0.7043
## 38.72 105 1 0.62288 0.03650 0.55529 0.6987
## 39.25 104 1 0.61692 0.03664 0.54912 0.6931
## 40.00 103 1 0.61096 0.03678 0.54297 0.6875
## 40.40 101 2 0.59898 0.03704 0.53062 0.6762
## 42.00 99 1 0.59296 0.03715 0.52443 0.6704
## 42.90 98 1 0.58694 0.03727 0.51826 0.6647
## 43.79 97 1 0.58092 0.03737 0.51210 0.6590
## 43.90 96 1 0.57490 0.03747 0.50596 0.6532
## 44.20 95 1 0.56888 0.03757 0.49982 0.6475
## 44.40 94 1 0.56286 0.03765 0.49370 0.6417
## 44.67 93 1 0.55684 0.03773 0.48759 0.6359
## 44.74 92 1 0.55082 0.03781 0.48149 0.6301
## 44.80 91 1 0.54480 0.03788 0.47540 0.6243
## 44.97 90 1 0.53878 0.03794 0.46933 0.6185
## 45.30 89 1 0.53276 0.03799 0.46327 0.6127
## 45.40 88 1 0.52674 0.03804 0.45722 0.6068
## 46.71 87 1 0.52072 0.03809 0.45118 0.6010
## 47.40 86 1 0.51470 0.03813 0.44515 0.5951
## 47.70 85 1 0.50868 0.03816 0.43913 0.5892
## 47.86 84 1 0.50266 0.03818 0.43313 0.5834
## 49.11 83 1 0.49664 0.03820 0.42714 0.5775
## 49.60 82 1 0.49062 0.03822 0.42116 0.5715
## 49.84 81 1 0.48460 0.03823 0.41519 0.5656
## 50.43 80 1 0.47858 0.03823 0.40923 0.5597
## 50.59 79 1 0.47256 0.03822 0.40328 0.5537
## 50.90 78 1 0.46654 0.03821 0.39735 0.5478
## 52.10 77 1 0.46052 0.03820 0.39143 0.5418
## 52.14 76 1 0.45450 0.03818 0.38551 0.5358
## 52.24 75 1 0.44848 0.03815 0.37961 0.5299
## 52.50 74 1 0.44246 0.03812 0.37373 0.5238
## 52.80 73 1 0.43644 0.03808 0.36785 0.5178
## 52.86 72 1 0.43043 0.03803 0.36198 0.5118
## 54.40 71 1 0.42441 0.03798 0.35613 0.5058
## 54.90 70 1 0.41839 0.03792 0.35029 0.4997
## 55.13 69 1 0.41237 0.03786 0.34446 0.4937
## 55.33 68 1 0.40635 0.03779 0.33864 0.4876
## 55.70 67 1 0.40033 0.03771 0.33284 0.4815
## 55.90 66 1 0.39431 0.03763 0.32704 0.4754
## 55.92 65 1 0.38829 0.03754 0.32126 0.4693
## 56.30 64 1 0.38227 0.03744 0.31549 0.4632
## 56.50 63 1 0.37625 0.03734 0.30973 0.4570
## 56.80 62 1 0.37023 0.03724 0.30399 0.4509
## 57.00 61 1 0.36421 0.03712 0.29826 0.4447
## 57.79 60 1 0.35819 0.03700 0.29254 0.4386
## 57.80 59 1 0.35217 0.03687 0.28683 0.4324
## 58.02 58 1 0.34615 0.03674 0.28113 0.4262
## 58.40 57 1 0.34013 0.03660 0.27545 0.4200
## 58.45 56 1 0.33411 0.03645 0.26978 0.4138
## 59.07 55 1 0.32809 0.03630 0.26413 0.4075
## 59.20 54 1 0.32207 0.03614 0.25849 0.4013
## 59.34 53 1 0.31605 0.03597 0.25286 0.3950
## 59.50 52 2 0.30412 0.03563 0.24173 0.3826
## 59.53 50 1 0.29810 0.03544 0.23615 0.3763
## 59.60 49 1 0.29208 0.03524 0.23057 0.3700
## 59.96 48 1 0.28606 0.03503 0.22501 0.3637
## 61.40 47 1 0.28004 0.03482 0.21947 0.3573
## 63.25 46 1 0.27401 0.03460 0.21394 0.3510
## 64.10 45 1 0.26799 0.03437 0.20843 0.3446
## 64.33 44 1 0.26197 0.03413 0.20293 0.3382
## 64.37 43 1 0.25595 0.03389 0.19744 0.3318
## 64.50 42 1 0.24993 0.03364 0.19198 0.3254
## 64.93 41 1 0.24390 0.03337 0.18653 0.3189
## 65.55 40 1 0.23788 0.03310 0.18110 0.3125
## 65.88 39 1 0.23186 0.03282 0.17568 0.3060
## 67.19 38 1 0.22584 0.03253 0.17029 0.2995
## 67.82 37 1 0.21982 0.03223 0.16491 0.2930
## 68.10 36 1 0.21379 0.03192 0.15955 0.2865
## 68.51 35 1 0.20777 0.03160 0.15421 0.2799
## 68.70 34 1 0.20175 0.03127 0.14889 0.2734
## 69.10 33 1 0.19573 0.03093 0.14360 0.2668
## 70.65 32 1 0.18971 0.03058 0.13832 0.2602
## 70.80 31 1 0.18368 0.03021 0.13306 0.2536
## 72.09 30 1 0.17766 0.02984 0.12783 0.2469
## 74.20 28 1 0.17143 0.02946 0.12241 0.2401
## 74.53 27 1 0.16520 0.02906 0.11702 0.2332
## 76.04 26 1 0.15896 0.02865 0.11165 0.2263
## 76.07 25 1 0.15273 0.02823 0.10632 0.2194
## 79.13 24 1 0.14650 0.02778 0.10102 0.2125
## 80.25 22 1 0.13999 0.02734 0.09547 0.2053
## 80.80 21 1 0.13348 0.02687 0.08997 0.1980
## 82.29 20 1 0.12697 0.02637 0.08451 0.1908
## 83.60 19 1 0.12046 0.02585 0.07909 0.1835
## 83.73 18 1 0.11395 0.02531 0.07373 0.1761
## 84.13 17 1 0.10744 0.02474 0.06842 0.1687
## 84.70 16 1 0.10093 0.02413 0.06316 0.1613
## 84.90 15 1 0.09442 0.02350 0.05797 0.1538
## 85.28 14 1 0.08791 0.02283 0.05284 0.1462
## 86.43 13 1 0.08140 0.02212 0.04779 0.1387
## 88.99 12 1 0.07489 0.02137 0.04281 0.1310
## 89.62 11 1 0.06839 0.02057 0.03792 0.1233
## 95.07 9 1 0.06119 0.01977 0.03248 0.1153
## 99.51 8 1 0.05400 0.01888 0.02721 0.1072
## 106.94 7 1 0.04681 0.01789 0.02213 0.0990
## 109.21 6 1 0.03963 0.01678 0.01728 0.0909
## 110.79 5 1 0.03244 0.01554 0.01269 0.0830
## 112.33 4 1 0.02527 0.01413 0.00844 0.0756
## 119.21 3 1 0.01811 0.01254 0.00466 0.0703
## 122.72 2 1 0.01098 0.01087 0.00158 0.0764
## 142.55 1 1 0.00404 Inf 0.00000 1.0000
##
## clinical_data$adjXRT=Y
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 19.0 17 1 0.9429 0.0572 0.837 1.000
## 25.6 13 1 0.8731 0.0877 0.717 1.000
## 47.8 7 1 0.7568 0.1393 0.528 1.000
## 64.9 6 1 0.6407 0.1661 0.385 1.000
## 74.4 5 1 0.5245 0.1796 0.268 1.000
## 85.6 4 1 0.4085 0.1829 0.170 0.983
## 105.2 2 1 0.2478 0.2074 0.048 1.000
## 118.6 1 1 0.0911 Inf 0.000 1.000autoplot(fhsurvival1_adjXRT,
censor.shape = '*', facets = TRUE, ncol = 2,xlab="Time", ylab="Survival Probability")
Adjuvant Chemotherapy Analysis
Also the chemo therapy helps but not as much as radiation therapy.
Kaplan-Meier non-parametric analysis
kmsurvival1_adjCTX <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$adjCTX)
summary(kmsurvival1_adjCTX)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$adjCTX)
##
## clinical_data$adjCTX=N
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 139 1 0.9928 0.00717 0.97886 1.0000
## 1.80 138 1 0.9856 0.01010 0.96601 1.0000
## 2.26 137 1 0.9784 0.01233 0.95456 1.0000
## 3.64 135 1 0.9712 0.01421 0.94372 0.9994
## 4.10 134 1 0.9639 0.01584 0.93337 0.9955
## 5.20 131 1 0.9566 0.01735 0.92316 0.9912
## 11.60 127 1 0.9490 0.01877 0.91294 0.9865
## 12.10 125 1 0.9414 0.02010 0.90286 0.9817
## 13.50 124 1 0.9338 0.02132 0.89298 0.9766
## 14.40 120 1 0.9261 0.02252 0.88296 0.9713
## 15.00 118 1 0.9182 0.02366 0.87300 0.9658
## 15.05 117 1 0.9104 0.02472 0.86318 0.9601
## 15.71 116 1 0.9025 0.02573 0.85348 0.9544
## 16.47 114 1 0.8946 0.02669 0.84379 0.9485
## 16.90 113 1 0.8867 0.02760 0.83420 0.9425
## 18.18 111 1 0.8787 0.02849 0.82460 0.9363
## 18.80 110 1 0.8707 0.02933 0.81509 0.9301
## 19.75 107 1 0.8626 0.03016 0.80544 0.9238
## 20.02 106 1 0.8544 0.03095 0.79587 0.9173
## 22.80 105 1 0.8463 0.03171 0.78637 0.9108
## 23.96 103 1 0.8381 0.03245 0.77683 0.9042
## 24.19 102 1 0.8299 0.03316 0.76736 0.8975
## 24.20 101 1 0.8216 0.03383 0.75795 0.8907
## 25.24 100 1 0.8134 0.03448 0.74859 0.8839
## 26.26 99 1 0.8052 0.03509 0.73929 0.8770
## 26.53 98 1 0.7970 0.03568 0.73004 0.8701
## 26.66 97 1 0.7888 0.03625 0.72084 0.8631
## 26.82 96 1 0.7806 0.03679 0.71169 0.8561
## 27.15 94 1 0.7723 0.03733 0.70247 0.8490
## 28.50 92 1 0.7639 0.03785 0.69317 0.8418
## 28.63 91 1 0.7555 0.03835 0.68392 0.8345
## 28.86 90 1 0.7471 0.03884 0.67471 0.8272
## 29.22 89 1 0.7387 0.03930 0.66555 0.8199
## 29.60 88 1 0.7303 0.03974 0.65642 0.8125
## 30.00 87 1 0.7219 0.04016 0.64733 0.8051
## 31.06 86 1 0.7135 0.04056 0.63828 0.7976
## 31.30 85 1 0.7051 0.04094 0.62927 0.7901
## 31.36 84 1 0.6967 0.04130 0.62029 0.7826
## 33.20 82 1 0.6882 0.04167 0.61122 0.7749
## 33.69 81 1 0.6797 0.04201 0.60218 0.7673
## 33.80 80 1 0.6712 0.04233 0.59318 0.7595
## 33.90 79 1 0.6627 0.04264 0.58421 0.7518
## 35.90 78 1 0.6542 0.04293 0.57527 0.7440
## 36.20 77 1 0.6457 0.04321 0.56637 0.7362
## 36.30 76 1 0.6372 0.04347 0.55750 0.7284
## 37.00 74 1 0.6286 0.04372 0.54851 0.7204
## 37.31 73 1 0.6200 0.04397 0.53957 0.7125
## 38.00 72 1 0.6114 0.04419 0.53065 0.7045
## 38.20 70 1 0.6027 0.04441 0.52162 0.6963
## 40.00 69 1 0.5939 0.04462 0.51262 0.6882
## 40.40 68 1 0.5852 0.04481 0.50365 0.6800
## 42.00 67 1 0.5765 0.04499 0.49471 0.6717
## 42.90 66 1 0.5677 0.04514 0.48580 0.6635
## 43.79 65 1 0.5590 0.04529 0.47693 0.6552
## 43.90 64 1 0.5503 0.04541 0.46808 0.6469
## 44.20 63 1 0.5415 0.04552 0.45927 0.6385
## 44.40 62 1 0.5328 0.04562 0.45048 0.6302
## 44.67 61 1 0.5241 0.04570 0.44173 0.6217
## 44.80 60 1 0.5153 0.04577 0.43300 0.6133
## 44.97 59 1 0.5066 0.04582 0.42430 0.6048
## 45.30 58 1 0.4979 0.04585 0.41564 0.5963
## 45.40 57 1 0.4891 0.04587 0.40700 0.5878
## 47.70 56 1 0.4804 0.04588 0.39839 0.5793
## 49.84 55 1 0.4717 0.04587 0.38981 0.5707
## 50.90 54 1 0.4629 0.04584 0.38126 0.5621
## 52.10 53 1 0.4542 0.04580 0.37273 0.5534
## 52.14 52 1 0.4455 0.04575 0.36424 0.5448
## 52.24 51 1 0.4367 0.04567 0.35578 0.5361
## 52.50 50 1 0.4280 0.04559 0.34734 0.5273
## 52.80 49 1 0.4192 0.04549 0.33894 0.5186
## 54.40 48 1 0.4105 0.04537 0.33056 0.5098
## 54.90 47 1 0.4018 0.04524 0.32222 0.5010
## 55.13 46 1 0.3930 0.04509 0.31390 0.4921
## 55.33 45 1 0.3843 0.04493 0.30562 0.4833
## 55.70 44 1 0.3756 0.04475 0.29736 0.4744
## 55.90 43 1 0.3668 0.04455 0.28914 0.4654
## 55.92 42 1 0.3581 0.04434 0.28095 0.4565
## 56.30 41 1 0.3494 0.04411 0.27279 0.4475
## 56.50 40 1 0.3406 0.04386 0.26466 0.4384
## 56.80 39 1 0.3319 0.04360 0.25657 0.4294
## 57.00 38 1 0.3232 0.04332 0.24851 0.4203
## 57.79 37 1 0.3144 0.04302 0.24048 0.4111
## 58.02 36 1 0.3057 0.04270 0.23249 0.4020
## 58.45 35 1 0.2970 0.04236 0.22453 0.3928
## 59.50 34 2 0.2795 0.04163 0.20873 0.3743
## 59.60 32 1 0.2708 0.04124 0.20089 0.3650
## 59.96 31 1 0.2620 0.04082 0.19308 0.3556
## 61.40 30 1 0.2533 0.04039 0.18532 0.3462
## 64.10 29 1 0.2446 0.03993 0.17759 0.3368
## 64.37 28 1 0.2358 0.03944 0.16991 0.3273
## 64.50 27 1 0.2271 0.03894 0.16228 0.3178
## 65.88 26 1 0.2184 0.03841 0.15469 0.3082
## 67.19 25 1 0.2096 0.03785 0.14714 0.2986
## 67.82 24 1 0.2009 0.03727 0.13965 0.2890
## 68.51 23 1 0.1922 0.03666 0.13221 0.2793
## 70.65 22 1 0.1834 0.03602 0.12483 0.2695
## 74.53 21 1 0.1747 0.03534 0.11750 0.2597
## 76.04 20 1 0.1660 0.03464 0.11023 0.2498
## 76.07 19 1 0.1572 0.03390 0.10303 0.2399
## 80.25 17 1 0.1480 0.03314 0.09539 0.2295
## 80.80 16 1 0.1387 0.03234 0.08785 0.2191
## 82.29 15 1 0.1295 0.03148 0.08040 0.2085
## 83.60 14 1 0.1202 0.03056 0.07306 0.1978
## 83.73 13 1 0.1110 0.02957 0.06583 0.1871
## 84.13 12 1 0.1017 0.02852 0.05873 0.1762
## 84.90 11 1 0.0925 0.02738 0.05176 0.1652
## 85.28 10 1 0.0832 0.02616 0.04495 0.1541
## 86.43 9 1 0.0740 0.02483 0.03832 0.1428
## 106.94 7 1 0.0634 0.02343 0.03074 0.1308
## 109.21 6 1 0.0528 0.02178 0.02356 0.1185
## 110.79 5 1 0.0423 0.01982 0.01687 0.1060
## 112.33 4 1 0.0317 0.01746 0.01078 0.0933
## 119.21 3 1 0.0211 0.01449 0.00552 0.0810
## 122.72 2 1 0.0106 0.01041 0.00153 0.0728
## 142.55 1 1 0.0000 NaN NA NA
##
## clinical_data$adjCTX=Y
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 4.24 86 1 0.9884 0.0116 0.9660 1.000
## 5.22 85 1 0.9767 0.0163 0.9454 1.000
## 10.20 78 1 0.9642 0.0203 0.9252 1.000
## 17.95 73 1 0.9510 0.0239 0.9052 0.999
## 18.70 72 1 0.9378 0.0270 0.8863 0.992
## 18.96 71 1 0.9246 0.0297 0.8682 0.985
## 19.98 70 1 0.9114 0.0321 0.8507 0.976
## 20.44 69 1 0.8982 0.0342 0.8336 0.968
## 22.02 66 1 0.8846 0.0363 0.8162 0.959
## 22.25 65 1 0.8710 0.0382 0.7992 0.949
## 24.00 62 1 0.8569 0.0401 0.7818 0.939
## 25.61 58 1 0.8421 0.0420 0.7637 0.929
## 26.92 57 1 0.8274 0.0438 0.7458 0.918
## 28.96 54 1 0.8120 0.0456 0.7274 0.907
## 30.90 52 1 0.7964 0.0473 0.7089 0.895
## 31.60 51 1 0.7808 0.0489 0.6906 0.883
## 31.92 50 1 0.7652 0.0504 0.6726 0.871
## 36.75 48 1 0.7493 0.0518 0.6544 0.858
## 36.92 47 1 0.7333 0.0531 0.6363 0.845
## 38.07 45 1 0.7170 0.0543 0.6181 0.832
## 38.72 44 1 0.7007 0.0555 0.6000 0.818
## 39.25 43 1 0.6844 0.0565 0.5821 0.805
## 40.40 41 1 0.6677 0.0576 0.5639 0.791
## 44.74 39 1 0.6506 0.0586 0.5453 0.776
## 46.71 38 1 0.6335 0.0595 0.5270 0.762
## 47.40 37 1 0.6164 0.0603 0.5088 0.747
## 47.80 36 1 0.5992 0.0610 0.4908 0.732
## 47.86 35 1 0.5821 0.0616 0.4731 0.716
## 49.11 34 1 0.5650 0.0621 0.4554 0.701
## 49.60 33 1 0.5479 0.0626 0.4380 0.685
## 50.43 32 1 0.5308 0.0629 0.4207 0.670
## 50.59 31 1 0.5136 0.0632 0.4036 0.654
## 52.86 30 1 0.4965 0.0633 0.3867 0.638
## 57.80 29 1 0.4794 0.0634 0.3699 0.621
## 58.40 28 1 0.4623 0.0634 0.3533 0.605
## 59.07 27 1 0.4452 0.0634 0.3368 0.588
## 59.20 26 1 0.4280 0.0632 0.3205 0.572
## 59.34 25 1 0.4109 0.0629 0.3044 0.555
## 59.53 24 1 0.3938 0.0626 0.2884 0.538
## 63.25 23 1 0.3767 0.0622 0.2726 0.521
## 64.33 22 1 0.3595 0.0617 0.2569 0.503
## 64.86 21 1 0.3424 0.0611 0.2414 0.486
## 64.93 20 1 0.3253 0.0604 0.2261 0.468
## 65.55 19 1 0.3082 0.0596 0.2110 0.450
## 68.10 18 1 0.2911 0.0587 0.1961 0.432
## 68.70 17 1 0.2739 0.0577 0.1813 0.414
## 69.10 16 1 0.2568 0.0565 0.1668 0.395
## 70.80 15 1 0.2397 0.0553 0.1525 0.377
## 72.09 14 1 0.2226 0.0539 0.1384 0.358
## 74.20 12 1 0.2040 0.0525 0.1232 0.338
## 74.36 11 1 0.1855 0.0509 0.1083 0.318
## 79.13 10 1 0.1669 0.0491 0.0938 0.297
## 84.70 9 1 0.1484 0.0470 0.0797 0.276
## 85.61 8 1 0.1298 0.0446 0.0662 0.255
## 88.99 6 1 0.1082 0.0421 0.0504 0.232
## 89.62 5 1 0.0866 0.0389 0.0359 0.209
## 95.07 4 1 0.0649 0.0347 0.0228 0.185
## 99.51 3 1 0.0433 0.0291 0.0116 0.162
## 105.17 2 1 0.0216 0.0211 0.0032 0.146
## 118.58 1 1 0.0000 NaN NA NAautoplot(kmsurvival1_adjCTX,
censor.shape = '*', facets = TRUE, ncol = 2,xlab="Time", ylab="Survival Probability")
Fleming-Harrington non-parametric analysis
fhsurvival1_adjCTX <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$adjCTX, type="fleming-harrington")
summary(fhsurvival1_adjCTX)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$adjCTX, type = "fleming-harrington")
##
## clinical_data$adjCTX=N
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 139 1 0.99283 0.00717 0.97888 1.000
## 1.80 138 1 0.98566 0.01010 0.96606 1.000
## 2.26 137 1 0.97849 0.01233 0.95463 1.000
## 3.64 135 1 0.97127 0.01421 0.94382 1.000
## 4.10 134 1 0.96405 0.01584 0.93349 0.996
## 5.20 131 1 0.95672 0.01735 0.92332 0.991
## 11.60 127 1 0.94922 0.01878 0.91312 0.987
## 12.10 125 1 0.94165 0.02010 0.90306 0.982
## 13.50 124 1 0.93409 0.02133 0.89321 0.977
## 14.40 120 1 0.92634 0.02253 0.88322 0.972
## 15.00 118 1 0.91852 0.02367 0.87329 0.966
## 15.05 117 1 0.91070 0.02473 0.86350 0.960
## 15.71 116 1 0.90289 0.02574 0.85383 0.955
## 16.47 114 1 0.89500 0.02670 0.84417 0.949
## 16.90 113 1 0.88712 0.02762 0.83461 0.943
## 18.18 111 1 0.87916 0.02850 0.82504 0.937
## 18.80 110 1 0.87120 0.02934 0.81555 0.931
## 19.75 107 1 0.86310 0.03018 0.80593 0.924
## 20.02 106 1 0.85500 0.03097 0.79639 0.918
## 22.80 105 1 0.84689 0.03173 0.78692 0.911
## 23.96 103 1 0.83871 0.03247 0.77742 0.905
## 24.19 102 1 0.83053 0.03318 0.76797 0.898
## 24.20 101 1 0.82234 0.03386 0.75859 0.891
## 25.24 100 1 0.81416 0.03451 0.74926 0.885
## 26.26 99 1 0.80598 0.03513 0.73999 0.878
## 26.53 98 1 0.79780 0.03572 0.73077 0.871
## 26.66 97 1 0.78961 0.03629 0.72160 0.864
## 26.82 96 1 0.78143 0.03683 0.71248 0.857
## 27.15 94 1 0.77316 0.03737 0.70328 0.850
## 28.50 92 1 0.76480 0.03790 0.69402 0.843
## 28.63 91 1 0.75645 0.03840 0.68480 0.836
## 28.86 90 1 0.74809 0.03889 0.67562 0.828
## 29.22 89 1 0.73973 0.03935 0.66648 0.821
## 29.60 88 1 0.73137 0.03980 0.65739 0.814
## 30.00 87 1 0.72301 0.04022 0.64833 0.806
## 31.06 86 1 0.71465 0.04062 0.63931 0.799
## 31.30 85 1 0.70630 0.04101 0.63032 0.791
## 31.36 84 1 0.69794 0.04138 0.62137 0.784
## 33.20 82 1 0.68948 0.04174 0.61233 0.776
## 33.69 81 1 0.68102 0.04209 0.60333 0.769
## 33.80 80 1 0.67256 0.04242 0.59435 0.761
## 33.90 79 1 0.66410 0.04273 0.58541 0.753
## 35.90 78 1 0.65564 0.04303 0.57651 0.746
## 36.20 77 1 0.64718 0.04330 0.56763 0.738
## 36.30 76 1 0.63872 0.04357 0.55879 0.730
## 37.00 74 1 0.63015 0.04383 0.54984 0.722
## 37.31 73 1 0.62157 0.04408 0.54092 0.714
## 38.00 72 1 0.61300 0.04431 0.53203 0.706
## 38.20 70 1 0.60430 0.04453 0.52303 0.698
## 40.00 69 1 0.59561 0.04475 0.51406 0.690
## 40.40 68 1 0.58691 0.04494 0.50512 0.682
## 42.00 67 1 0.57822 0.04512 0.49621 0.674
## 42.90 66 1 0.56952 0.04529 0.48734 0.666
## 43.79 65 1 0.56083 0.04543 0.47849 0.657
## 43.90 64 1 0.55213 0.04557 0.46967 0.649
## 44.20 63 1 0.54344 0.04568 0.46089 0.641
## 44.40 62 1 0.53475 0.04579 0.45213 0.632
## 44.67 61 1 0.52605 0.04587 0.44340 0.624
## 44.80 60 1 0.51736 0.04595 0.43470 0.616
## 44.97 59 1 0.50866 0.04600 0.42603 0.607
## 45.30 58 1 0.49997 0.04605 0.41739 0.599
## 45.40 57 1 0.49127 0.04607 0.40878 0.590
## 47.70 56 1 0.48258 0.04609 0.40020 0.582
## 49.84 55 1 0.47388 0.04608 0.39165 0.573
## 50.90 54 1 0.46519 0.04607 0.38312 0.565
## 52.10 53 1 0.45649 0.04603 0.37463 0.556
## 52.14 52 1 0.44780 0.04599 0.36616 0.548
## 52.24 51 1 0.43910 0.04592 0.35772 0.539
## 52.50 50 1 0.43041 0.04585 0.34931 0.530
## 52.80 49 1 0.42171 0.04575 0.34093 0.522
## 54.40 48 1 0.41302 0.04565 0.33258 0.513
## 54.90 47 1 0.40432 0.04552 0.32426 0.504
## 55.13 46 1 0.39563 0.04539 0.31596 0.495
## 55.33 45 1 0.38693 0.04523 0.30770 0.487
## 55.70 44 1 0.37824 0.04506 0.29947 0.478
## 55.90 43 1 0.36954 0.04488 0.29127 0.469
## 55.92 42 1 0.36085 0.04468 0.28310 0.460
## 56.30 41 1 0.35215 0.04446 0.27496 0.451
## 56.50 40 1 0.34346 0.04422 0.26685 0.442
## 56.80 39 1 0.33476 0.04397 0.25878 0.433
## 57.00 38 1 0.32607 0.04370 0.25074 0.424
## 57.79 37 1 0.31738 0.04342 0.24273 0.415
## 58.02 36 1 0.30868 0.04312 0.23476 0.406
## 58.45 35 1 0.29999 0.04279 0.22682 0.397
## 59.50 34 2 0.28285 0.04213 0.21123 0.379
## 59.60 32 1 0.27415 0.04175 0.20340 0.370
## 59.96 31 1 0.26544 0.04135 0.19560 0.360
## 61.40 30 1 0.25674 0.04093 0.18784 0.351
## 64.10 29 1 0.24804 0.04049 0.18012 0.342
## 64.37 28 1 0.23934 0.04003 0.17244 0.332
## 64.50 27 1 0.23064 0.03955 0.16481 0.323
## 65.88 26 1 0.22193 0.03904 0.15722 0.313
## 67.19 25 1 0.21323 0.03850 0.14968 0.304
## 67.82 24 1 0.20453 0.03794 0.14218 0.294
## 68.51 23 1 0.19583 0.03736 0.13474 0.285
## 70.65 22 1 0.18712 0.03674 0.12735 0.275
## 74.53 21 1 0.17842 0.03610 0.12001 0.265
## 76.04 20 1 0.16972 0.03543 0.11274 0.256
## 76.07 19 1 0.16102 0.03472 0.10552 0.246
## 80.25 17 1 0.15182 0.03401 0.09788 0.235
## 80.80 16 1 0.14262 0.03325 0.09032 0.225
## 82.29 15 1 0.13342 0.03244 0.08285 0.215
## 83.60 14 1 0.12423 0.03157 0.07549 0.204
## 83.73 13 1 0.11503 0.03065 0.06823 0.194
## 84.13 12 1 0.10583 0.02967 0.06110 0.183
## 84.90 11 1 0.09664 0.02861 0.05409 0.173
## 85.28 10 1 0.08744 0.02748 0.04723 0.162
## 86.43 9 1 0.07824 0.02626 0.04053 0.151
## 106.94 7 1 0.06783 0.02506 0.03288 0.140
## 109.21 6 1 0.05742 0.02366 0.02560 0.129
## 110.79 5 1 0.04701 0.02204 0.01875 0.118
## 112.33 4 1 0.03661 0.02016 0.01244 0.108
## 119.21 3 1 0.02623 0.01798 0.00685 0.101
## 122.72 2 1 0.01591 0.01567 0.00231 0.110
## 142.55 1 1 0.00585 Inf 0.00000 1.000
##
## clinical_data$adjCTX=Y
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 4.24 86 1 0.9884 0.0116 0.96604 1.000
## 5.22 85 1 0.9769 0.0163 0.94554 1.000
## 10.20 78 1 0.9644 0.0203 0.92544 1.000
## 17.95 73 1 0.9513 0.0239 0.90552 0.999
## 18.70 72 1 0.9382 0.0270 0.88671 0.993
## 18.96 71 1 0.9251 0.0297 0.86866 0.985
## 19.98 70 1 0.9119 0.0321 0.85119 0.977
## 20.44 69 1 0.8988 0.0342 0.83417 0.968
## 22.02 66 1 0.8853 0.0363 0.81690 0.959
## 22.25 65 1 0.8718 0.0382 0.79998 0.950
## 24.00 62 1 0.8578 0.0401 0.78269 0.940
## 25.61 58 1 0.8432 0.0421 0.76461 0.930
## 26.92 57 1 0.8285 0.0439 0.74684 0.919
## 28.96 54 1 0.8133 0.0457 0.72855 0.908
## 30.90 52 1 0.7978 0.0474 0.71012 0.896
## 31.60 51 1 0.7823 0.0490 0.69196 0.885
## 31.92 50 1 0.7668 0.0505 0.67405 0.872
## 36.75 48 1 0.7510 0.0519 0.65591 0.860
## 36.92 47 1 0.7352 0.0532 0.63800 0.847
## 38.07 45 1 0.7191 0.0545 0.61982 0.834
## 38.72 44 1 0.7029 0.0557 0.60186 0.821
## 39.25 43 1 0.6867 0.0567 0.58409 0.807
## 40.40 41 1 0.6702 0.0578 0.56600 0.794
## 44.74 39 1 0.6532 0.0588 0.54755 0.779
## 46.71 38 1 0.6363 0.0598 0.52930 0.765
## 47.40 37 1 0.6193 0.0606 0.51125 0.750
## 47.80 36 1 0.6023 0.0613 0.49338 0.735
## 47.86 35 1 0.5854 0.0620 0.47570 0.720
## 49.11 34 1 0.5684 0.0625 0.45819 0.705
## 49.60 33 1 0.5514 0.0630 0.44084 0.690
## 50.43 32 1 0.5345 0.0634 0.42367 0.674
## 50.59 31 1 0.5175 0.0636 0.40666 0.659
## 52.86 30 1 0.5005 0.0639 0.38980 0.643
## 57.80 29 1 0.4836 0.0640 0.37311 0.627
## 58.40 28 1 0.4666 0.0640 0.35657 0.611
## 59.07 27 1 0.4496 0.0640 0.34019 0.594
## 59.20 26 1 0.4327 0.0639 0.32397 0.578
## 59.34 25 1 0.4157 0.0637 0.30791 0.561
## 59.53 24 1 0.3987 0.0634 0.29200 0.545
## 63.25 23 1 0.3818 0.0630 0.27625 0.528
## 64.33 22 1 0.3648 0.0626 0.26067 0.511
## 64.86 21 1 0.3479 0.0620 0.24526 0.493
## 64.93 20 1 0.3309 0.0614 0.23001 0.476
## 65.55 19 1 0.3139 0.0607 0.21494 0.458
## 68.10 18 1 0.2970 0.0598 0.20005 0.441
## 68.70 17 1 0.2800 0.0589 0.18536 0.423
## 69.10 16 1 0.2630 0.0579 0.17085 0.405
## 70.80 15 1 0.2461 0.0568 0.15656 0.387
## 72.09 14 1 0.2291 0.0555 0.14249 0.368
## 74.20 12 1 0.2108 0.0543 0.12726 0.349
## 74.36 11 1 0.1925 0.0528 0.11237 0.330
## 79.13 10 1 0.1742 0.0512 0.09786 0.310
## 84.70 9 1 0.1558 0.0494 0.08375 0.290
## 85.61 8 1 0.1375 0.0473 0.07010 0.270
## 88.99 6 1 0.1164 0.0453 0.05428 0.250
## 89.62 5 1 0.0953 0.0428 0.03953 0.230
## 95.07 4 1 0.0742 0.0396 0.02608 0.211
## 99.51 3 1 0.0532 0.0357 0.01425 0.199
## 105.17 2 1 0.0323 0.0315 0.00477 0.218
## 118.58 1 1 0.0119 Inf 0.00000 1.000autoplot(fhsurvival1_adjCTX,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Age
- People older than 80 are collapsing so fast.
- People between 20 and 40 death rate are normal butwith a huge amount of events at each time
- People between 60 and 80 are the strongest group.
Create age groups
clinical_data$age_groups <- ifelse(clinical_data$age_diag >= 20 & clinical_data$age_diag < 40, "20-40",
ifelse(clinical_data$age_diag >= 40 & clinical_data$age_diag < 60, "40-60",
ifelse(clinical_data$age_diag >= 60 & clinical_data$age_diag < 80, "60-80", "> 80")))
## Convert it to factor
clinical_data$age_groups <- factor(clinical_data$age_groups)
## Perform the estimations using Kaplan-Meier non-parametric
kmsurvival1_age <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$age_groups)
summary(kmsurvival1_age)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$age_groups)
##
## clinical_data$age_groups=> 80
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 4.1 28 1 0.9643 0.0351 0.89794 1.000
## 12.1 26 1 0.9272 0.0496 0.83491 1.000
## 13.5 25 1 0.8901 0.0599 0.78013 1.000
## 16.5 23 1 0.8514 0.0687 0.72693 0.997
## 20.0 20 1 0.8088 0.0773 0.67066 0.975
## 20.0 19 1 0.7663 0.0841 0.61788 0.950
## 22.2 18 1 0.7237 0.0896 0.56777 0.922
## 24.2 17 1 0.6811 0.0939 0.51986 0.892
## 28.6 15 1 0.6357 0.0980 0.46994 0.860
## 28.9 14 1 0.5903 0.1010 0.42216 0.825
## 31.1 13 1 0.5449 0.1029 0.37632 0.789
## 37.0 12 1 0.4995 0.1039 0.33229 0.751
## 43.8 10 1 0.4495 0.1048 0.28465 0.710
## 54.9 9 1 0.3996 0.1044 0.23947 0.667
## 55.9 8 1 0.3496 0.1026 0.19672 0.621
## 56.3 7 1 0.2997 0.0994 0.15649 0.574
## 59.1 6 1 0.2497 0.0945 0.11894 0.524
## 64.1 5 1 0.1998 0.0878 0.08441 0.473
## 65.9 4 1 0.1498 0.0788 0.05346 0.420
## 70.7 3 1 0.0999 0.0665 0.02709 0.368
## 76.1 2 1 0.0499 0.0485 0.00744 0.335
## 80.2 1 1 0.0000 NaN NA NA
##
## clinical_data$age_groups=20-40
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 17.9 6 1 0.833 0.152 0.5827 1
## 47.8 4 1 0.625 0.213 0.3200 1
## 50.4 3 1 0.417 0.222 0.1468 1
## 59.5 2 1 0.208 0.184 0.0368 1
## 105.2 1 1 0.000 NaN NA NA
##
## clinical_data$age_groups=40-60
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 53 1 0.9811 0.0187 0.9452 1.000
## 2.26 52 1 0.9623 0.0262 0.9123 1.000
## 15.05 45 1 0.9409 0.0332 0.8780 1.000
## 18.70 43 1 0.9190 0.0390 0.8457 0.999
## 19.75 41 1 0.8966 0.0440 0.8144 0.987
## 23.96 38 1 0.8730 0.0488 0.7825 0.974
## 27.15 36 1 0.8487 0.0531 0.7508 0.959
## 28.96 33 1 0.8230 0.0574 0.7179 0.944
## 31.30 32 1 0.7973 0.0611 0.6861 0.926
## 31.60 31 1 0.7716 0.0643 0.6553 0.908
## 33.20 29 1 0.7450 0.0674 0.6240 0.889
## 39.25 27 1 0.7174 0.0703 0.5920 0.869
## 43.90 25 1 0.6887 0.0731 0.5593 0.848
## 44.20 24 1 0.6600 0.0755 0.5275 0.826
## 44.74 23 1 0.6313 0.0775 0.4964 0.803
## 44.97 22 1 0.6026 0.0791 0.4659 0.779
## 46.71 21 1 0.5739 0.0803 0.4362 0.755
## 47.40 20 1 0.5452 0.0813 0.4071 0.730
## 47.86 19 1 0.5165 0.0819 0.3785 0.705
## 57.79 18 1 0.4878 0.0822 0.3506 0.679
## 58.40 17 1 0.4591 0.0823 0.3232 0.652
## 59.20 16 1 0.4304 0.0820 0.2963 0.625
## 59.53 15 1 0.4017 0.0814 0.2701 0.598
## 64.50 14 1 0.3730 0.0805 0.2444 0.569
## 64.86 13 1 0.3443 0.0792 0.2194 0.541
## 69.10 12 1 0.3156 0.0776 0.1949 0.511
## 70.80 11 1 0.2870 0.0757 0.1711 0.481
## 72.09 10 1 0.2583 0.0734 0.1480 0.451
## 74.20 8 1 0.2260 0.0709 0.1221 0.418
## 74.36 7 1 0.1937 0.0678 0.0976 0.384
## 79.13 6 1 0.1614 0.0637 0.0745 0.350
## 89.62 5 1 0.1291 0.0586 0.0531 0.314
## 99.51 3 1 0.0861 0.0525 0.0260 0.285
## 110.79 2 1 0.0430 0.0402 0.0069 0.268
## 119.21 1 1 0.0000 NaN NA NA
##
## clinical_data$age_groups=60-80
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 1.80 135 1 0.9926 0.00738 0.97823 1.0000
## 3.64 134 1 0.9852 0.01040 0.96502 1.0000
## 4.24 133 1 0.9778 0.01269 0.95323 1.0000
## 5.20 131 1 0.9703 0.01462 0.94208 0.9994
## 5.22 130 1 0.9628 0.01630 0.93142 0.9953
## 10.20 125 1 0.9551 0.01790 0.92070 0.9909
## 11.60 123 1 0.9474 0.01937 0.91018 0.9861
## 14.40 120 1 0.9395 0.02075 0.89968 0.9811
## 15.00 118 1 0.9315 0.02205 0.88929 0.9758
## 15.71 116 1 0.9235 0.02328 0.87898 0.9703
## 16.90 115 1 0.9155 0.02442 0.86883 0.9646
## 18.18 114 1 0.9074 0.02549 0.85882 0.9588
## 18.80 113 1 0.8994 0.02650 0.84893 0.9529
## 18.96 112 1 0.8914 0.02745 0.83916 0.9468
## 20.44 111 1 0.8833 0.02836 0.82948 0.9407
## 22.02 110 1 0.8753 0.02921 0.81989 0.9345
## 22.80 107 1 0.8671 0.03006 0.81016 0.9281
## 24.00 105 1 0.8589 0.03089 0.80041 0.9216
## 24.19 103 1 0.8505 0.03170 0.79062 0.9150
## 25.24 101 1 0.8421 0.03248 0.78080 0.9082
## 25.61 100 1 0.8337 0.03323 0.77104 0.9014
## 26.26 99 1 0.8253 0.03395 0.76135 0.8946
## 26.53 98 1 0.8169 0.03463 0.75172 0.8876
## 26.66 97 1 0.8084 0.03528 0.74216 0.8806
## 26.82 96 1 0.8000 0.03590 0.73264 0.8736
## 26.92 95 1 0.7916 0.03650 0.72318 0.8665
## 28.50 93 1 0.7831 0.03709 0.71366 0.8592
## 29.22 92 1 0.7746 0.03765 0.70418 0.8520
## 29.60 91 1 0.7661 0.03818 0.69475 0.8447
## 30.00 90 1 0.7575 0.03870 0.68537 0.8373
## 30.90 89 1 0.7490 0.03919 0.67603 0.8299
## 31.36 88 1 0.7405 0.03966 0.66673 0.8225
## 31.92 87 1 0.7320 0.04010 0.65748 0.8150
## 33.69 86 1 0.7235 0.04053 0.64826 0.8075
## 33.80 85 1 0.7150 0.04094 0.63908 0.7999
## 33.90 84 1 0.7065 0.04133 0.62994 0.7923
## 35.90 83 1 0.6980 0.04169 0.62084 0.7847
## 36.20 82 1 0.6894 0.04205 0.61177 0.7770
## 36.30 81 1 0.6809 0.04238 0.60274 0.7693
## 36.75 80 1 0.6724 0.04270 0.59374 0.7615
## 36.92 79 1 0.6639 0.04300 0.58477 0.7538
## 37.31 77 1 0.6553 0.04329 0.57570 0.7459
## 38.00 75 1 0.6466 0.04359 0.56652 0.7379
## 38.07 74 1 0.6378 0.04387 0.55738 0.7299
## 38.20 73 1 0.6291 0.04413 0.54827 0.7218
## 38.72 72 1 0.6203 0.04437 0.53920 0.7137
## 40.00 71 1 0.6116 0.04460 0.53015 0.7056
## 40.40 70 2 0.5941 0.04500 0.51216 0.6892
## 42.00 67 1 0.5853 0.04520 0.50306 0.6809
## 42.90 66 1 0.5764 0.04537 0.49398 0.6726
## 44.40 65 1 0.5675 0.04553 0.48495 0.6642
## 44.67 64 1 0.5587 0.04568 0.47594 0.6558
## 44.80 63 1 0.5498 0.04580 0.46696 0.6473
## 45.30 62 1 0.5409 0.04592 0.45802 0.6388
## 45.40 61 1 0.5321 0.04601 0.44910 0.6303
## 47.70 60 1 0.5232 0.04609 0.44022 0.6218
## 49.11 59 1 0.5143 0.04616 0.43137 0.6132
## 49.60 58 1 0.5055 0.04620 0.42254 0.6046
## 49.84 57 1 0.4966 0.04624 0.41375 0.5960
## 50.59 56 1 0.4877 0.04625 0.40499 0.5873
## 50.90 55 1 0.4789 0.04625 0.39626 0.5787
## 52.10 54 1 0.4700 0.04624 0.38756 0.5699
## 52.14 53 1 0.4611 0.04621 0.37888 0.5612
## 52.24 52 1 0.4522 0.04616 0.37024 0.5524
## 52.50 51 1 0.4434 0.04610 0.36163 0.5436
## 52.80 50 1 0.4345 0.04603 0.35305 0.5348
## 52.86 49 1 0.4256 0.04593 0.34450 0.5259
## 54.40 48 1 0.4168 0.04582 0.33598 0.5170
## 55.13 47 1 0.4079 0.04570 0.32749 0.5081
## 55.33 46 1 0.3990 0.04556 0.31904 0.4991
## 55.70 45 1 0.3902 0.04540 0.31061 0.4901
## 55.92 44 1 0.3813 0.04523 0.30221 0.4811
## 56.50 43 1 0.3724 0.04504 0.29385 0.4720
## 56.80 42 1 0.3636 0.04483 0.28552 0.4630
## 57.00 41 1 0.3547 0.04460 0.27722 0.4538
## 57.80 40 1 0.3458 0.04436 0.26896 0.4447
## 58.02 39 1 0.3370 0.04410 0.26073 0.4355
## 58.45 38 1 0.3281 0.04382 0.25253 0.4263
## 59.34 37 1 0.3192 0.04353 0.24437 0.4170
## 59.50 36 1 0.3104 0.04321 0.23625 0.4077
## 59.60 35 1 0.3015 0.04288 0.22816 0.3984
## 59.96 34 1 0.2926 0.04252 0.22011 0.3891
## 61.40 33 1 0.2838 0.04215 0.21209 0.3797
## 63.25 32 1 0.2749 0.04175 0.20412 0.3702
## 64.33 31 1 0.2660 0.04134 0.19618 0.3607
## 64.37 30 1 0.2572 0.04090 0.18829 0.3512
## 64.93 29 1 0.2483 0.04044 0.18044 0.3417
## 65.55 28 1 0.2394 0.03996 0.17263 0.3321
## 67.19 27 1 0.2306 0.03945 0.16487 0.3224
## 67.82 26 1 0.2217 0.03891 0.15716 0.3127
## 68.10 25 1 0.2128 0.03835 0.14949 0.3030
## 68.51 24 1 0.2040 0.03777 0.14188 0.2932
## 68.70 23 1 0.1951 0.03715 0.13432 0.2834
## 74.53 22 1 0.1862 0.03651 0.12681 0.2735
## 76.04 21 1 0.1774 0.03583 0.11936 0.2635
## 80.80 19 1 0.1680 0.03514 0.11152 0.2531
## 82.29 18 1 0.1587 0.03440 0.10375 0.2427
## 83.60 17 1 0.1493 0.03362 0.09607 0.2322
## 83.73 16 1 0.1400 0.03279 0.08848 0.2216
## 84.13 15 1 0.1307 0.03191 0.08098 0.2109
## 84.70 14 1 0.1213 0.03096 0.07359 0.2001
## 84.90 13 1 0.1120 0.02995 0.06632 0.1892
## 85.28 12 1 0.1027 0.02888 0.05917 0.1782
## 85.61 11 1 0.0933 0.02772 0.05216 0.1671
## 86.43 9 1 0.0830 0.02651 0.04436 0.1552
## 88.99 8 1 0.0726 0.02514 0.03683 0.1431
## 95.07 7 1 0.0622 0.02359 0.02960 0.1308
## 106.94 6 1 0.0519 0.02182 0.02273 0.1183
## 109.21 5 1 0.0415 0.01977 0.01630 0.1056
## 112.33 4 1 0.0311 0.01734 0.01044 0.0927
## 118.58 3 1 0.0207 0.01433 0.00536 0.0803
## 122.72 2 1 0.0104 0.01025 0.00149 0.0720
## 142.55 1 1 0.0000 NaN NA NAautoplot(kmsurvival1_age,
censor.shape = '*', facets = TRUE, ncol = 2,xlab="Time", ylab="Survival Probability")
Fleming-Harrington non-parametric analysis
fhsurvival1_age <- survfit(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~ clinical_data$age_groups, type="fleming-harrington")
summary(fhsurvival1_age)## Call: survfit(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## clinical_data$age_groups, type = "fleming-harrington")
##
## clinical_data$age_groups=> 80
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 4.1 28 1 0.9649 0.0351 0.8985 1.000
## 12.1 26 1 0.9285 0.0497 0.8361 1.000
## 13.5 25 1 0.8921 0.0600 0.7819 1.000
## 16.5 23 1 0.8541 0.0689 0.7293 1.000
## 20.0 20 1 0.8125 0.0777 0.6737 0.980
## 20.0 19 1 0.7708 0.0847 0.6216 0.956
## 22.2 18 1 0.7292 0.0903 0.5721 0.929
## 24.2 17 1 0.6875 0.0948 0.5247 0.901
## 28.6 15 1 0.6432 0.0992 0.4755 0.870
## 28.9 14 1 0.5988 0.1024 0.4283 0.837
## 31.1 13 1 0.5545 0.1047 0.3829 0.803
## 37.0 12 1 0.5102 0.1061 0.3394 0.767
## 43.8 10 1 0.4616 0.1076 0.2923 0.729
## 54.9 9 1 0.4131 0.1079 0.2475 0.689
## 55.9 8 1 0.3645 0.1070 0.2051 0.648
## 56.3 7 1 0.3160 0.1048 0.1650 0.605
## 59.1 6 1 0.2675 0.1012 0.1274 0.562
## 64.1 5 1 0.2190 0.0963 0.0925 0.518
## 65.9 4 1 0.1706 0.0897 0.0608 0.478
## 70.7 3 1 0.1222 0.0814 0.0331 0.451
## 76.1 2 1 0.0741 0.0720 0.0110 0.497
## 80.2 1 1 0.0273 Inf 0.0000 1.000
##
## clinical_data$age_groups=20-40
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 17.9 6 1 0.846 0.155 0.5918 1
## 47.8 4 1 0.659 0.225 0.3375 1
## 50.4 3 1 0.472 0.251 0.1664 1
## 59.5 2 1 0.287 0.254 0.0506 1
## 105.2 1 1 0.105 Inf 0.0000 1
##
## clinical_data$age_groups=40-60
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.92 53 1 0.9813 0.0187 0.94535 1.000
## 2.26 52 1 0.9626 0.0262 0.91264 1.000
## 15.05 45 1 0.9415 0.0332 0.87856 1.000
## 18.70 43 1 0.9198 0.0390 0.84645 1.000
## 19.75 41 1 0.8977 0.0441 0.81534 0.988
## 23.96 38 1 0.8743 0.0488 0.78368 0.975
## 27.15 36 1 0.8504 0.0532 0.75226 0.961
## 28.96 33 1 0.8250 0.0575 0.71964 0.946
## 31.30 32 1 0.7996 0.0613 0.68814 0.929
## 31.60 31 1 0.7742 0.0645 0.65758 0.912
## 33.20 29 1 0.7480 0.0676 0.62652 0.893
## 39.25 27 1 0.7208 0.0706 0.59486 0.873
## 43.90 25 1 0.6925 0.0735 0.56246 0.853
## 44.20 24 1 0.6643 0.0760 0.53089 0.831
## 44.74 23 1 0.6360 0.0780 0.50007 0.809
## 44.97 22 1 0.6078 0.0797 0.46993 0.786
## 46.71 21 1 0.5795 0.0811 0.44043 0.762
## 47.40 20 1 0.5512 0.0822 0.41154 0.738
## 47.86 19 1 0.5230 0.0829 0.38324 0.714
## 57.79 18 1 0.4947 0.0834 0.35550 0.688
## 58.40 17 1 0.4664 0.0836 0.32832 0.663
## 59.20 16 1 0.4382 0.0834 0.30169 0.636
## 59.53 15 1 0.4099 0.0830 0.27561 0.610
## 64.50 14 1 0.3817 0.0823 0.25008 0.582
## 64.86 13 1 0.3534 0.0813 0.22513 0.555
## 69.10 12 1 0.3251 0.0800 0.20077 0.527
## 70.80 11 1 0.2969 0.0783 0.17703 0.498
## 72.09 10 1 0.2686 0.0763 0.15394 0.469
## 74.20 8 1 0.2371 0.0744 0.12813 0.439
## 74.36 7 1 0.2055 0.0719 0.10353 0.408
## 79.13 6 1 0.1740 0.0686 0.08027 0.377
## 89.62 5 1 0.1424 0.0646 0.05855 0.346
## 99.51 3 1 0.1021 0.0623 0.03086 0.337
## 110.79 2 1 0.0619 0.0578 0.00992 0.386
## 119.21 1 1 0.0228 Inf 0.00000 1.000
##
## clinical_data$age_groups=60-80
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 1.80 135 1 0.99262 0.00738 0.97826 1.0000
## 3.64 134 1 0.98524 0.01040 0.96507 1.0000
## 4.24 133 1 0.97786 0.01269 0.95331 1.0000
## 5.20 131 1 0.97042 0.01462 0.94218 0.9995
## 5.22 130 1 0.96299 0.01631 0.93155 0.9955
## 10.20 125 1 0.95531 0.01790 0.92086 0.9911
## 11.60 123 1 0.94758 0.01937 0.91037 0.9863
## 14.40 120 1 0.93972 0.02076 0.89990 0.9813
## 15.00 118 1 0.93179 0.02206 0.88954 0.9760
## 15.71 116 1 0.92379 0.02328 0.87926 0.9706
## 16.90 115 1 0.91579 0.02443 0.86914 0.9649
## 18.18 114 1 0.90779 0.02550 0.85916 0.9592
## 18.80 113 1 0.89979 0.02651 0.84930 0.9533
## 18.96 112 1 0.89179 0.02747 0.83955 0.9473
## 20.44 111 1 0.88380 0.02837 0.82990 0.9412
## 22.02 110 1 0.87580 0.02923 0.82034 0.9350
## 22.80 107 1 0.86765 0.03008 0.81065 0.9287
## 24.00 105 1 0.85943 0.03091 0.80093 0.9222
## 24.19 103 1 0.85112 0.03172 0.79117 0.9156
## 25.24 101 1 0.84274 0.03251 0.78137 0.9089
## 25.61 100 1 0.83435 0.03326 0.77165 0.9022
## 26.26 99 1 0.82597 0.03397 0.76199 0.8953
## 26.53 98 1 0.81758 0.03466 0.75240 0.8884
## 26.66 97 1 0.80920 0.03531 0.74286 0.8815
## 26.82 96 1 0.80081 0.03594 0.73338 0.8744
## 26.92 95 1 0.79243 0.03654 0.72395 0.8674
## 28.50 93 1 0.78395 0.03713 0.71446 0.8602
## 29.22 92 1 0.77548 0.03769 0.70501 0.8530
## 29.60 91 1 0.76700 0.03823 0.69561 0.8457
## 30.00 90 1 0.75853 0.03875 0.68626 0.8384
## 30.90 89 1 0.75005 0.03924 0.67695 0.8310
## 31.36 88 1 0.74158 0.03971 0.66769 0.8236
## 31.92 87 1 0.73310 0.04016 0.65846 0.8162
## 33.69 86 1 0.72463 0.04059 0.64928 0.8087
## 33.80 85 1 0.71615 0.04100 0.64013 0.8012
## 33.90 84 1 0.70768 0.04140 0.63102 0.7936
## 35.90 83 1 0.69920 0.04177 0.62195 0.7861
## 36.20 82 1 0.69073 0.04212 0.61291 0.7784
## 36.30 81 1 0.68225 0.04246 0.60390 0.7708
## 36.75 80 1 0.67378 0.04278 0.59493 0.7631
## 36.92 79 1 0.66530 0.04309 0.58599 0.7553
## 37.31 77 1 0.65672 0.04339 0.57695 0.7475
## 38.00 75 1 0.64802 0.04369 0.56781 0.7396
## 38.07 74 1 0.63932 0.04397 0.55870 0.7316
## 38.20 73 1 0.63062 0.04424 0.54962 0.7236
## 38.72 72 1 0.62192 0.04448 0.54057 0.7155
## 40.00 71 1 0.61323 0.04472 0.53156 0.7074
## 40.40 70 2 0.59595 0.04514 0.51373 0.6913
## 42.00 67 1 0.58712 0.04534 0.50466 0.6831
## 42.90 66 1 0.57830 0.04552 0.49561 0.6748
## 44.40 65 1 0.56947 0.04569 0.48660 0.6664
## 44.67 64 1 0.56064 0.04584 0.47762 0.6581
## 44.80 63 1 0.55181 0.04597 0.46868 0.6497
## 45.30 62 1 0.54298 0.04609 0.45976 0.6413
## 45.40 61 1 0.53415 0.04619 0.45087 0.6328
## 47.70 60 1 0.52532 0.04628 0.44202 0.6243
## 49.11 59 1 0.51649 0.04635 0.43319 0.6158
## 49.60 58 1 0.50767 0.04641 0.42439 0.6073
## 49.84 57 1 0.49884 0.04645 0.41563 0.5987
## 50.59 56 1 0.49001 0.04647 0.40689 0.5901
## 50.90 55 1 0.48118 0.04648 0.39819 0.5815
## 52.10 54 1 0.47235 0.04647 0.38951 0.5728
## 52.14 53 1 0.46352 0.04645 0.38086 0.5641
## 52.24 52 1 0.45469 0.04641 0.37225 0.5554
## 52.50 51 1 0.44586 0.04636 0.36366 0.5467
## 52.80 50 1 0.43704 0.04629 0.35510 0.5379
## 52.86 49 1 0.42821 0.04621 0.34657 0.5291
## 54.40 48 1 0.41938 0.04611 0.33808 0.5202
## 55.13 47 1 0.41055 0.04599 0.32961 0.5114
## 55.33 46 1 0.40172 0.04586 0.32118 0.5025
## 55.70 45 1 0.39289 0.04572 0.31277 0.4935
## 55.92 44 1 0.38406 0.04555 0.30440 0.4846
## 56.50 43 1 0.37523 0.04537 0.29606 0.4756
## 56.80 42 1 0.36641 0.04518 0.28775 0.4666
## 57.00 41 1 0.35758 0.04496 0.27947 0.4575
## 57.80 40 1 0.34875 0.04473 0.27122 0.4484
## 58.02 39 1 0.33992 0.04449 0.26301 0.4393
## 58.45 38 1 0.33109 0.04422 0.25484 0.4302
## 59.34 37 1 0.32226 0.04394 0.24669 0.4210
## 59.50 36 1 0.31343 0.04364 0.23858 0.4118
## 59.60 35 1 0.30461 0.04332 0.23051 0.4025
## 59.96 34 1 0.29578 0.04298 0.22247 0.3932
## 61.40 33 1 0.28695 0.04262 0.21447 0.3839
## 63.25 32 1 0.27812 0.04224 0.20651 0.3746
## 64.33 31 1 0.26929 0.04184 0.19859 0.3652
## 64.37 30 1 0.26046 0.04143 0.19071 0.3557
## 64.93 29 1 0.25164 0.04098 0.18287 0.3463
## 65.55 28 1 0.24281 0.04052 0.17507 0.3368
## 67.19 27 1 0.23398 0.04003 0.16732 0.3272
## 67.82 26 1 0.22515 0.03952 0.15961 0.3176
## 68.10 25 1 0.21632 0.03899 0.15195 0.3080
## 68.51 24 1 0.20749 0.03842 0.14434 0.2983
## 68.70 23 1 0.19867 0.03783 0.13678 0.2886
## 74.53 22 1 0.18984 0.03722 0.12927 0.2788
## 76.04 21 1 0.18101 0.03657 0.12183 0.2689
## 80.80 19 1 0.17173 0.03591 0.11398 0.2587
## 82.29 18 1 0.16245 0.03522 0.10621 0.2485
## 83.60 17 1 0.15317 0.03448 0.09852 0.2381
## 83.73 16 1 0.14389 0.03370 0.09092 0.2277
## 84.13 15 1 0.13461 0.03286 0.08342 0.2172
## 84.70 14 1 0.12533 0.03198 0.07601 0.2067
## 84.90 13 1 0.11605 0.03103 0.06871 0.1960
## 85.28 12 1 0.10677 0.03003 0.06153 0.1853
## 85.61 11 1 0.09749 0.02895 0.05448 0.1745
## 86.43 9 1 0.08724 0.02787 0.04664 0.1632
## 88.99 8 1 0.07699 0.02666 0.03905 0.1518
## 95.07 7 1 0.06674 0.02530 0.03175 0.1403
## 106.94 6 1 0.05649 0.02377 0.02476 0.1289
## 109.21 5 1 0.04625 0.02204 0.01818 0.1177
## 112.33 4 1 0.03602 0.02007 0.01209 0.1074
## 118.58 3 1 0.02581 0.01783 0.00667 0.0999
## 122.72 2 1 0.01566 0.01547 0.00226 0.1087
## 142.55 1 1 0.00576 Inf 0.00000 1.0000autoplot(fhsurvival1_age,
censor.shape = '*', facets = TRUE, ncol = 2, xlab="Time", ylab="Survival Probability")
Semi-Parameter Analysis
Cox proportional hazard model - coefficients and hazard rates
First we need to create a factor of the parameter to be used in semi_paramteric and parametric analysis
factors <- cbind(clinical_data$location, clinical_data$dukes_stage, clinical_data$age_diag,
clinical_data$gender, clinical_data$adjXRT, clinical_data$adjCTX)
coxph <- coxph(Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
factors, method="breslow")
summary(coxph)## Call:
## coxph(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## factors, method = "breslow")
##
## n= 226, number of events= 176
##
## coef exp(coef) se(coef) z Pr(>|z|)
## factors1 0.032699 1.033239 0.085067 0.384 0.7007
## factors2 0.145615 1.156750 0.122390 1.190 0.2341
## factors3 0.013573 1.013666 0.006898 1.968 0.0491 *
## factors4 -0.114084 0.892183 0.153394 -0.744 0.4570
## factors5 -0.783852 0.456643 0.399812 -1.961 0.0499 *
## factors6 -0.077501 0.925426 0.213092 -0.364 0.7161
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## factors1 1.0332 0.9678 0.8746 1.2207
## factors2 1.1568 0.8645 0.9100 1.4703
## factors3 1.0137 0.9865 1.0001 1.0275
## factors4 0.8922 1.1208 0.6605 1.2051
## factors5 0.4566 2.1899 0.2086 0.9998
## factors6 0.9254 1.0806 0.6095 1.4052
##
## Concordance= 0.58 (se = 0.026 )
## Rsquare= 0.059 (max possible= 0.999 )
## Likelihood ratio test= 13.83 on 6 df, p=0.03164
## Wald test = 12.14 on 6 df, p=0.05897
## Score (logrank) test = 12.48 on 6 df, p=0.05211Paramteric
Exponential
exponential <- survreg(Surv(clinical_data$dfs_time,clinical_data$dfs_event) ~ factors, dist="exponential")
summary(exponential)##
## Call:
## survreg(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## factors, dist = "exponential")
## Value Std. Error z p
## (Intercept) 3.891455 0.76409 5.0929 3.53e-07
## factors1 -0.041423 0.08207 -0.5047 6.14e-01
## factors2 0.000229 0.12088 0.0019 9.98e-01
## factors3 -0.008022 0.00665 -1.2060 2.28e-01
## factors4 0.050161 0.15278 0.3283 7.43e-01
## factors5 0.652034 0.38759 1.6823 9.25e-02
## factors6 0.016175 0.20925 0.0773 9.38e-01
##
## Scale fixed at 1
##
## Exponential distribution
## Loglik(model)= -880.1 Loglik(intercept only)= -884.1
## Chisq= 7.89 on 6 degrees of freedom, p= 0.25
## Number of Newton-Raphson Iterations: 4
## n= 226Weibull
weibull <- survreg(Surv(clinical_data$dfs_time,clinical_data$dfs_event) ~ factors, dist="weibull")
summary(weibull)##
## Call:
## survreg(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## factors, dist = "weibull")
## Value Std. Error z p
## (Intercept) 4.17311 0.38770 10.764 5.11e-27
## factors1 -0.01608 0.04321 -0.372 7.10e-01
## factors2 -0.07165 0.06158 -1.163 2.45e-01
## factors3 -0.00696 0.00348 -2.002 4.52e-02
## factors4 0.05396 0.07805 0.691 4.89e-01
## factors5 0.40205 0.20276 1.983 4.74e-02
## factors6 0.02840 0.10839 0.262 7.93e-01
## Log(scale) -0.66881 0.05806 -11.518 1.06e-30
##
## Scale= 0.512
##
## Weibull distribution
## Loglik(model)= -831.5 Loglik(intercept only)= -838.4
## Chisq= 13.77 on 6 degrees of freedom, p= 0.032
## Number of Newton-Raphson Iterations: 7
## n= 226log-logistic
loglogistic <- survreg(Surv(clinical_data$dfs_time,clinical_data$dfs_event) ~ factors, dist="loglogistic")
summary(loglogistic)##
## Call:
## survreg(formula = Surv(clinical_data$dfs_time, clinical_data$dfs_event) ~
## factors, dist = "loglogistic")
## Value Std. Error z p
## (Intercept) 4.02692 0.49261 8.175 2.97e-16
## factors1 -0.06100 0.04870 -1.252 2.10e-01
## factors2 -0.07700 0.07900 -0.975 3.30e-01
## factors3 -0.00602 0.00412 -1.462 1.44e-01
## factors4 0.02548 0.09615 0.265 7.91e-01
## factors5 0.33845 0.22291 1.518 1.29e-01
## factors6 0.12132 0.12874 0.942 3.46e-01
## Log(scale) -0.97595 0.06254 -15.605 6.74e-55
##
## Scale= 0.377
##
## Log logistic distribution
## Loglik(model)= -847.1 Loglik(intercept only)= -853.2
## Chisq= 12.07 on 6 degrees of freedom, p= 0.06
## Number of Newton-Raphson Iterations: 4
## n= 226Comparison between those methods
plot(kmsurvival_month)
curve(plnorm(x, coef(weibull)[1], weibull$scale, lower.tail=FALSE), from=0, to=140, col="blue", ylim=c(0,1), lwd=2, add=T, lty=5, xlab="", ylab="")
curve(plnorm(x, coef(loglogistic)[1], loglogistic$scale, lower.tail=FALSE), from=0, to=140, col="green", ylim=c(0,1), lwd=2, add=T, lty=5, xlab="", ylab="")
curve(plnorm(x, coef(exponential)[1], exponential$scale, lower.tail=FALSE), from=0, to=140, col="red", ylim=c(0,1), lwd=2, add=T, lty=5, xlab="", ylab="")
legend('topright',c("None-Parametric", "weibull", "log", "exponential"), col=c("black", "blue", "green", "red"), lty=c(1,1), lwd=c(5,5), cex=1.2, inset=c(.05,0), bty="n")
title(main="Parametric methods vs. Non Parametric", ylab = "Percent of Surviving Patients", xlab="Time")