setwd("C:/Work Files/8190 MLM/Fall 2024/R Code and Examples")Survival Analysis Example
library(tidyverse)── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
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✔ lubridate 1.9.3 ✔ tidyr 1.3.1
✔ purrr 1.0.2
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✖ dplyr::filter() masks stats::filter()
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(survival)Warning: package 'survival' was built under R version 4.4.2library(survminer)Warning: package 'survminer' was built under R version 4.4.2Loading required package: ggpubrWarning: package 'ggpubr' was built under R version 4.4.2
Attaching package: 'survminer'
The following object is masked from 'package:survival':
myelomalibrary(dataMaid)
Attaching package: 'dataMaid'
The following object is masked from 'package:dplyr':
summarizedata(lung)Warning in data(lung): data set 'lung' not foundhead(lung) inst time status age sex ph.ecog ph.karno pat.karno meal.cal wt.loss
1 3 306 2 74 1 1 90 100 1175 NA
2 3 455 2 68 1 0 90 90 1225 15
3 3 1010 1 56 1 0 90 90 NA 15
4 5 210 2 57 1 1 90 60 1150 11
5 1 883 2 60 1 0 100 90 NA 0
6 12 1022 1 74 1 1 50 80 513 0# makeCodebook(lung, replace = TRUE, file = "Lung_cancer_codebook.html")
#?lung# Fit Kaplan-Meier survival model
km_fit <- survfit(Surv(time, status) ~ 1, data = lung)
# Summary of the model
summary(km_fit)Call: survfit(formula = Surv(time, status) ~ 1, data = lung)
time n.risk n.event survival std.err lower 95% CI upper 95% CI
5 228 1 0.9956 0.00438 0.9871 1.000
11 227 3 0.9825 0.00869 0.9656 1.000
12 224 1 0.9781 0.00970 0.9592 0.997
13 223 2 0.9693 0.01142 0.9472 0.992
15 221 1 0.9649 0.01219 0.9413 0.989
26 220 1 0.9605 0.01290 0.9356 0.986
30 219 1 0.9561 0.01356 0.9299 0.983
31 218 1 0.9518 0.01419 0.9243 0.980
53 217 2 0.9430 0.01536 0.9134 0.974
54 215 1 0.9386 0.01590 0.9079 0.970
59 214 1 0.9342 0.01642 0.9026 0.967
60 213 2 0.9254 0.01740 0.8920 0.960
61 211 1 0.9211 0.01786 0.8867 0.957
62 210 1 0.9167 0.01830 0.8815 0.953
65 209 2 0.9079 0.01915 0.8711 0.946
71 207 1 0.9035 0.01955 0.8660 0.943
79 206 1 0.8991 0.01995 0.8609 0.939
81 205 2 0.8904 0.02069 0.8507 0.932
88 203 2 0.8816 0.02140 0.8406 0.925
92 201 1 0.8772 0.02174 0.8356 0.921
93 199 1 0.8728 0.02207 0.8306 0.917
95 198 2 0.8640 0.02271 0.8206 0.910
105 196 1 0.8596 0.02302 0.8156 0.906
107 194 2 0.8507 0.02362 0.8056 0.898
110 192 1 0.8463 0.02391 0.8007 0.894
116 191 1 0.8418 0.02419 0.7957 0.891
118 190 1 0.8374 0.02446 0.7908 0.887
122 189 1 0.8330 0.02473 0.7859 0.883
131 188 1 0.8285 0.02500 0.7810 0.879
132 187 2 0.8197 0.02550 0.7712 0.871
135 185 1 0.8153 0.02575 0.7663 0.867
142 184 1 0.8108 0.02598 0.7615 0.863
144 183 1 0.8064 0.02622 0.7566 0.859
145 182 2 0.7975 0.02667 0.7469 0.852
147 180 1 0.7931 0.02688 0.7421 0.848
153 179 1 0.7887 0.02710 0.7373 0.844
156 178 2 0.7798 0.02751 0.7277 0.836
163 176 3 0.7665 0.02809 0.7134 0.824
166 173 2 0.7577 0.02845 0.7039 0.816
167 171 1 0.7532 0.02863 0.6991 0.811
170 170 1 0.7488 0.02880 0.6944 0.807
175 167 1 0.7443 0.02898 0.6896 0.803
176 165 1 0.7398 0.02915 0.6848 0.799
177 164 1 0.7353 0.02932 0.6800 0.795
179 162 2 0.7262 0.02965 0.6704 0.787
180 160 1 0.7217 0.02981 0.6655 0.783
181 159 2 0.7126 0.03012 0.6559 0.774
182 157 1 0.7081 0.03027 0.6511 0.770
183 156 1 0.7035 0.03041 0.6464 0.766
186 154 1 0.6989 0.03056 0.6416 0.761
189 152 1 0.6943 0.03070 0.6367 0.757
194 149 1 0.6897 0.03085 0.6318 0.753
197 147 1 0.6850 0.03099 0.6269 0.749
199 145 1 0.6803 0.03113 0.6219 0.744
201 144 2 0.6708 0.03141 0.6120 0.735
202 142 1 0.6661 0.03154 0.6071 0.731
207 139 1 0.6613 0.03168 0.6020 0.726
208 138 1 0.6565 0.03181 0.5970 0.722
210 137 1 0.6517 0.03194 0.5920 0.717
212 135 1 0.6469 0.03206 0.5870 0.713
218 134 1 0.6421 0.03218 0.5820 0.708
222 132 1 0.6372 0.03231 0.5769 0.704
223 130 1 0.6323 0.03243 0.5718 0.699
226 126 1 0.6273 0.03256 0.5666 0.694
229 125 1 0.6223 0.03268 0.5614 0.690
230 124 1 0.6172 0.03280 0.5562 0.685
239 121 2 0.6070 0.03304 0.5456 0.675
245 117 1 0.6019 0.03316 0.5402 0.670
246 116 1 0.5967 0.03328 0.5349 0.666
267 112 1 0.5913 0.03341 0.5294 0.661
268 111 1 0.5860 0.03353 0.5239 0.656
269 110 1 0.5807 0.03364 0.5184 0.651
270 108 1 0.5753 0.03376 0.5128 0.645
283 104 1 0.5698 0.03388 0.5071 0.640
284 103 1 0.5642 0.03400 0.5014 0.635
285 101 2 0.5531 0.03424 0.4899 0.624
286 99 1 0.5475 0.03434 0.4841 0.619
288 98 1 0.5419 0.03444 0.4784 0.614
291 97 1 0.5363 0.03454 0.4727 0.608
293 94 1 0.5306 0.03464 0.4669 0.603
301 91 1 0.5248 0.03475 0.4609 0.597
303 89 1 0.5189 0.03485 0.4549 0.592
305 87 1 0.5129 0.03496 0.4488 0.586
306 86 1 0.5070 0.03506 0.4427 0.581
310 85 2 0.4950 0.03523 0.4306 0.569
320 82 1 0.4890 0.03532 0.4244 0.563
329 81 1 0.4830 0.03539 0.4183 0.558
337 79 1 0.4768 0.03547 0.4121 0.552
340 78 1 0.4707 0.03554 0.4060 0.546
345 77 1 0.4646 0.03560 0.3998 0.540
348 76 1 0.4585 0.03565 0.3937 0.534
350 75 1 0.4524 0.03569 0.3876 0.528
351 74 1 0.4463 0.03573 0.3815 0.522
353 73 2 0.4340 0.03578 0.3693 0.510
361 70 1 0.4278 0.03581 0.3631 0.504
363 69 2 0.4154 0.03583 0.3508 0.492
364 67 1 0.4092 0.03582 0.3447 0.486
371 65 2 0.3966 0.03581 0.3323 0.473
387 60 1 0.3900 0.03582 0.3258 0.467
390 59 1 0.3834 0.03582 0.3193 0.460
394 58 1 0.3768 0.03580 0.3128 0.454
426 55 1 0.3700 0.03580 0.3060 0.447
428 54 1 0.3631 0.03579 0.2993 0.440
429 53 1 0.3563 0.03576 0.2926 0.434
433 52 1 0.3494 0.03573 0.2860 0.427
442 51 1 0.3426 0.03568 0.2793 0.420
444 50 1 0.3357 0.03561 0.2727 0.413
450 48 1 0.3287 0.03555 0.2659 0.406
455 47 1 0.3217 0.03548 0.2592 0.399
457 46 1 0.3147 0.03539 0.2525 0.392
460 44 1 0.3076 0.03530 0.2456 0.385
473 43 1 0.3004 0.03520 0.2388 0.378
477 42 1 0.2933 0.03508 0.2320 0.371
519 39 1 0.2857 0.03498 0.2248 0.363
520 38 1 0.2782 0.03485 0.2177 0.356
524 37 2 0.2632 0.03455 0.2035 0.340
533 34 1 0.2554 0.03439 0.1962 0.333
550 32 1 0.2475 0.03423 0.1887 0.325
558 30 1 0.2392 0.03407 0.1810 0.316
567 28 1 0.2307 0.03391 0.1729 0.308
574 27 1 0.2221 0.03371 0.1650 0.299
583 26 1 0.2136 0.03348 0.1571 0.290
613 24 1 0.2047 0.03325 0.1489 0.281
624 23 1 0.1958 0.03297 0.1407 0.272
641 22 1 0.1869 0.03265 0.1327 0.263
643 21 1 0.1780 0.03229 0.1247 0.254
654 20 1 0.1691 0.03188 0.1169 0.245
655 19 1 0.1602 0.03142 0.1091 0.235
687 18 1 0.1513 0.03090 0.1014 0.226
689 17 1 0.1424 0.03034 0.0938 0.216
705 16 1 0.1335 0.02972 0.0863 0.207
707 15 1 0.1246 0.02904 0.0789 0.197
728 14 1 0.1157 0.02830 0.0716 0.187
731 13 1 0.1068 0.02749 0.0645 0.177
735 12 1 0.0979 0.02660 0.0575 0.167
765 10 1 0.0881 0.02568 0.0498 0.156
791 9 1 0.0783 0.02462 0.0423 0.145
814 7 1 0.0671 0.02351 0.0338 0.133
883 4 1 0.0503 0.02285 0.0207 0.123# Plot the survival curve
ggsurvplot(km_fit, data = lung,
xlab = "Time (days)",
ylab = "Survival Probability",
title = "Kaplan-Meier Survival Curve")
# Fit Kaplan-Meier curves by a grouping variable (e.g., sex)
km_fit_group <- survfit(Surv(time, status) ~ sex, data = lung)
# Log-rank test
survdiff(Surv(time, status) ~ sex, data = lung)Call:
survdiff(formula = Surv(time, status) ~ sex, data = lung)
N Observed Expected (O-E)^2/E (O-E)^2/V
sex=1 138 112 91.6 4.55 10.3
sex=2 90 53 73.4 5.68 10.3
Chisq= 10.3 on 1 degrees of freedom, p= 0.001 # Plot the survival curves by group
ggsurvplot(km_fit_group, data = lung,
pval = TRUE,
conf.int = TRUE,
legend.labs = c("Male", "Female"),
title = "Survival by Sex")
# Fit a Cox proportional hazards model
cox_model <- coxph(Surv(time, status) ~ age + sex + ph.karno, data = lung)
# Summary of the model
summary(cox_model)Call:
coxph(formula = Surv(time, status) ~ age + sex + ph.karno, data = lung)
n= 227, number of events= 164
(1 observation deleted due to missingness)
coef exp(coef) se(coef) z Pr(>|z|)
age 0.012375 1.012452 0.009405 1.316 0.18821
sex -0.497170 0.608249 0.167713 -2.964 0.00303 **
ph.karno -0.013322 0.986767 0.005880 -2.266 0.02348 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
age 1.0125 0.9877 0.9940 1.0313
sex 0.6082 1.6441 0.4378 0.8450
ph.karno 0.9868 1.0134 0.9755 0.9982
Concordance= 0.637 (se = 0.025 )
Likelihood ratio test= 18.81 on 3 df, p=3e-04
Wald test = 18.73 on 3 df, p=3e-04
Score (logrank) test = 19.05 on 3 df, p=3e-04# Visualize adjusted survival curves for different levels of a covariate
# Visualize adjusted survival curves for different levels of a covariate
ggadjustedcurves(cox_model, data = lung, variable = "sex", method = "average")
# Test proportional hazards assumption
cox.zph(cox_model) chisq df p
age 0.478 1 0.4892
sex 3.085 1 0.0790
ph.karno 8.017 1 0.0046
GLOBAL 10.359 3 0.0157# Plot Schoenfeld residuals
ggcoxzph(cox.zph(cox_model))
cox_model_tv <- coxph(Surv(time, status) ~ tt(age) + sex,
data = lung,
tt = function(x, t, ...) x * t)
summary(cox_model_tv)Call:
coxph(formula = Surv(time, status) ~ tt(age) + sex, data = lung,
tt = function(x, t, ...) x * t)
n= 228, number of events= 165
coef exp(coef) se(coef) z Pr(>|z|)
tt(age) 3.571e-05 1.000e+00 2.789e-05 1.280 0.20043
sex -5.256e-01 5.912e-01 1.672e-01 -3.143 0.00167 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
tt(age) 1.0000 1.000 1.000 1.0001
sex 0.5912 1.691 0.426 0.8205
Concordance= 0.603 (se = 0.025 )
Likelihood ratio test= 12.31 on 2 df, p=0.002
Wald test = 11.71 on 2 df, p=0.003
Score (logrank) test = 11.95 on 2 df, p=0.003cox_model_strata <- coxph(Surv(time, status) ~ age + strata(sex), data = lung)
summary(cox_model_strata)Call:
coxph(formula = Surv(time, status) ~ age + strata(sex), data = lung)
n= 228, number of events= 165
coef exp(coef) se(coef) z Pr(>|z|)
age 0.016215 1.016347 0.009187 1.765 0.0776 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
age 1.016 0.9839 0.9982 1.035
Concordance= 0.546 (se = 0.026 )
Likelihood ratio test= 3.18 on 1 df, p=0.07
Wald test = 3.12 on 1 df, p=0.08
Score (logrank) test = 3.12 on 1 df, p=0.08