SURVIVAL ASS 3
CYNTHIA
2025-03-03
#survival packages
library(survival)
library(survminer)## Loading required package: ggplot2## Loading required package: ggpubr##
## Attaching package: 'survminer'## The following object is masked from 'package:survival':
##
## myelomalibrary(surveillance)## Loading required package: sp## Loading required package: xtable## This is surveillance 1.24.1; see 'package?surveillance' or
## https://surveillance.R-Forge.R-project.org/ for an overview.#survival data from R
data()
data("diabetic")
head(diabetic)## id laser age eye trt risk time status
## 1 5 argon 28 left 0 9 46.23 0
## 2 5 argon 28 right 1 9 46.23 0
## 3 14 xenon 12 left 1 8 42.50 0
## 4 14 xenon 12 right 0 6 31.30 1
## 5 16 xenon 9 left 1 11 42.27 0
## 6 16 xenon 9 right 0 11 42.27 0#recode status
diabetic$event <- ifelse(diabetic$status == 0, 0, 1)#forming a survival object(combines time and event)
surv_function <- Surv(time = diabetic$time, event = diabetic$event)
print(surv_function)## [1] 46.23+ 46.23+ 42.50+ 31.30 42.27+ 42.27+ 20.60+ 20.60+ 0.30 38.77+
## [11] 65.23+ 54.27 63.50+ 10.80 23.17+ 23.17+ 1.47+ 1.47+ 58.07+ 13.83
## [21] 48.53+ 46.43 44.40+ 7.90 39.57+ 39.57+ 30.83 38.57 66.27+ 14.10
## [31] 6.90 20.17 41.40 58.43+ 58.20+ 58.20+ 57.43+ 57.43+ 56.03+ 56.03+
## [41] 67.53+ 67.53+ 61.40+ 0.60 10.27 1.63 66.20+ 66.20+ 13.83 5.67
## [51] 58.83+ 29.97 60.27+ 26.37 1.33 5.77 35.53 5.90 21.90 25.63
## [61] 14.80 33.90 6.20 1.73 22.00 46.90+ 31.13+ 31.13+ 22.00 30.20
## [71] 70.90+ 70.90+ 25.80 13.87 48.30 5.73 53.43+ 53.43+ 1.90 51.10+
## [81] 9.90 9.90 34.20+ 34.20+ 2.67 46.73+ 18.73+ 13.83 32.03+ 4.27
## [91] 13.90 69.87+ 66.80+ 66.80+ 64.73+ 64.73+ 1.70 1.70 1.77 43.03
## [101] 29.03+ 29.03+ 56.57+ 56.57+ 8.30 8.30 21.57+ 18.43 31.57+ 31.57+
## [111] 31.63 31.63+ 39.77+ 39.77+ 6.53 18.70 18.90+ 18.90+ 56.80+ 22.23
## [121] 55.60+ 14.00 42.17 42.17 5.33 10.70+ 59.80 66.33+ 5.83 52.33+
## [131] 58.17+ 2.17 48.43 14.30 25.83+ 25.83+ 45.40+ 45.40+ 47.60+ 47.60+
## [141] 9.60 13.33 42.10+ 42.10+ 39.93+ 39.93+ 7.60 14.27 1.80 34.57
## [151] 4.30 65.80+ 12.20 4.10 60.93+ 60.93+ 57.20+ 57.20+ 38.07+ 12.73
## [161] 54.10+ 54.10 59.27+ 9.40 9.90 21.57 54.10+ 54.10+ 50.47+ 50.47+
## [171] 46.17+ 46.17+ 46.30+ 46.30+ 38.83+ 38.83+ 44.60+ 44.60+ 43.07+ 43.07+
## [181] 40.03+ 26.23 41.60+ 18.03 38.07+ 38.07+ 65.23+ 65.23+ 7.07 66.77+
## [191] 13.77 13.77 9.63 9.63+ 46.23+ 46.23+ 1.50 45.73+ 33.63 33.63
## [201] 40.17+ 40.17+ 27.60 63.33 38.47 1.63 55.23+ 55.23+ 25.30 52.77+
## [211] 46.20 57.17+ 9.87+ 1.70 57.90+ 57.90+ 5.90+ 5.90+ 32.20+ 32.20+
## [221] 10.33 0.83 50.90+ 6.13 25.93 43.67+ 38.30+ 38.30+ 38.77+ 19.40
## [231] 21.97 38.07+ 38.30+ 38.30+ 70.03+ 26.20 18.03 62.57+ 1.57 13.83
## [241] 46.50+ 13.37 1.97 11.07 42.47+ 22.20 38.73+ 38.73+ 51.13+ 51.13+
## [251] 46.50+ 6.10 11.30 2.10 17.73 42.30+ 26.47+ 26.47+ 10.77+ 10.77+
## [261] 55.33+ 55.33+ 58.67+ 58.67+ 4.97 12.93 26.47 54.20+ 49.57+ 49.57+
## [271] 9.87 24.43 50.23+ 50.23+ 30.40 13.97 43.33+ 43.33 42.23+ 42.23+
## [281] 74.93+ 74.93+ 66.93+ 66.93+ 73.43+ 73.43+ 67.47+ 38.57 3.67+ 3.67
## [291] 67.03+ 48.87 65.60+ 65.60+ 15.83 15.83+ 20.07+ 8.83 67.43+ 67.43+
## [301] 1.47+ 1.47+ 62.93+ 22.13 6.30 56.97+ 59.70+ 18.93 19.00 13.80
## [311] 55.13+ 55.13+ 5.43 13.57 42.20+ 42.20+ 38.27+ 38.27+ 7.10+ 7.10
## [321] 26.17 63.63+ 24.73 59.00+ 54.37+ 54.37+ 54.60+ 10.97 21.10 63.87+
## [331] 62.37+ 43.70 62.80+ 62.80+ 63.33+ 14.37 58.53+ 58.53+ 58.07+ 58.07+
## [341] 58.50+ 58.50+ 14.37+ 1.50 54.73+ 38.40 50.63+ 2.83 51.10+ 51.10+
## [351] 49.93+ 6.57 46.27+ 46.27 10.60+ 10.60+ 42.77+ 42.77+ 34.37 42.27+
## [361] 42.07+ 42.07+ 38.77+ 38.77+ 61.83 74.97+ 66.97+ 6.57 38.87 68.30+
## [371] 46.63 42.43 67.07+ 67.07+ 2.70 2.70+ 63.80+ 63.80+ 32.63+ 32.63+
## [381] 62.00+ 62.00+ 54.80+ 13.10 8.00+ 8.00+ 42.33 51.60+ 49.97+ 2.90
## [391] 45.90+ 1.43 41.93+ 41.93+#fitting the KM model using a single curve(~1)
fit <- survfit(surv_function ~ 1) KM curve
plot(fit,xlab = "Time", ylab = "Survival Probability", main = "Kaplan-Meier Survival Curve")
#the KM median curve ##a measure of central tendancy
summary(fit)## Call: survfit(formula = surv_function ~ 1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.30 394 1 0.997 0.00253 0.993 1.000
## 0.60 393 1 0.995 0.00358 0.988 1.000
## 0.83 392 1 0.992 0.00438 0.984 1.000
## 1.33 391 1 0.990 0.00505 0.980 1.000
## 1.43 390 1 0.987 0.00564 0.976 0.998
## 1.50 385 2 0.982 0.00667 0.969 0.995
## 1.57 383 1 0.980 0.00713 0.966 0.994
## 1.63 382 2 0.974 0.00796 0.959 0.990
## 1.70 380 3 0.967 0.00906 0.949 0.985
## 1.73 377 1 0.964 0.00939 0.946 0.983
## 1.77 376 1 0.962 0.00971 0.943 0.981
## 1.80 375 1 0.959 0.01001 0.940 0.979
## 1.90 374 1 0.957 0.01031 0.937 0.977
## 1.97 373 1 0.954 0.01060 0.933 0.975
## 2.10 372 1 0.951 0.01087 0.930 0.973
## 2.17 371 1 0.949 0.01114 0.927 0.971
## 2.67 370 1 0.946 0.01140 0.924 0.969
## 2.70 369 1 0.944 0.01166 0.921 0.967
## 2.83 367 1 0.941 0.01191 0.918 0.965
## 2.90 366 1 0.939 0.01215 0.915 0.963
## 3.67 365 1 0.936 0.01238 0.912 0.961
## 4.10 363 1 0.933 0.01262 0.909 0.958
## 4.27 362 1 0.931 0.01284 0.906 0.956
## 4.30 361 1 0.928 0.01306 0.903 0.954
## 4.97 360 1 0.926 0.01328 0.900 0.952
## 5.33 359 1 0.923 0.01349 0.897 0.950
## 5.43 358 1 0.921 0.01370 0.894 0.948
## 5.67 357 1 0.918 0.01390 0.891 0.946
## 5.73 356 1 0.915 0.01410 0.888 0.943
## 5.77 355 1 0.913 0.01429 0.885 0.941
## 5.83 354 1 0.910 0.01448 0.882 0.939
## 5.90 353 1 0.908 0.01467 0.879 0.937
## 6.10 350 1 0.905 0.01485 0.876 0.935
## 6.13 349 1 0.902 0.01504 0.873 0.932
## 6.20 348 1 0.900 0.01521 0.871 0.930
## 6.30 347 1 0.897 0.01539 0.868 0.928
## 6.53 346 1 0.895 0.01556 0.865 0.926
## 6.57 345 2 0.889 0.01590 0.859 0.921
## 6.90 343 1 0.887 0.01606 0.856 0.919
## 7.07 342 1 0.884 0.01622 0.853 0.917
## 7.10 341 1 0.882 0.01638 0.850 0.914
## 7.60 339 1 0.879 0.01654 0.847 0.912
## 7.90 338 1 0.877 0.01669 0.844 0.910
## 8.30 335 2 0.871 0.01700 0.839 0.905
## 8.83 333 1 0.869 0.01715 0.836 0.903
## 9.40 332 1 0.866 0.01729 0.833 0.901
## 9.60 331 1 0.863 0.01744 0.830 0.898
## 9.63 330 1 0.861 0.01758 0.827 0.896
## 9.87 328 1 0.858 0.01772 0.824 0.894
## 9.90 326 3 0.850 0.01814 0.815 0.887
## 10.27 323 1 0.848 0.01827 0.813 0.884
## 10.33 322 1 0.845 0.01840 0.810 0.882
## 10.80 316 1 0.842 0.01854 0.807 0.879
## 10.97 315 1 0.840 0.01867 0.804 0.877
## 11.07 314 1 0.837 0.01880 0.801 0.875
## 11.30 313 1 0.834 0.01893 0.798 0.872
## 12.20 312 1 0.832 0.01906 0.795 0.870
## 12.73 311 1 0.829 0.01918 0.792 0.867
## 12.93 310 1 0.826 0.01931 0.789 0.865
## 13.10 309 1 0.824 0.01943 0.786 0.863
## 13.33 308 1 0.821 0.01955 0.784 0.860
## 13.37 307 1 0.818 0.01967 0.781 0.858
## 13.57 306 1 0.816 0.01978 0.778 0.855
## 13.77 305 2 0.810 0.02001 0.772 0.850
## 13.80 303 1 0.808 0.02012 0.769 0.848
## 13.83 302 4 0.797 0.02056 0.758 0.838
## 13.87 298 1 0.794 0.02066 0.755 0.836
## 13.90 297 1 0.792 0.02076 0.752 0.833
## 13.97 296 1 0.789 0.02086 0.749 0.831
## 14.00 295 1 0.786 0.02096 0.746 0.828
## 14.10 294 1 0.784 0.02106 0.743 0.826
## 14.27 293 1 0.781 0.02116 0.740 0.823
## 14.30 292 1 0.778 0.02126 0.738 0.821
## 14.37 291 1 0.775 0.02135 0.735 0.818
## 14.80 289 1 0.773 0.02144 0.732 0.816
## 15.83 288 1 0.770 0.02154 0.729 0.814
## 17.73 286 1 0.767 0.02163 0.726 0.811
## 18.03 285 2 0.762 0.02181 0.720 0.806
## 18.43 283 1 0.759 0.02190 0.718 0.804
## 18.70 282 1 0.757 0.02199 0.715 0.801
## 18.93 278 1 0.754 0.02207 0.712 0.798
## 19.00 277 1 0.751 0.02216 0.709 0.796
## 19.40 276 1 0.748 0.02225 0.706 0.793
## 20.17 274 1 0.746 0.02233 0.703 0.791
## 21.10 271 1 0.743 0.02242 0.700 0.788
## 21.57 270 1 0.740 0.02251 0.697 0.786
## 21.90 268 1 0.737 0.02259 0.695 0.783
## 21.97 267 1 0.735 0.02267 0.692 0.781
## 22.00 266 2 0.729 0.02284 0.686 0.775
## 22.13 264 1 0.726 0.02292 0.683 0.773
## 22.20 263 1 0.724 0.02300 0.680 0.770
## 22.23 262 1 0.721 0.02307 0.677 0.768
## 24.43 259 1 0.718 0.02315 0.674 0.765
## 24.73 258 1 0.715 0.02323 0.671 0.762
## 25.30 257 1 0.713 0.02331 0.668 0.760
## 25.63 256 1 0.710 0.02338 0.665 0.757
## 25.80 255 1 0.707 0.02345 0.663 0.755
## 25.93 252 1 0.704 0.02353 0.660 0.752
## 26.17 251 1 0.701 0.02360 0.657 0.749
## 26.20 250 1 0.699 0.02367 0.654 0.747
## 26.23 249 1 0.696 0.02374 0.651 0.744
## 26.37 248 1 0.693 0.02381 0.648 0.741
## 26.47 247 1 0.690 0.02388 0.645 0.739
## 27.60 244 1 0.687 0.02395 0.642 0.736
## 29.97 241 1 0.684 0.02402 0.639 0.733
## 30.20 240 1 0.682 0.02409 0.636 0.731
## 30.40 239 1 0.679 0.02416 0.633 0.728
## 30.83 238 1 0.676 0.02422 0.630 0.725
## 31.30 235 1 0.673 0.02429 0.627 0.722
## 31.63 232 1 0.670 0.02436 0.624 0.720
## 33.63 225 2 0.664 0.02450 0.618 0.714
## 33.90 223 1 0.661 0.02457 0.615 0.711
## 34.37 220 1 0.658 0.02464 0.612 0.708
## 34.57 219 1 0.655 0.02471 0.609 0.705
## 35.53 218 1 0.652 0.02478 0.605 0.703
## 38.40 207 1 0.649 0.02486 0.602 0.700
## 38.47 206 1 0.646 0.02494 0.599 0.697
## 38.57 205 2 0.640 0.02509 0.592 0.691
## 38.87 195 1 0.636 0.02518 0.589 0.688
## 41.40 185 1 0.633 0.02527 0.585 0.684
## 42.17 177 2 0.626 0.02549 0.578 0.678
## 42.33 167 1 0.622 0.02561 0.574 0.674
## 42.43 166 1 0.618 0.02573 0.570 0.671
## 43.03 161 1 0.614 0.02585 0.566 0.667
## 43.33 158 1 0.611 0.02598 0.562 0.664
## 43.70 155 1 0.607 0.02611 0.557 0.660
## 46.20 145 1 0.602 0.02626 0.553 0.656
## 46.27 140 1 0.598 0.02643 0.548 0.652
## 46.43 136 1 0.594 0.02660 0.544 0.648
## 46.63 133 1 0.589 0.02677 0.539 0.644
## 48.30 128 1 0.585 0.02695 0.534 0.640
## 48.43 127 1 0.580 0.02713 0.529 0.636
## 48.87 125 1 0.575 0.02731 0.524 0.631
## 54.10 104 1 0.570 0.02760 0.518 0.627
## 54.27 99 1 0.564 0.02791 0.512 0.622
## 59.80 56 1 0.554 0.02918 0.500 0.614
## 61.83 51 1 0.543 0.03056 0.486 0.606
## 63.33 43 1 0.531 0.03235 0.471 0.598median_KM<- summary(fit)$table["median"]
print(median_KM)## median
## NA#KM median curve
plot(fit, xlab = "Time", ylab = "Survival Probability", main = "Kaplan-Meier with Median")
abline(h = 0.25, lty = 3, col = "brown")
abline(v = median_KM, lty = 3, col = "brown")
text(median_KM, 0.35, paste("Median:", round(median_KM, 1)), pos = 4, col = "brown")
#KM with C.I
plot(fit, xlab = "Time", ylab = "Survival Probability",
main = "Kaplan-Meier with Confidence Intervals",
conf.int = TRUE)
#predictor variable
km_trt <- survfit(surv_function ~ trt, data = diabetic)kaplan meier treatment group
plot(km_trt, xlab = "Time", ylab = "Survival Probability",
main = "Kaplan-Meier by Treatment Group",
col = c("purple", "yellow"))
legend("topright", legend = c("Placebo", "D-penicillamine"), col = c("purple", "yellow"), lty = 3) 
#mark.time
plot(fit, xlab = "Time", ylab = "Survival Probability",
main = "Kaplan-Meier with Marks", mark.time = TRUE)
#KM plot
plot(fit, main="KM Survival Curve", xlab="Time", ylab="Survival probability")
#Nelson Aalen plot
plot(fit,xlab = "Time", ylab = "Survival Probability", main = "Nelson Aalen Survival Curve")
#NA analysis
summary(fit)## Call: survfit(formula = surv_function ~ 1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.30 394 1 0.997 0.00253 0.993 1.000
## 0.60 393 1 0.995 0.00358 0.988 1.000
## 0.83 392 1 0.992 0.00438 0.984 1.000
## 1.33 391 1 0.990 0.00505 0.980 1.000
## 1.43 390 1 0.987 0.00564 0.976 0.998
## 1.50 385 2 0.982 0.00667 0.969 0.995
## 1.57 383 1 0.980 0.00713 0.966 0.994
## 1.63 382 2 0.974 0.00796 0.959 0.990
## 1.70 380 3 0.967 0.00906 0.949 0.985
## 1.73 377 1 0.964 0.00939 0.946 0.983
## 1.77 376 1 0.962 0.00971 0.943 0.981
## 1.80 375 1 0.959 0.01001 0.940 0.979
## 1.90 374 1 0.957 0.01031 0.937 0.977
## 1.97 373 1 0.954 0.01060 0.933 0.975
## 2.10 372 1 0.951 0.01087 0.930 0.973
## 2.17 371 1 0.949 0.01114 0.927 0.971
## 2.67 370 1 0.946 0.01140 0.924 0.969
## 2.70 369 1 0.944 0.01166 0.921 0.967
## 2.83 367 1 0.941 0.01191 0.918 0.965
## 2.90 366 1 0.939 0.01215 0.915 0.963
## 3.67 365 1 0.936 0.01238 0.912 0.961
## 4.10 363 1 0.933 0.01262 0.909 0.958
## 4.27 362 1 0.931 0.01284 0.906 0.956
## 4.30 361 1 0.928 0.01306 0.903 0.954
## 4.97 360 1 0.926 0.01328 0.900 0.952
## 5.33 359 1 0.923 0.01349 0.897 0.950
## 5.43 358 1 0.921 0.01370 0.894 0.948
## 5.67 357 1 0.918 0.01390 0.891 0.946
## 5.73 356 1 0.915 0.01410 0.888 0.943
## 5.77 355 1 0.913 0.01429 0.885 0.941
## 5.83 354 1 0.910 0.01448 0.882 0.939
## 5.90 353 1 0.908 0.01467 0.879 0.937
## 6.10 350 1 0.905 0.01485 0.876 0.935
## 6.13 349 1 0.902 0.01504 0.873 0.932
## 6.20 348 1 0.900 0.01521 0.871 0.930
## 6.30 347 1 0.897 0.01539 0.868 0.928
## 6.53 346 1 0.895 0.01556 0.865 0.926
## 6.57 345 2 0.889 0.01590 0.859 0.921
## 6.90 343 1 0.887 0.01606 0.856 0.919
## 7.07 342 1 0.884 0.01622 0.853 0.917
## 7.10 341 1 0.882 0.01638 0.850 0.914
## 7.60 339 1 0.879 0.01654 0.847 0.912
## 7.90 338 1 0.877 0.01669 0.844 0.910
## 8.30 335 2 0.871 0.01700 0.839 0.905
## 8.83 333 1 0.869 0.01715 0.836 0.903
## 9.40 332 1 0.866 0.01729 0.833 0.901
## 9.60 331 1 0.863 0.01744 0.830 0.898
## 9.63 330 1 0.861 0.01758 0.827 0.896
## 9.87 328 1 0.858 0.01772 0.824 0.894
## 9.90 326 3 0.850 0.01814 0.815 0.887
## 10.27 323 1 0.848 0.01827 0.813 0.884
## 10.33 322 1 0.845 0.01840 0.810 0.882
## 10.80 316 1 0.842 0.01854 0.807 0.879
## 10.97 315 1 0.840 0.01867 0.804 0.877
## 11.07 314 1 0.837 0.01880 0.801 0.875
## 11.30 313 1 0.834 0.01893 0.798 0.872
## 12.20 312 1 0.832 0.01906 0.795 0.870
## 12.73 311 1 0.829 0.01918 0.792 0.867
## 12.93 310 1 0.826 0.01931 0.789 0.865
## 13.10 309 1 0.824 0.01943 0.786 0.863
## 13.33 308 1 0.821 0.01955 0.784 0.860
## 13.37 307 1 0.818 0.01967 0.781 0.858
## 13.57 306 1 0.816 0.01978 0.778 0.855
## 13.77 305 2 0.810 0.02001 0.772 0.850
## 13.80 303 1 0.808 0.02012 0.769 0.848
## 13.83 302 4 0.797 0.02056 0.758 0.838
## 13.87 298 1 0.794 0.02066 0.755 0.836
## 13.90 297 1 0.792 0.02076 0.752 0.833
## 13.97 296 1 0.789 0.02086 0.749 0.831
## 14.00 295 1 0.786 0.02096 0.746 0.828
## 14.10 294 1 0.784 0.02106 0.743 0.826
## 14.27 293 1 0.781 0.02116 0.740 0.823
## 14.30 292 1 0.778 0.02126 0.738 0.821
## 14.37 291 1 0.775 0.02135 0.735 0.818
## 14.80 289 1 0.773 0.02144 0.732 0.816
## 15.83 288 1 0.770 0.02154 0.729 0.814
## 17.73 286 1 0.767 0.02163 0.726 0.811
## 18.03 285 2 0.762 0.02181 0.720 0.806
## 18.43 283 1 0.759 0.02190 0.718 0.804
## 18.70 282 1 0.757 0.02199 0.715 0.801
## 18.93 278 1 0.754 0.02207 0.712 0.798
## 19.00 277 1 0.751 0.02216 0.709 0.796
## 19.40 276 1 0.748 0.02225 0.706 0.793
## 20.17 274 1 0.746 0.02233 0.703 0.791
## 21.10 271 1 0.743 0.02242 0.700 0.788
## 21.57 270 1 0.740 0.02251 0.697 0.786
## 21.90 268 1 0.737 0.02259 0.695 0.783
## 21.97 267 1 0.735 0.02267 0.692 0.781
## 22.00 266 2 0.729 0.02284 0.686 0.775
## 22.13 264 1 0.726 0.02292 0.683 0.773
## 22.20 263 1 0.724 0.02300 0.680 0.770
## 22.23 262 1 0.721 0.02307 0.677 0.768
## 24.43 259 1 0.718 0.02315 0.674 0.765
## 24.73 258 1 0.715 0.02323 0.671 0.762
## 25.30 257 1 0.713 0.02331 0.668 0.760
## 25.63 256 1 0.710 0.02338 0.665 0.757
## 25.80 255 1 0.707 0.02345 0.663 0.755
## 25.93 252 1 0.704 0.02353 0.660 0.752
## 26.17 251 1 0.701 0.02360 0.657 0.749
## 26.20 250 1 0.699 0.02367 0.654 0.747
## 26.23 249 1 0.696 0.02374 0.651 0.744
## 26.37 248 1 0.693 0.02381 0.648 0.741
## 26.47 247 1 0.690 0.02388 0.645 0.739
## 27.60 244 1 0.687 0.02395 0.642 0.736
## 29.97 241 1 0.684 0.02402 0.639 0.733
## 30.20 240 1 0.682 0.02409 0.636 0.731
## 30.40 239 1 0.679 0.02416 0.633 0.728
## 30.83 238 1 0.676 0.02422 0.630 0.725
## 31.30 235 1 0.673 0.02429 0.627 0.722
## 31.63 232 1 0.670 0.02436 0.624 0.720
## 33.63 225 2 0.664 0.02450 0.618 0.714
## 33.90 223 1 0.661 0.02457 0.615 0.711
## 34.37 220 1 0.658 0.02464 0.612 0.708
## 34.57 219 1 0.655 0.02471 0.609 0.705
## 35.53 218 1 0.652 0.02478 0.605 0.703
## 38.40 207 1 0.649 0.02486 0.602 0.700
## 38.47 206 1 0.646 0.02494 0.599 0.697
## 38.57 205 2 0.640 0.02509 0.592 0.691
## 38.87 195 1 0.636 0.02518 0.589 0.688
## 41.40 185 1 0.633 0.02527 0.585 0.684
## 42.17 177 2 0.626 0.02549 0.578 0.678
## 42.33 167 1 0.622 0.02561 0.574 0.674
## 42.43 166 1 0.618 0.02573 0.570 0.671
## 43.03 161 1 0.614 0.02585 0.566 0.667
## 43.33 158 1 0.611 0.02598 0.562 0.664
## 43.70 155 1 0.607 0.02611 0.557 0.660
## 46.20 145 1 0.602 0.02626 0.553 0.656
## 46.27 140 1 0.598 0.02643 0.548 0.652
## 46.43 136 1 0.594 0.02660 0.544 0.648
## 46.63 133 1 0.589 0.02677 0.539 0.644
## 48.30 128 1 0.585 0.02695 0.534 0.640
## 48.43 127 1 0.580 0.02713 0.529 0.636
## 48.87 125 1 0.575 0.02731 0.524 0.631
## 54.10 104 1 0.570 0.02760 0.518 0.627
## 54.27 99 1 0.564 0.02791 0.512 0.622
## 59.80 56 1 0.554 0.02918 0.500 0.614
## 61.83 51 1 0.543 0.03056 0.486 0.606
## 63.33 43 1 0.531 0.03235 0.471 0.598median_NA<- summary(fit)$table["median"]
print(median_NA)## median
## NA#Nelson Aalen curve with median
plot(fit, xlab = "Time", ylab = "Survival Probability", main = "Nelson Aalen with Median")
abline(h = 0.25, lty = 3, col = "blue")
abline(v = median_NA, lty = 3, col = "blue")
#log rank test- for comparison of two or more groups
log_rank <- survdiff(surv_function ~ trt, data = diabetic)
print(log_rank)## Call:
## survdiff(formula = surv_function ~ trt, data = diabetic)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 101 71.8 11.9 22.2
## trt=1 197 54 83.2 10.3 22.2
##
## Chisq= 22.2 on 1 degrees of freedom, p= 2e-06##p value is < 0.05, we reject the null hypothesis and conclude that there is a statistically significant difference between the curves. #cox proportional hazard summarized model
cox_model <- coxph(surv_function ~ age + trt, data = diabetic)
print(summary(cox_model))## Call:
## coxph(formula = surv_function ~ age + trt, data = diabetic)
##
## n= 394, number of events= 155
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age 0.004034 1.004042 0.005472 0.737 0.461
## trt -0.782149 0.457422 0.168971 -4.629 3.68e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age 1.0040 0.996 0.9933 1.015
## trt 0.4574 2.186 0.3285 0.637
##
## Concordance= 0.591 (se = 0.025 )
## Likelihood ratio test= 22.91 on 2 df, p=1e-05
## Wald test = 21.7 on 2 df, p=2e-05
## Score (logrank) test = 22.78 on 2 df, p=1e-05#coxph assumptions
cox_zph_result <- cox.zph(cox_model)
print(cox_zph_result)## chisq df p
## age 0.319 1 0.57
## trt 0.528 1 0.47
## GLOBAL 0.902 2 0.64plot(cox_zph_result)
#plot cox model
plot(fit,xlab = "Time", ylab = "Survival Probability", main = "Cox model Survival Curve")
#The End!!!