Homework 2
Evan Hardinger
2026-02-03
Q1.
library(psfmi)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(survival)
mye <- read.csv("C:/Users/riema/Downloads/myeloma.csv")
str(mye)## 'data.frame': 48 obs. of 10 variables:
## $ patient: int 1 2 3 4 5 6 7 8 9 10 ...
## $ time : int 13 52 6 40 10 7 66 10 10 14 ...
## $ status : int 1 0 1 1 1 0 1 0 1 1 ...
## $ age : int 66 66 53 69 65 57 52 60 70 70 ...
## $ sex : int 1 1 2 1 1 2 1 1 1 1 ...
## $ bun : int 25 13 15 10 20 12 21 41 37 40 ...
## $ ca : int 10 11 13 10 10 8 10 9 12 11 ...
## $ hb : num 14.6 12 11.4 10.2 13.2 9.9 12.8 14 7.5 10.6 ...
## $ pcells : int 18 100 33 30 66 45 11 70 47 27 ...
## $ protein: int 1 0 1 1 0 0 1 1 0 0 ...summary(mye)## patient time status age sex
## Min. : 1.00 Min. : 1.00 Min. :0.00 Min. :50.00 Min. :1.000
## 1st Qu.:12.75 1st Qu.: 6.75 1st Qu.:0.75 1st Qu.:58.75 1st Qu.:1.000
## Median :24.50 Median :14.50 Median :1.00 Median :62.50 Median :1.000
## Mean :24.50 Mean :23.38 Mean :0.75 Mean :62.90 Mean :1.396
## 3rd Qu.:36.25 3rd Qu.:37.00 3rd Qu.:1.00 3rd Qu.:68.25 3rd Qu.:2.000
## Max. :48.00 Max. :91.00 Max. :1.00 Max. :77.00 Max. :2.000
## bun ca hb pcells
## Min. : 6.00 Min. : 8.000 Min. : 4.90 Min. : 3.00
## 1st Qu.: 13.75 1st Qu.: 9.000 1st Qu.: 8.65 1st Qu.: 21.25
## Median : 21.00 Median :10.000 Median :10.20 Median : 33.00
## Mean : 33.92 Mean : 9.938 Mean :10.25 Mean : 42.94
## 3rd Qu.: 39.25 3rd Qu.:10.000 3rd Qu.:12.57 3rd Qu.: 63.00
## Max. :172.00 Max. :15.000 Max. :14.60 Max. :100.00
## protein
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.3125
## 3rd Qu.:1.0000
## Max. :1.0000# Make sure sex is treated as a factor
mye$sex <- factor(mye$sex, levels = c(1,2), labels = c("Male","Female"))
S <- Surv(time = mye$time, event = mye$status)
# Fit Cox Proportional Hazards model
cox_fit <- coxph(S ~ bun + ca + hb + pcells + protein + age + sex, data = mye)
# Display model summary
summary(cox_fit)## Call:
## coxph(formula = S ~ bun + ca + hb + pcells + protein + age +
## sex, data = mye)
##
## n= 48, number of events= 36
##
## coef exp(coef) se(coef) z Pr(>|z|)
## bun 0.022661 1.022919 0.006110 3.709 0.000208 ***
## ca 0.013265 1.013353 0.132681 0.100 0.920363
## hb -0.133017 0.875450 0.068527 -1.941 0.052249 .
## pcells -0.001359 0.998642 0.006588 -0.206 0.836585
## protein -0.683269 0.504964 0.429395 -1.591 0.111556
## age -0.018056 0.982106 0.027833 -0.649 0.516521
## sexFemale -0.249473 0.779211 0.403093 -0.619 0.535985
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## bun 1.0229 0.9776 1.0107 1.035
## ca 1.0134 0.9868 0.7813 1.314
## hb 0.8755 1.1423 0.7654 1.001
## pcells 0.9986 1.0014 0.9858 1.012
## protein 0.5050 1.9803 0.2177 1.172
## age 0.9821 1.0182 0.9300 1.037
## sexFemale 0.7792 1.2833 0.3536 1.717
##
## Concordance= 0.705 (se = 0.048 )
## Likelihood ratio test= 17.53 on 7 df, p=0.01
## Wald test = 20.01 on 7 df, p=0.006
## Score (logrank) test = 25.59 on 7 df, p=6e-04##Q2.
pro <- read.csv("C:/Users/riema/Downloads/prostatic.csv")
str(pro)## 'data.frame': 38 obs. of 8 variables:
## $ patient : int 1 2 3 4 5 6 7 8 9 10 ...
## $ treatment: int 1 2 2 1 2 1 1 1 2 1 ...
## $ time : int 65 61 60 58 51 51 14 43 16 52 ...
## $ status : int 0 0 0 0 0 0 1 0 0 0 ...
## $ age : int 67 60 77 64 65 61 73 60 73 73 ...
## $ shb : num 13.4 14.6 15.6 16.2 14.1 13.5 12.4 13.6 13.8 11.7 ...
## $ size : int 34 4 3 6 21 8 18 7 8 5 ...
## $ index : int 8 10 8 9 9 8 11 9 9 9 ...summary(pro)## patient treatment time status
## Min. : 1.00 Min. :1.000 Min. : 2.00 Min. :0.0000
## 1st Qu.:10.25 1st Qu.:1.000 1st Qu.:42.25 1st Qu.:0.0000
## Median :19.50 Median :2.000 Median :56.00 Median :0.0000
## Mean :19.50 Mean :1.526 Mean :49.74 Mean :0.1579
## 3rd Qu.:28.75 3rd Qu.:2.000 3rd Qu.:65.00 3rd Qu.:0.0000
## Max. :38.00 Max. :2.000 Max. :70.00 Max. :1.0000
## age shb size index
## Min. :51.00 Min. :10.70 Min. : 2.00 Min. : 6.000
## 1st Qu.:65.00 1st Qu.:13.43 1st Qu.: 4.00 1st Qu.: 8.000
## Median :71.00 Median :13.85 Median : 7.50 Median : 9.000
## Mean :68.63 Mean :13.94 Mean :10.47 Mean : 9.132
## 3rd Qu.:73.00 3rd Qu.:14.68 3rd Qu.:13.75 3rd Qu.:10.000
## Max. :77.00 Max. :16.40 Max. :37.00 Max. :12.000S <- Surv(time = pro$time, event = pro$status)
cox_age <- coxph(S ~ age, data = pro)
cox_shb <- coxph(S ~ shb, data = pro)
cox_size <- coxph(S ~ size, data = pro)
cox_index <- coxph(S ~ index, data = pro)
summary(cox_age)## Call:
## coxph(formula = S ~ age, data = pro)
##
## n= 38, number of events= 6
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age -0.01683 0.98331 0.05879 -0.286 0.775
##
## exp(coef) exp(-coef) lower .95 upper .95
## age 0.9833 1.017 0.8763 1.103
##
## Concordance= 0.46 (se = 0.123 )
## Likelihood ratio test= 0.08 on 1 df, p=0.8
## Wald test = 0.08 on 1 df, p=0.8
## Score (logrank) test = 0.08 on 1 df, p=0.8summary(cox_shb)## Call:
## coxph(formula = S ~ shb, data = pro)
##
## n= 38, number of events= 6
##
## coef exp(coef) se(coef) z Pr(>|z|)
## shb 0.1231 1.1310 0.3168 0.389 0.698
##
## exp(coef) exp(-coef) lower .95 upper .95
## shb 1.131 0.8841 0.6078 2.105
##
## Concordance= 0.503 (se = 0.15 )
## Likelihood ratio test= 0.15 on 1 df, p=0.7
## Wald test = 0.15 on 1 df, p=0.7
## Score (logrank) test = 0.15 on 1 df, p=0.7summary(cox_size)## Call:
## coxph(formula = S ~ size, data = pro)
##
## n= 38, number of events= 6
##
## coef exp(coef) se(coef) z Pr(>|z|)
## size 0.10143 1.10676 0.03739 2.713 0.00667 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## size 1.107 0.9035 1.029 1.191
##
## Concordance= 0.763 (se = 0.118 )
## Likelihood ratio test= 7.31 on 1 df, p=0.007
## Wald test = 7.36 on 1 df, p=0.007
## Score (logrank) test = 9.64 on 1 df, p=0.002summary(cox_index)## Call:
## coxph(formula = S ~ index, data = pro)
##
## n= 38, number of events= 6
##
## coef exp(coef) se(coef) z Pr(>|z|)
## index 0.8794 2.4094 0.3473 2.532 0.0113 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## index 2.409 0.415 1.22 4.759
##
## Concordance= 0.84 (se = 0.072 )
## Likelihood ratio test= 7.22 on 1 df, p=0.007
## Wald test = 6.41 on 1 df, p=0.01
## Score (logrank) test = 7.26 on 1 df, p=0.007So tumor size and Gleason index have p-values less than 0.05, therefore they are significantly associated with survival time.
pro$treatment <- factor(pro$treatment, levels = c(1,2), labels = c("Placebo","DES"))
cox_adj <- coxph(S ~ treatment + size + index, data = pro)
summary(cox_adj)## Call:
## coxph(formula = S ~ treatment + size + index, data = pro)
##
## n= 38, number of events= 6
##
## coef exp(coef) se(coef) z Pr(>|z|)
## treatmentDES -1.11272 0.32866 1.20313 -0.925 0.3550
## size 0.08257 1.08608 0.04746 1.740 0.0819 .
## index 0.71025 2.03450 0.33791 2.102 0.0356 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## treatmentDES 0.3287 3.0426 0.03109 3.474
## size 1.0861 0.9207 0.98961 1.192
## index 2.0345 0.4915 1.04913 3.945
##
## Concordance= 0.873 (se = 0.071 )
## Likelihood ratio test= 13.78 on 3 df, p=0.003
## Wald test = 10.29 on 3 df, p=0.02
## Score (logrank) test = 14.9 on 3 df, p=0.002Q3.
lung <- read.csv("C:/Users/riema/Downloads/lung.csv")
str(lung) ## 'data.frame': 196 obs. of 7 variables:
## $ patient: int 1 2 3 4 5 6 7 8 9 10 ...
## $ time : int 2324 108 2939 1258 2904 444 158 1686 142 1624 ...
## $ status : int 1 1 0 0 0 1 1 1 1 1 ...
## $ age : int 59 28 55 62 51 59 55 53 47 53 ...
## $ gender : int 1 1 1 1 1 1 2 2 1 2 ...
## $ bmi : num 29.6 22.6 32.1 30 30.4 26.9 24.6 26.8 32.2 15.7 ...
## $ disease: int 1 3 2 2 2 2 1 1 2 1 ...summary(lung)## patient time status age
## Min. : 1.00 Min. : 3.0 Min. :0.0000 Min. :18.00
## 1st Qu.: 49.75 1st Qu.: 182.2 1st Qu.:0.0000 1st Qu.:41.75
## Median : 98.50 Median : 843.5 Median :1.0000 Median :53.00
## Mean : 98.50 Mean :1182.2 Mean :0.6276 Mean :48.56
## 3rd Qu.:147.25 3rd Qu.:2387.5 3rd Qu.:1.0000 3rd Qu.:58.00
## Max. :196.00 Max. :2939.0 Max. :1.0000 Max. :67.00
## gender bmi disease
## Min. :1.000 Min. :14.00 Min. :1.000
## 1st Qu.:1.000 1st Qu.:19.50 1st Qu.:1.000
## Median :1.000 Median :22.60 Median :2.000
## Mean :1.429 Mean :23.42 Mean :2.168
## 3rd Qu.:2.000 3rd Qu.:27.52 3rd Qu.:3.000
## Max. :2.000 Max. :35.20 Max. :4.000S <- Surv(time = lung$time, event = lung$status)
km_fit <- survfit(S ~ 1, data = lung)
summary(km_fit)## Call: survfit(formula = S ~ 1, data = lung)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 3 196 1 0.995 0.00509 0.985 1.000
## 4 195 1 0.990 0.00718 0.976 1.000
## 16 193 1 0.985 0.00878 0.968 1.000
## 21 192 1 0.980 0.01013 0.960 1.000
## 22 191 1 0.974 0.01130 0.953 0.997
## 25 190 1 0.969 0.01235 0.945 0.994
## 29 189 1 0.964 0.01330 0.938 0.991
## 31 188 2 0.954 0.01501 0.925 0.984
## 38 186 2 0.944 0.01651 0.912 0.977
## 55 184 1 0.939 0.01720 0.905 0.973
## 61 183 1 0.933 0.01785 0.899 0.969
## 63 182 1 0.928 0.01847 0.893 0.965
## 65 181 1 0.923 0.01907 0.886 0.961
## 70 180 1 0.918 0.01964 0.880 0.957
## 73 179 1 0.913 0.02019 0.874 0.953
## 76 178 1 0.908 0.02072 0.868 0.949
## 80 177 1 0.903 0.02123 0.862 0.945
## 85 176 1 0.897 0.02172 0.856 0.941
## 88 175 1 0.892 0.02219 0.850 0.937
## 92 174 1 0.887 0.02265 0.844 0.933
## 95 173 1 0.882 0.02309 0.838 0.929
## 104 172 1 0.877 0.02352 0.832 0.924
## 108 171 1 0.872 0.02393 0.826 0.920
## 114 170 1 0.867 0.02434 0.820 0.916
## 121 169 2 0.856 0.02511 0.809 0.907
## 123 167 1 0.851 0.02547 0.803 0.903
## 124 166 1 0.846 0.02583 0.797 0.898
## 128 165 1 0.841 0.02618 0.791 0.894
## 132 164 1 0.836 0.02652 0.786 0.890
## 134 163 1 0.831 0.02685 0.780 0.885
## 136 162 1 0.826 0.02717 0.774 0.881
## 142 161 1 0.821 0.02748 0.768 0.876
## 148 160 1 0.815 0.02778 0.763 0.872
## 151 159 1 0.810 0.02807 0.757 0.867
## 153 158 1 0.805 0.02836 0.751 0.863
## 158 157 3 0.790 0.02918 0.735 0.849
## 159 154 1 0.785 0.02943 0.729 0.845
## 162 153 1 0.780 0.02969 0.723 0.840
## 165 152 1 0.774 0.02993 0.718 0.835
## 169 151 1 0.769 0.03017 0.712 0.831
## 174 150 1 0.764 0.03040 0.707 0.826
## 175 149 1 0.759 0.03063 0.701 0.821
## 177 148 1 0.754 0.03084 0.696 0.817
## 184 147 1 0.749 0.03106 0.690 0.812
## 192 146 2 0.739 0.03147 0.679 0.803
## 199 144 1 0.733 0.03166 0.674 0.798
## 203 143 1 0.728 0.03186 0.668 0.793
## 209 142 1 0.723 0.03204 0.663 0.789
## 231 141 1 0.718 0.03222 0.658 0.784
## 237 140 1 0.713 0.03240 0.652 0.779
## 239 139 1 0.708 0.03257 0.647 0.775
## 257 138 1 0.703 0.03273 0.641 0.770
## 273 136 1 0.697 0.03290 0.636 0.765
## 278 135 1 0.692 0.03306 0.630 0.760
## 288 134 1 0.687 0.03321 0.625 0.755
## 290 133 1 0.682 0.03336 0.620 0.751
## 294 132 1 0.677 0.03351 0.614 0.746
## 310 131 1 0.672 0.03365 0.609 0.741
## 311 130 1 0.666 0.03378 0.603 0.736
## 313 129 1 0.661 0.03391 0.598 0.731
## 320 128 1 0.656 0.03404 0.593 0.726
## 335 125 1 0.651 0.03417 0.587 0.721
## 343 124 1 0.646 0.03429 0.582 0.716
## 354 123 1 0.640 0.03441 0.576 0.711
## 371 121 1 0.635 0.03453 0.571 0.706
## 410 120 1 0.630 0.03465 0.565 0.701
## 431 118 1 0.624 0.03477 0.560 0.696
## 437 117 1 0.619 0.03488 0.554 0.691
## 444 116 1 0.614 0.03498 0.549 0.686
## 461 115 1 0.608 0.03508 0.543 0.681
## 535 113 1 0.603 0.03518 0.538 0.676
## 549 112 1 0.598 0.03528 0.532 0.671
## 563 111 1 0.592 0.03537 0.527 0.666
## 625 109 1 0.587 0.03546 0.521 0.661
## 642 108 1 0.581 0.03554 0.516 0.655
## 683 106 1 0.576 0.03563 0.510 0.650
## 689 105 1 0.570 0.03571 0.505 0.645
## 697 104 1 0.565 0.03578 0.499 0.640
## 711 103 2 0.554 0.03592 0.488 0.629
## 744 101 1 0.548 0.03598 0.482 0.624
## 749 100 1 0.543 0.03604 0.477 0.618
## 797 99 1 0.538 0.03609 0.471 0.613
## 890 98 1 0.532 0.03613 0.466 0.608
## 962 96 1 0.526 0.03618 0.460 0.602
## 967 95 1 0.521 0.03622 0.455 0.597
## 969 94 1 0.515 0.03626 0.449 0.592
## 1032 92 1 0.510 0.03629 0.443 0.586
## 1104 89 1 0.504 0.03634 0.438 0.581
## 1125 87 1 0.498 0.03638 0.432 0.575
## 1173 85 1 0.492 0.03642 0.426 0.569
## 1208 84 1 0.487 0.03645 0.420 0.564
## 1290 81 1 0.481 0.03650 0.414 0.558
## 1321 80 1 0.475 0.03653 0.408 0.552
## 1405 76 1 0.468 0.03658 0.402 0.546
## 1419 75 1 0.462 0.03662 0.396 0.540
## 1474 74 1 0.456 0.03665 0.389 0.534
## 1477 73 1 0.450 0.03668 0.383 0.528
## 1553 71 1 0.443 0.03671 0.377 0.521
## 1624 69 1 0.437 0.03673 0.370 0.515
## 1686 68 1 0.430 0.03675 0.364 0.509
## 1836 67 1 0.424 0.03676 0.358 0.502
## 1901 66 1 0.418 0.03676 0.351 0.496
## 1987 65 1 0.411 0.03675 0.345 0.490
## 1991 64 1 0.405 0.03673 0.339 0.483
## 2071 62 1 0.398 0.03672 0.332 0.477
## 2162 60 1 0.392 0.03670 0.326 0.470
## 2212 59 1 0.385 0.03667 0.319 0.464
## 2230 58 1 0.378 0.03663 0.313 0.457
## 2303 56 1 0.372 0.03660 0.306 0.451
## 2317 55 1 0.365 0.03655 0.300 0.444
## 2324 54 1 0.358 0.03649 0.293 0.437
## 2349 53 1 0.351 0.03642 0.287 0.430
## 2375 51 1 0.344 0.03635 0.280 0.424
## 2378 50 1 0.337 0.03627 0.273 0.417
## 2479 44 1 0.330 0.03625 0.266 0.409
## 2550 35 1 0.320 0.03642 0.256 0.400cage <- coxph(S ~ age, data = lung)
cgen <- coxph(S ~ gender, data = lung)
cbmi <- coxph(S ~ bmi, data = lung)
summary(cage)## Call:
## coxph(formula = S ~ age, data = lung)
##
## n= 196, number of events= 123
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age 0.002686 1.002690 0.007549 0.356 0.722
##
## exp(coef) exp(-coef) lower .95 upper .95
## age 1.003 0.9973 0.988 1.018
##
## Concordance= 0.535 (se = 0.028 )
## Likelihood ratio test= 0.13 on 1 df, p=0.7
## Wald test = 0.13 on 1 df, p=0.7
## Score (logrank) test = 0.13 on 1 df, p=0.7summary(cgen)## Call:
## coxph(formula = S ~ gender, data = lung)
##
## n= 196, number of events= 123
##
## coef exp(coef) se(coef) z Pr(>|z|)
## gender -0.1532 0.8580 0.1840 -0.833 0.405
##
## exp(coef) exp(-coef) lower .95 upper .95
## gender 0.858 1.166 0.5982 1.231
##
## Concordance= 0.53 (se = 0.023 )
## Likelihood ratio test= 0.7 on 1 df, p=0.4
## Wald test = 0.69 on 1 df, p=0.4
## Score (logrank) test = 0.69 on 1 df, p=0.4summary(cbmi)## Call:
## coxph(formula = S ~ bmi, data = lung)
##
## n= 196, number of events= 123
##
## coef exp(coef) se(coef) z Pr(>|z|)
## bmi 0.02111 1.02134 0.01916 1.102 0.271
##
## exp(coef) exp(-coef) lower .95 upper .95
## bmi 1.021 0.9791 0.9837 1.06
##
## Concordance= 0.539 (se = 0.027 )
## Likelihood ratio test= 1.2 on 1 df, p=0.3
## Wald test = 1.21 on 1 df, p=0.3
## Score (logrank) test = 1.22 on 1 df, p=0.3cox_adj <- coxph(S ~ age + gender + bmi, data = lung)
summary(cox_adj)## Call:
## coxph(formula = S ~ age + gender + bmi, data = lung)
##
## n= 196, number of events= 123
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age -0.0002291 0.9997709 0.0080964 -0.028 0.977
## gender -0.1088577 0.8968580 0.1905332 -0.571 0.568
## bmi 0.0183592 1.0185287 0.0209644 0.876 0.381
##
## exp(coef) exp(-coef) lower .95 upper .95
## age 0.9998 1.0002 0.9840 1.016
## gender 0.8969 1.1150 0.6174 1.303
## bmi 1.0185 0.9818 0.9775 1.061
##
## Concordance= 0.551 (se = 0.027 )
## Likelihood ratio test= 1.53 on 3 df, p=0.7
## Wald test = 1.54 on 3 df, p=0.7
## Score (logrank) test = 1.54 on 3 df, p=0.7ph_test <- cox.zph(cox_adj)
print(ph_test)## chisq df p
## age 0.105 1 0.75
## gender 1.893 1 0.17
## bmi 1.493 1 0.22
## GLOBAL 2.718 3 0.44plot(ph_test)
ph_test$table## chisq df p
## age 0.1047716 1 0.7461769
## gender 1.8928713 1 0.1688784
## bmi 1.4931801 1 0.2217237
## GLOBAL 2.7183117 3 0.4371244None have a p-value of less than 0.05, so none of them appear to be time dependent
Q4.
library(dplyr)
library(survival)
jasa <- read.csv("C:/Users/riema/Downloads/jasa.csv")
jasa2 <- subset(jasa, futime > 0)
jasa2$id<-seq_len(nrow(jasa2))
td <- tmerge(
data1 = jasa2,
data2 = jasa2,
id =id,
death = event(futime, fustat),
transplant0 = tdc(wait.time)
)
names(td)## [1] "birth.dt" "accept.dt" "tx.date" "fu.date" "fustat"
## [6] "surgery" "age" "futime" "wait.time" "transplant"
## [11] "mismatch" "hla.a2" "mscore" "reject" "id"
## [16] "tstart" "tstop" "death" "transplant0"cox_td <- coxph(
Surv(tstart, tstop, death) ~ transplant0 + age + mscore,
data = td
)
summary(cox_td)## Call:
## coxph(formula = Surv(tstart, tstop, death) ~ transplant0 + age +
## mscore, data = td)
##
## n= 127, number of events= 41
## (41 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## transplant0 2.75015 15.64499 1.10408 2.491 0.0127 *
## age 0.05674 1.05838 0.02313 2.453 0.0142 *
## mscore 0.46274 1.58842 0.28345 1.633 0.1026
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## transplant0 15.645 0.06392 1.7971 136.199
## age 1.058 0.94484 1.0115 1.107
## mscore 1.588 0.62956 0.9114 2.768
##
## Concordance= 0.708 (se = 0.045 )
## Likelihood ratio test= 22.14 on 3 df, p=6e-05
## Wald test = 14.99 on 3 df, p=0.002
## Score (logrank) test = 17.46 on 3 df, p=6e-04test <- cox.zph(cox_td)
test## chisq df p
## transplant0 0.449 1 0.50
## age 1.881 1 0.17
## mscore 0.917 1 0.34
## GLOBAL 3.396 3 0.33None of the p-values are less than 0.05, therefore we can determine that the proportional hazards assumption for this model holds.
Treating the transplant as a time-dependent covariate allows the model to produce an estimate of the effect of the transplant by comparing mortality risk of patients who are waiting and patients who have recieved a transplant.
The hazards ratio given from our transplant0 covariate indicate that a patient’s risk of death is approximately 94% lower than before transplant.