Cox Proportional Hazards Model for Survival Analysis

> Survival= read.csv('Survival.csv')
> head(Survival)
ID X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 time1 status1 time2
1 066-0556 0 0 1 1 1 0 1 0 1 0 1 0 0 1129 0 366
2 041-2483 0 1 1 0 0 0 0 0 1 0 1 0 0 823 0 187
3 014-0836 0 0 1 1 1 0 0 0 1 0 0 0 0 797 0 366
4 033-0648 0 1 1 1 1 1 0 0 1 0 1 0 0 764 0 366
5 067-0126 0 1 1 1 1 0 0 0 1 0 0 0 0 741 0 366
6 066-0522 1 0 1 1 1 0 0 0 1 0 0 0 0 720 0 366
status2
1 0
2 0
3 0
4 0
5 0
6 0
> dim(Survival)
[1] 10687 18
> library(survival)
> dim(Survival)
[1] 10687 18
> y = Surv(Survival$time1,Survival$status1==1)
> x =Surv(Survival$time2,Survival$status2==1)
> model1= coxph(y~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12, data = Survival)
> summary(model1)
Call:
coxph(formula = y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 +
X10 + X11 + X12, data = Survival)
n= 10687, number of events= 638
coef exp(coef) se(coef) z Pr(>|z|)

X1 -0.37767 0.68546 0.11201 -3.372 0.000747 ***
X2 0.40135 1.49385 0.05183 7.743 9.69e-15 ***
X3 -1.78953 0.16704 0.09085 -19.698 < 2e-16 ***
X4 -1.17933 0.30748 0.08792 -13.414 < 2e-16 ***
X5 -0.73531 0.47936 0.10084 -7.292 3.05e-13 ***
X6 0.74169 2.09947 0.08930 8.306 < 2e-16 ***
X7 0.47168 1.60269 0.08303 5.681 1.34e-08 ***
X8 0.53454 1.70666 0.10934 4.889 1.01e-06 ***
X9 -0.91524 0.40042 0.24974 -3.665 0.000248 ***
X10 0.43303 1.54192 0.12677 3.416 0.000636 ***
X11 -0.31732 0.72810 0.08507 -3.730 0.000191 ***
X12 0.33538 1.39847 0.08924 3.758 0.000171 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
exp(coef) exp(-coef) lower .95 upper .95
X1 0.6855 1.4589 0.5504 0.8537
X2 1.4938 0.6694 1.3495 1.6536
X3 0.1670 5.9866 0.1398 0.1996
X4 0.3075 3.2522 0.2588 0.3653
X5 0.4794 2.0861 0.3934 0.5841
X6 2.0995 0.4763 1.7624 2.5010
X7 1.6027 0.6240 1.3620 1.8859
X8 1.7067 0.5859 1.3775 2.1146
X9 0.4004 2.4974 0.2454 0.6533
X10 1.5419 0.6485 1.2027 1.9768
X11 0.7281 1.3734 0.6163 0.8602
X12 1.3985 0.7151 1.1741 1.6658
Concordance= 0.84 (se = 0.012 )
Rsquare= 0.142 (max possible= 0.663 )
Likelihood ratio test= 1632 on 12 df, p=<2e-16

Wald test = 1911 on 12 df, p=<2e-16
Score (logrank) test = 3280 on 12 df, p=<2e-16
> model2 = coxph(y~X1+X2+X8+X12+X13,data = Survival)
> summary(model2)
Call:
coxph(formula = y ~ X1 + X2 + X8 + X12 + X13, data = Survival)
n= 10687, number of events= 638
coef exp(coef) se(coef) z Pr(>|z|)
X1 -0.54984 0.57704 0.11042 -4.979 6.38e-07 ***
X2 0.54871 1.73102 0.05209 10.534 < 2e-16 ***
X8 1.18657 3.27582 0.10872 10.914 < 2e-16 ***
X12 0.56976 1.76785 0.09221 6.179 6.46e-10 ***
X13 -0.25291 0.77654 0.24649 -1.026 0.305
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
exp(coef) exp(-coef) lower .95 upper .95
X1 0.5770 1.7330 0.4647 0.7165
X2 1.7310 0.5777 1.5630 1.9171
X8 3.2758 0.3053 2.6471 4.0538
X12 1.7678 0.5657 1.4755 2.1181
X13 0.7765 1.2878 0.4790 1.2589
Concordance= 0.734 (se = 0.011 )
Rsquare= 0.045 (max possible= 0.663 )
Likelihood ratio test= 487.6 on 5 df, p=<2e-16
Wald test = 543 on 5 df, p=<2e-16
Score (logrank) test = 673 on 5 df, p=<2e-16