# How to interpret concordance index in Cox models?

I'm new using the survival package in R. Consider an example provided with the package:

library(survival)
fit <- coxph(Surv(time, status) ~ ph.ecog + age + sex, lung)


If I compute the concordance index, I get:

survConcordance(Surv(time, status) ~ predict(fit, lung), lung)

Call:
survConcordance(formula = Surv(time, status) ~ predict(fit, lung),
data = lung)

n=227 (1 observation deleted due to missingness)
Concordance= 0.6371355 se= 0.0261339
concordant discordant  tied.risk  tied.time   std(c-d)
12544.000   7117.000    126.000     28.000   1034.223


What I would like to understand is the interpretation of the concordance index if I change the prediction type, i.e.:

survConcordance(Surv(time, status) ~ predict(fit, lung, type = "expected"), lung)

Call:
survConcordance(formula = Surv(time, status) ~ predict(fit, lung, type = "expected"), data = lung)

n=227 (1 observation deleted due to missingness)
Concordance= 0.1505787 se= 0.02613595
concordant discordant  tied.risk  tied.time   std(c-d)
2978.000  16806.000      3.000     28.000   1034.304


Is it correct to do this? If yes, what does it mean to change from 0.6371355 to 0.1505787? If not, what would be the correct way to check the expected number of events given the covariates and follow-up time?

• The decrease in concordance suggests worse fit. I recommend using the AIC and not a censored c-index or other concordance measure to determine fit. Nov 30, 2017 at 23:31
• Look at the distribution of predicted values for both ways of getting predictions. Note that linear predictor in the Cox model is such that larger is higher hazard so shorter survival time. Predicted life length runs the opposite so you'll get $c$ and $1 - c$. Dec 1, 2017 at 12:42