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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?

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    $\begingroup$ 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. $\endgroup$
    – Todd D
    Nov 30, 2017 at 23:31
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    $\begingroup$ 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 $1 - c$. $\endgroup$
    – Frank Harrell
    Dec 1, 2017 at 12:42

1 Answer 1

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From the documentation on predict.coxph, the choices for type are

" the linear predictor ("lp"), the risk score exp(lp) ("risk"), the expected number of events given the covariates and follow-up time ("expected"), and the terms of the linear predictor ("terms"). The survival probability for a subject is equal to exp(-expected)"

These are not all numerically the same things. As far as I know, the concordance index for survival analysis is designed to run only on the predicted risk, which is the default output of the coxph function.

For example, the documentation on concordance.index function in the survcomp package says that the input x must be a predicted risk.

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