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How would you go about validating a Cox PH model with censored data?

I am trying to run a Cox PH model on a dataset with observations that failed, and observations that are censored. Normally, I use a half and half build and test split, and then run the model on the testing data to validate. Is the mean close to the test data actual mean? And then I look at univariate plot of my predicted to actual for variables in my dataset to see if I am missing anything important.

Because of the censored data, I am having trouble doing this. My original thought was that I would only need to validate the results against the observations that failed, but the censored observations only decrease the hazard rate, so I will always over-predict the mean survival time of the observations that failed. In addition I can't look at the univariate plots because the means do not match! So there is no value in "seeing where the model is missing", because it is missing everything (the mean).

How would you go about validating a Cox PH model with censored data?

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  • $\begingroup$ I think there is a version of Somer's D that takes censoring into account. Ie, for two observations xi & xj in the test set, if the predicted values are hat xi > hat xj, do the observed values match? $\endgroup$ – gung - Reinstate Monica Mar 25 '15 at 16:31
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The split sample approach to validating a survival model only works well in my experience if the total sample size exceed about 20,000. Otherwise the analysis is too much at the whim of the random split. As @gung stated there is a generalized c-index for this problem, often stated as Somers' Dxy and implemented in the R Hmisc package rcorr.cens function. But to study general strategies for validating statistical indexes and calibration curves for time-to-event models see my course handouts that are linked to from http://biostat.mc.vanderbilt.edu/rms .

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