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Re: st: Cox regression proportion of variance explained

From   Steven Samuels <>
Subject   Re: st: Cox regression proportion of variance explained
Date   Thu, 23 Jun 2011 09:38:57 -0400



I suggest that you use the square of Somers' D, a rank statistic that measures how concordant predicted hazards are with observed failure times. The square of D will, like R-square, range between 0 & 1. In fact, for survival data, I believe that D itself will also range between 0 & 1, although the lower end points of CIs might be <0.

You can get Somers' D by running -estat concordance- after -stcox-. Roger Newson's -somersd- (from SSC) will provide confidence intervals. See Roger's article: Newson RB. Comparing the predictive power of survival models using Harrell’s c or Somers’ D. The Stata Journal 2010; 10(3): 339–358. A preprint is available at:

Heagerty and Zeng propose that concordance measures of predictive accuracy in survival models are natural extensions to the proportion of variation measures. See: Heagerty, P. J., & Zheng, Y. (2005). Survival model predictive accuracy and ROC curves. Biometrics, 61(1), 92-105, available at,%20Biometrics%202005.pdf. 


Steven J. Samuels
Consulting Statistician
18 Cantine's Island
Saugerties, NY 12477 USA
Voice: 845-246-0774
Fax:  206-202-4783

On Jun 22, 2011, at 6:48 PM, Elizabeth Kim Murphy wrote:

Dear all,

A reviewer has asked me for the proportion of variance explained by my Cox regression model (I'm looking at risk factors for self-harm over time). I've done Google searches, and I have seen the threads on the FAQ section about r-square (, but I am still not sure of the best solution specific to Cox regression. 

Can anyone suggest a statistic that estimates the proportion of variance in outcome explained by a Cox regression model, or point me in the right direction? Also, can this be computed in Stata? 

Thank you for your consideration,

Liz Murphy

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