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From |
Steven Samuels <sjsamuels@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Cox regression proportion of variance explained |

Date |
Thu, 23 Jun 2011 16:33:19 -0400 |

Elizabeth thanked me privately. I would only suggest now that she use Somers' D instead of D squared. Roger reminded me off-list that D has a clear interpretation as a difference in probabilities. D-squared does not, nor is it a "proportion of variation" in the way that R-square is. And, in the survival setup 0 ≤ D ≤ 1. Heagerty and Zeng advocate for the concordance statistics analogous to Harrell's C and D, not their squares. Some are averages of AUCs, which do not have R-square like interpretations either. All-in-all, I think that D is better for Elizabeth's purposes than D-squared. Steve sjsamuels@gmail.com Elizabeth: 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: http://www.imperial.ac.uk/nhli/r.newson/papers/predsurv.pdf 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 http://www.statmed.medicina.unimib.it/statisticalps2011/materiale/Heagerty%20and%20Zheng,%20Biometrics%202005.pdf. Steve Steven J. Samuels Consulting Statistician 18 Cantine's Island Saugerties, NY 12477 USA Voice: 845-246-0774 Fax: 206-202-4783 sjsamuels@gmail.com 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 (http://www.stata.com/statalist/archive/2009-04/msg01186.html), 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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: Cox regression proportion of variance explained***From:*Elizabeth Kim Murphy <Elizabethkim.Murphy@postgrad.manchester.ac.uk>

**References**:**st: Cox regression proportion of variance explained***From:*Elizabeth Kim Murphy <Elizabethkim.Murphy@postgrad.manchester.ac.uk>

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