Abstract #300250

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JSM 2003 Abstract #300250
Activity Number: 59
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Biometrics Section
Abstract - #300250
Title: Explained Randomness in Proportional Hazards Models
Author(s): Ronghui Xu*+
Companies: Harvard School of Public Health
Address: Dept. of Biostatistics, Boston, MA, 02115-6009,
Keywords: correlation ; explained variation ; information gain
Abstract:

A coefficient of explained randomness, analogous to explained variation but for nonlinear models, was presented by Kent (1983). The construct hinges upon the notion of Kullback-Leibler information gain. Kent and O'Quigley (1988) developed these ideas, obtaining simple, multiple, and partial coefficients for the situation of proportional hazards regression. Their approach was based upon the idea of transforming a general proportional hazards model to a specific one of Weibull form. Xu and O'Quigley (1999) developed a more direct approach, more in harmony with the semiparametric nature of the proportional hazards model, thereby simplifying inference and allowing, for instance, the use of time-dependent covariates. Our purpose of is to provide a further simplification. We also point out that a sample-based coefficient suggested in the SAS survival analysis guide can be interpreted as an estimate of explained randomness when there is no censoring. When there is censoring the SAS coefficient would not seem satisfactory in that its population counterpart depends on an independent censoring mechanism. However, there is a quick fix and we argue in favor of its use.

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