Yet another measure of explained variation for survival models

Janez Stare, PhD

Institute of Biomedical Informatics, Medical Faculty Ljubljana, Slovenia

Wednesday, November 11, 1:30-2:30pm, MRBIII Conference Room 1220

Intended Audience: Persons interested in applied statistics, statistical theory, epidemiology, health services research, clinical trials methodology, statistical computing, statistical graphics, R users or potential users

There is no shortage of proposed measures of prognostic values of survival models in statistical literature. They come under different names (explained variation, correlation, explained randomness ...), but their goal is common: to define something analogous to the coefficient of determination (R2) in linear regression. Such measures will typically (surprisingly, not all of them do!) lie between 0 and 1, reaching 1 under a `perfect' model. Some of the measures are only defined for the Cox model, and only a few can meaningfully deal with time-dependent covariates and time-dependent effects. I will present a new measure that has no problem with time-dependency, is easily calculated, has a straightforward interpretation, and can be used with any survival model.
In fact, it is naturally adapted for comparison of different models. The measure is based on the conditional ranks of the failing subjects. I will show that our measure has an interpretation of a measure of explained variation. Here variation is understood, following Nagelkerke, as any measure of the degree to which the (conditional) distribution is not degenerate. I will further show some results concerning the variance of the estimator and its unbiasedness under censoring. Another desirable property is the measure's linear dependency on the sum of the ranks, making the improvements in the fit easy to understand. I will give the population definition, discuss some other properties of the estimator, and illustrate its usage on some real data sets.

Topic revision: r5 - 26 Apr 2013, JohnBock

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