Predictive capability of proportional hazards regression

A measure of the predictive capability of a proportional hazards regression is derived. The measure is based on the residuals appropriate to proportional hazards regression. A population version is presented and can be seen not to depend on the censoring mechanism under the provision that any such censoring be independent or conditionally independent of the failure mechanism given the covariate. For the special case of a Weibull regression model, for which the covariate distribution follows binary, uniform, normal, or exponential laws, we derive analytic results. These alone give credence to the measure which can be seen to reflect strength of regression effect, as quantified by the parameter estimate, although on a scale between 0 and 1, independently of the intercept or shape parameter of the particular Weibull law and only weakly dependent on the covariate distribution. Extensions to partial and multiple measures of predictive ability are straightforward. An example is provided.