Detection and remedy of scale-disparityin the proportional hazard model
by
Debasis Sengupta
ISI, Calcutta, India
Coauthors: Shyamsundar Sahoo (ISI, Calcutta, India)

The problem of heteroscedasticity in the linear model is well known. There are data-analytic procedures for detecting and correcting systematic heteroscedasticity. In this talk we deal with the analogos problem of scale disparity in the Proportional Hazards (PH) model. Specifically, we assume that a scale-corrected life-time follows the PH model, where the scale depends on the covariates. We propose a graphical method for detecting scale disparity. This method is similar to the plot of residual vs. covariates in the case of the linear model. It is shown via simulations is that whenever the scale factor is a function of a particular covariate, the plot can be used to estimate this function, and subsequently to take corrective action. In the special case of the two-sample problem, we propose a class of estimation strategies for the corrective scale factor. The inclusion of a possible scale factor extends the domain of applicability of the PH model. A limited theoretical study of the extent of this extension is also made.

Date received: October 30, 2000