Score tests for homogeneity of regression effect in the proportional hazards model

A simple model, containing the proportional hazards regression model as a special case, is presented. The purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested. Rank-invariant score tests for linear, quadratic, or exponential trends can, for instance, all be undertaken within this framework. In the case of the two-sample problem the required calculations are shown to take a particularly simple form. Special consideration is given to the two-sample case in which there is an inversion of the regression effect, i.e., where the hazard functions cross at some given point. Both of the motivating examples are concerned with this problem. Computational aspects are relatively straightforward and some discussion on this is provided.