Origin-invariant relative risk functions for case-control and survival studies

Abstract

Several parametric families of relative risk functions have been proposed as models for matched case-control and survival data. Some advantages accrue to those in which relative risks are invariant under arbitrary translations of the origin of the covariate space, such as in the reassignment of values to dichotomous factors. It is shown in this paper that the family proposed by Guerrero & Johnson, which includes the commonly-used exponential and linear relative risk functions, has the simplest form of this origin invariance property. A differential equation that general origin-invariant relative risk functions must satisfy is derived. The effect of covariate translations on the parameter space is also discussed.