A test for proportional hazards assumption within the class of exponential conditional mean models

Abstract

Two classes of econometric estimators are popular for modeling outcomes with idiosyncratic characteristics such as those present in medical costs data: (1) estimators based on the exponential conditional mean models where the mean function of the outcome is equal to exponential of the linear predictor and (2) estimators based on the proportional hazard assumption where hazard function of the outcome is equal to exponential of the linear predictor. Recent work has provided guidance both on choosing between the two classes of estimators and also on choosing among alternative estimators within the exponential conditional mean framework. The present work extends this literature by proposing a test for identifying the proportional hazards assumption within the class of exponential conditional mean models, thereby eliminating the need to run both classes of models in order to make informative choices. We implement this test using the generalized gamma regression model, thereby allowing the analyst to select between both parametric alternatives and also the semi-parametric Cox model from one cohesive framework. Our simulation results indicate that the proposed test perform as well as the traditional test of proportional hazards assumption following a Cox regression based on power and Type I error under a variety of data generating mechanisms. We illustrate its use in an analysis of physician visits.