Effects of Proportional Hazard Assumption on Variable Selection Methods for Censored Data

Abstract

The Cox proportional hazard (PH) model is widely used to determine the effects of risk factors and treatments (covariates) on survival time of subjects that might be right censored. The selection of covariates depends crucially on the specific form of the conditional hazard model, which is often assumed to be PH, accelerated failure time (AFT), or proportional odds (PO). However, we show that none of these semiparametric models allow for the crossing of the survival functions and hence such strong assumptions may adversely affect the selection of variables. Moreover, the most commonly used PH assumption may also be violated when there is a delayed effect of the risk factors. Taking into account all of these modeling assumptions, this study examines the effect of the PH assumption on covariate selection when the data generating model may have non-PH. In particular, variable selection under two alternative models are explored: (i) the penalized PH model (using the elastic-net penalty) and (ii) the linear spline based hazard regression model. We apply the aforementioned models to the ACTG-175 dataset and simulated datasets with survival times generated from the Weibull and log-normal distributions. We also examine the effect on covariate selection of stratifying the analysis on the off-treatment indicator.