Omitting Covariates from the Proportional Hazards Model

The problem of omitting covariates from the proportional hazards model (PHM) when comparing two treatment groups was considered by Lagakos and Schoenfeld (1984). The absolute value of the parameter estimate of treatment effect is decreased, in expectation, when covariates are omitted from the PHM, resulting in an inefficient test for treatment comparison. Based on the asymptotic distribution of the score statistic when the hazard functions for the two treatment groups are nonproportional, the asymptotic relative efficiency (ARE) of the PHM score test for treatment difference was derived comparing the correctly specified PHM to the misspecified non-PHM. They considered the following: nonproportional treatment hazards, treatment-covariate interactions, omitted covariates, and mismodeled covariates. Although the basic results of Lagakos and Schoenfeld on the ARE for nonproportional models appear correct, the extension of these results to the ARE of omitting covariates is incorrect.