Estimation of Main Effect When Covariates Have Non-Proportional Hazards

The Cox proportional hazards (PH) regression model has been widely used to analyze survival data in clinical trials and observational studies. In addition to estimating the main treatment or exposure group effect, it is common to adjust for additional covariates using the Cox model. It is well known that violation of the PH assumption can lead to estimates that are biased and difficult to interpret, and model checking has become a routine procedure. However, such checking might focus on the primary group comparisons, and the assumption can still be violated when adjusting for many of the potential covariates. We study the effect of violation of the PH assumption of the covariates on the estimation of the main group effect in the Cox model. The results are summarized in terms of the bias and the coverage properties of the confidence intervals. Overall in randomized clinical trials, the bias caused by misspecifying the PH assumption on the covariates is no more than 15% in absolute value regardless of sample size. In observational studies where the covariates are likely correlated with the group variable, however, the bias can be very severe. The coverage properties largely depend on sample size, as expected, as bias becomes dominating with increasing sample size. These findings should serve as cautionary notes when adjusting for potential confounders in observational studies, as the violation of PH assumption on the confounders can lead to erroneous results.