Comparing partial likelihood and robust estimation methods for the cox regression model

The Cox proportional hazards model is ubiquitous in time-to-event studies of political processes. Plausible deviations from correct specification and operationalization caused by problems such as measurement error or omitted variables can produce substantial bias when the Cox model is estimated by conventional partial likelihood maximization (PLM). One alternative is an iteratively reweighted robust (IRR) estimator, which can reduce this bias. However, the utility of IRR is limited by the fact that there is currently no method for determining whether PLM or IRR is more appropriate for a particular sample of data. Here, we develop and evaluate a novel test for selecting between the two estimators. Then, we apply the test to political science data. We demonstrate that PLM and IRR can each be optimal, that our test is effective in choosing between them, and that substantive conclusions can depend on which one is used.