Principled selection of baseline covariates to account for censoring in randomized trials with a survival endpoint

The analysis of randomized trials with time-to-event endpoints is nearly always plagued by the problem of censoring. In practice, such analyses typically invoke the assumption of noninformative censoring. While this assumption usually becomes more plausible as more baseline covariates are being adjusted for, such adjustment also raises concerns. Prespecification of which covariates will be adjusted for (and how) is difficult, thus prompting the use of data-driven variable selection procedures, which may impede valid inferences to be drawn. The adjustment for covariates moreover adds concerns about model misspecification, and the fact that each change in adjustment set also changes the censoring assumption and the treatment effect estimand. In this article, we discuss these concerns and propose a simple variable selection strategy designed to produce a valid test of the null in large samples. The proposal can be implemented using off-the-shelf software for (penalized) Cox regression, and is empirically found to work well in simulation studies and real data analyses.