  The analysis of randomized trials with time-to-event endpoints is nearly
always plagued by the problem of censoring. As the censoring mechanism is
usually unknown, analyses typically employ the assumption of non-informative
censoring. While this assumption usually becomes more plausible as more
baseline covariates are being adjusted for, such adjustment also raises
concerns. Pre-specification 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 paper, we discuss these concerns and
propose a simple variable selection strategy that aims 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.
