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

Abstract

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.

Ensuring Valid Inference for Cox Hazard Ratios After Variable Selection

“…This proposed “poor man's approach” extends earlier work on randomized experiments (see Van Lancker et al., 2021) to observational data. The second proposal that we will make in this paper is more rigorous and builds on the theory of high‐dimensional inference (see Bradic et al., 2011; Huang et al., 2013).…”

“…In particular, our approach will typically only miss variables for which 𝛽, 𝛾, and 𝜂 are of the order 1∕ √ 𝑛. This is however not problematic as the bias in the test statistic will be of the order 1∕𝑛, which is small enough (compared to the order of magnitude of the standard error, 1∕ √ 𝑛) that the Type I error will not be inflated (see e.g., Belloni et al 2016;Van Lancker et al 2021).…”

“…Imperfect selection may lead to collider‐bias (sometimes referred to as selection bias, sampling bias, ascertainment bias) between A and T in the risk set at each time point, which can in turn induce a distorted association where there is no effect in the general population. This is even problematic in randomized trials, whose analysis is immune to confounding bias (see Van Lancker et al., 2021).…”

“…(2014, 2016) and Van Lancker et al. (2021), we will first make a simple proposal to overcome the previous problems. Next, we will compare this proposal with a more rigorous but complex approach.…”

Doubly Robust Inference for Hazard Ratio under Informative Censoring with Machine Learning

“…In practice, this assumption can be violated which leads to informative censoring, and the censoring time may well depend on additional covariates. This issue was recently highlighted in Van Lancker et al (2021), who aimed to develop procedures to select baseline covariates in order to be adjusted for in the Cox regression model. Such adjustment, however, changes the effect estimand, making it difficult to compare across different adjustment sets.…”