Ensuring valid inference for hazard ratios after variable selection

TL;DR

This paper introduces a novel method for valid inference of hazard ratios after variable selection in observational survival studies, addressing confounding and censoring issues with high-dimensional data.

Contribution

It proposes a simple, implementable procedure using penalized Cox regression for valid hypothesis testing of exposure effects under high-dimensional confounders.

Findings

Methods provide valid inferences in high-dimensional settings

Proposed tests are uniformly valid under sparsity conditions

Simulation studies confirm robustness and accuracy

Abstract

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmeasured confounding. The major complication that we face with survival data is that the key confounding variables may not be those that explain the censoring mechanism. In this paper, we overcome this problem using a novel and simple procedure that can be implemented using off-the-shelf software for penalized Cox regression. In particular, we will propose tests of the null hypothesis that the exposure has no effect on the considered survival endpoint, which are uniformly valid under standard sparsity conditions. Simulation results show that the proposed methods yield valid inferences even when covariates are high-dimensional.