Using Survival Information in Truncation by Death Problems Without the Monotonicity Assumption

TL;DR

This paper addresses the challenge of estimating causal effects in clinical trials with truncation by death, proposing methods that leverage detailed survival data and copula models to improve inference without relying on the monotonicity assumption.

Contribution

It introduces a novel approach that uses survival information and copula models to sharpen bounds on causal effects, relaxing the monotonicity assumption.

Findings

Utilizes survival data to tighten bounds on causal effects.

Employs copula models to relax the monotonicity assumption.

Improves inference accuracy in truncation by death scenarios.

Abstract

In some randomized clinical trials, patients may die before the measurements of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes. This is called the truncation by death problem. Under the potential outcomes framework, the only well-defined causal effect on the outcome is within the subgroup of patients who would always survive under both treatment and control. Because the definition of the subgroup depends on the potential values of the survival status that could not be observed jointly, without making strong parametric assumptions, we cannot identify the causal effect of interest and consequently can only obtain bounds of it. Unfortunately, however, many bounds are too wide to be useful. We propose to use detailed survival information before and after the measurements of the outcomes to sharpen the bounds of the subgroup causal effect. Because survival times contain useful information about the final outcome, carefully utilizing them could improve statistical inference without imposing strong parametric assumptions. Moreover, we propose to use a copula model to relax the commonly-invoked but often doubtful monotonicity assumption that the treatment extends the survival time for all patients.