Nonparametric Sensitivity Analysis for the Survivor Average Causal Effect: Sharp Bounds for Vaccine Efficacy

Abstract

In studies in which the endpoint of interest is measurable only on a subset of units who experience a prior event, quantifying the effect of a treatment is subject to confounding that cannot be controlled by design. Techniques for handling this issue have focused on the survivor average causal effect, which generally captures the effect of an intervention on the measured endpoint only in the principal stratum that would have experienced the prior event regardless of treatment assignment. A core assumption of such methods is the supposition that any hypothetical value of the endpoint for units outside of this principal stratum is epistemically invalid; however, this assumption is either overly restrictive or inconsistent with domain knowledge in many settings. Focusing on evaluating the causal effect of vaccination on viral load (only clinically meaningful in the infected), we provide a novel, nonparametric characterization of the survivor average causal effect in terms of the average treatment effect. Our partial identification strategy yields sensitivity parameters that eschew stringent modeling assumptions, allowing for bounds on the causal effect to be quantified easily in real-world studies. Following an analogous strategy, we use the canonical decomposition of the average treatment effect into the natural direct and indirect effects to introduce the survivor natural direct and indirect effects, for which we provide similar nonparametric partial identification. We complement these partial identification strategies and effect decomposition with theoretical developments required for the robust, asymptotically efficient estimation of key components of our sensitivity models. We demonstrate the utility of these novel mediation effects, and our overarching strategy, by breaking down the causal effect of vaccine versus placebo assignment on viral load through clinically identified immunologic markers in a recent vaccine efficacy trial.