A sensitivity analysis for the average derivative effect

TL;DR

This paper develops a sensitivity analysis framework for the average derivative effect in observational studies with continuous exposures, providing bounds, estimators, and confidence intervals to assess robustness against unmeasured confounding.

Contribution

It introduces closed-form bounds and flexible estimators for the ADE under a new sensitivity model involving the odds ratio of propensity scores.

Findings

Bounds for ADE under the sensitivity model are derived.

Estimators and confidence intervals are proposed and validated through simulations.

Applications demonstrate the method's utility in real-world studies.

Abstract

In observational studies, exposures are often continuous rather than binary or discrete. At the same time, sensitivity analysis is an important tool that can help determine the robustness of a causal conclusion to a certain level of unmeasured confounding, which can never be ruled out in an observational study. Sensitivity analysis approaches for continuous exposures have now been proposed for several causal estimands. In this article, we focus on the average derivative effect (ADE). We obtain closed-form bounds for the ADE under a sensitivity model that constrains the odds ratio (at any two dose levels) between the latent and observed generalized propensity score. We propose flexible, efficient estimators for the bounds, as well as point-wise and simultaneous (over the sensitivity parameter) confidence intervals. We examine the finite sample performance of the methods through simulations and illustrate the methods on a study assessing the effect of parental income on educational attainment and a study assessing the price elasticity of petrol.