Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies through Quadratically Constrained Linear Programming

TL;DR

This paper introduces a novel sensitivity analysis method for multiple outcomes in observational studies, using quadratically constrained linear programming to improve power while controlling error rates.

Contribution

It develops a new approach that enforces consistent unmeasured confounding effects across outcomes, enhancing sensitivity analysis in matched observational studies.

Findings

Improves power of sensitivity analysis for multiple outcomes.

Controls familywise error rate effectively.

Demonstrated on smoking and naphthalene exposure study.

Abstract

A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable, accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest. This stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed. Existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant, which in turn results in an overly pessimistic assessment of a study's sensitivity to unobserved biases. By solving a quadratically constrained linear program, we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatment assignment probabilities across outcomes for each individual in the study. We show that this allows for uniform improvements in the power of a sensitivity analysis not only for testing the overall null of no effect, but also for null hypotheses on \textit{specific} outcome variables while strongly controlling the familywise error rate. We illustrate our method through an observational study on the effect of smoking on naphthalene exposure.