Sensitivity Analysis for Quantiles of Hidden Biases in Matched Observational Studies

TL;DR

This paper introduces a robust sensitivity analysis method for quantiles of hidden biases in matched observational studies, improving upon existing maximum bias approaches by providing more nuanced and reliable assessments of unmeasured confounding effects.

Contribution

It generalizes Rosenbaum's sensitivity analysis to quantiles of hidden biases, offering a more robust and valid approach applicable to various outcomes and test statistics.

Findings

Quantiles of hidden biases can be effectively analyzed.

The method is valid across all quantiles, not just the maximum.

An R package implementation is provided.

Abstract

Causal conclusions from observational studies may be sensitive to unmeasured confounding. In such cases, a sensitivity analysis is often conducted, which tries to infer the minimum amount of hidden biases or the minimum strength of unmeasured confounding needed in order to explain away the observed association between treatment and outcome. If the needed bias is large, then the treatment is likely to have significant effects. The Rosenbaum sensitivity analysis is a modern approach for conducting sensitivity analysis in matched observational studies. It investigates what magnitude the maximum of hidden biases from all matched sets needs to be in order to explain away the observed association. However, such a sensitivity analysis can be overly conservative and pessimistic, especially when investigators suspect that some matched sets may have exceptionally large hidden biases. In this paper, we generalize Rosenbaum's framework to conduct sensitivity analysis on quantiles of hidden biases from all matched sets, which are more robust than the maximum. Moreover, the proposed sensitivity analysis is simultaneously valid across all quantiles of hidden biases and is thus a free lunch added to the conventional sensitivity analysis. The proposed approach works for general outcomes, general matched studies and general test statistics. In addition, we demonstrate that the proposed sensitivity analysis also works for bounded null hypotheses when the test statistic satisfies certain properties. An R package implementing the proposed approach is available online.