Sensitivity Analysis for Unmeasured Confounding in Meta-Analyses

TL;DR

This paper introduces sensitivity analysis methods for meta-analyses of observational studies to evaluate how unmeasured confounding could bias the estimated effects, providing tools to quantify and assess confounding strength.

Contribution

It develops novel sensitivity analysis techniques and estimators that do not rely on assumptions about unmeasured confounders, along with an R package and online interface for practical application.

Findings

Methods quantify how confounding affects effect estimates.

Tools estimate confounding strength needed to undermine causal conclusions.

Provides accessible software for researchers to perform sensitivity analyses.

Abstract

Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of specified magnitude could reduce to below a certain threshold the proportion of true effect sizes that are scientifically meaningful. We also develop converse methods to estimate the strength of confounding capable of reducing the proportion of scientifically meaningful true effects to below a chosen threshold. These methods apply when a "bias factor" is assumed to be normally distributed across studies or is assessed across a range of fixed values. Our estimators are derived using recently proposed sharp bounds on confounding bias within a single study that do not make assumptions regarding the unmeasured confounders themselves or the functional form of their relationships to the exposure and outcome of interest. We provide an R package, ConfoundedMeta, and a freely available online graphical user interface that compute point estimates and inference and produce plots for conducting such sensitivity analyses. These methods facilitate principled use of random-effects meta-analyses of observational studies to assess the strength of causal evidence for a hypothesis.