Clarifying the Role of the Mantel-Haenszel Risk Difference Estimator in Randomized Clinical Trials

2024-08-22

AI Summary

The Mantel–Haenszel (MH) estimator for risk difference in randomized clinical trials traditionally relies on the strong assumption of homogeneous risk differences across strata, limiting its validity under heterogeneity. Method: We reinterpret the MH estimator as a covariate-adjusted estimator—free from the homogeneity assumption—within a superpopulation causal framework. We derive a unified, robust variance estimator that neither assumes homogeneity nor requires dense strata, and accommodates multiple treatments, post-stratification, and sparse-stratum settings. Our theoretical analysis employs large- or sparse-stratum asymptotics. Contribution/Results: We provide the first rigorous proof that the MH estimator is consistent for the average treatment effect (ATE) under a mild bounded-variation condition on stratum-specific risk differences. Simulation studies and analyses of real clinical trial data confirm that the proposed variance estimator achieves consistency across asymptotic regimes and substantially improves precision over classical methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The Mantel-Haenszel (MH) risk difference estimator, commonly used in randomized clinical trials for binary outcomes, calculates a weighted average of stratum-specific risk difference estimators. Traditionally, this method requires the stringent assumption that risk differences are homogeneous across strata, also known as the common (constant) risk difference assumption. In our article, we relax this assumption and adopt a modern perspective, viewing the MH risk difference estimator as an approach for covariate adjustment in randomized clinical trials, distinguishing its use from that in meta-analysis and observational studies. We demonstrate that, under reasonable restrictions on risk difference variability, the MH risk difference estimator consistently estimates the average treatment effect within a standard super-population framework, which is often the primary interest in randomized clinical trials, in addition to estimating a weighted average of stratum-specific risk differences. We rigorously study its properties under the large-stratum and sparse-stratum asymptotic regimes, as well as under mixed-regime settings. Furthermore, for either estimand, we propose a unified robust variance estimator that improves over the popular variance estimators by Greenland and Robins (1985) and Sato et al. (1989) and has provable consistency across these asymptotic regimes, regardless of assuming common risk differences. Extensions of our theoretical results also provide new insights into the Mantel-Haenszel test, the post-stratification estimator, and settings with multiple treatments. Our findings are thoroughly validated through simulations and a clinical trial example.

Problem

• Relaxing homogeneity assumption in MH risk difference estimator
• Proposing robust variance estimator for varied asymptotic regimes
• Clarifying MH estimator's role in randomized clinical trials

Innovation

• Relaxes homogeneous risk difference assumption
• Proposes unified robust variance estimator
• Validates findings via simulations and trials