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

Music City Center 

The Mantel-Haenszel (MH) risk difference estimator is widely used for binary outcomes in randomized clinical trials. This estimator computes a weighted average of stratum-specific risk differences and traditionally requires the stringent assumption of homogeneous risk difference across strata. In our study, we relax this assumption and demonstrate that the MH risk difference estimator consistently estimates the average treatment effect. Furthermore, we rigorously study its properties under two asymptotic frameworks: one characterized by a small number of large strata and the other by a large number of small strata. Additionally, a unified robust variance estimator that improves over the popular Greenland's and Sato's variance estimators is proposed, and we prove that it is applicable across both asymptotic scenarios. Our findings are validated through simulations and real data applications.

Average treatment effect

Covariate adjustment

Robust variance estimation

Stratified 2 × 2 table

Difference of proportion 

Biometrics Section