The Power of the Mantel‐Haenszel Test when Adjustment is by the True or Estimated Propensity Score

The power of the Mantel‐Haenszel test for no treatment effect in the case of binary exposure and response variates was examined through simulation studies when subclasses were formed on the basis of the true and estimated propensity scores and by direct stratification on two continuous covariates. The power of these tests was also compared to the score test in a misspecified logistic regression model. In general adjustment by the true propensity score was most likely to reject a false null hypothesis, the score test was more likely to reject a false null hypothesis than the Mantel‐Haenszel test when adjustment is by the estimated propensity score or subclassification on the covariates. There was litte difference in the observed powers of the Mantel‐Haenszel tests between adjustment by the estimated propensity score and subclassification on the covariates.