Accounting for matching structure in post-matching analysis of observational studies

Abstract

Matching design is commonly used in social science and health research with observational data, as it is robust to outcome model misspecification and has the intuitive interpretation similar to blocked randomization design. Estimate the population average treatment effect with propensity score adjustment is very popular. From a practical perspective, however, it is not clear whether the post-matching analysis should adjust for the matching structure. Analytical strategies with and without accounting for matching design have appeared in literature. For continuous outcomes, the implication is more on the variance estimation. But for binary outcomes, the non-collapsibility problem for the odds ratio adds another layer of complexity in choosing between estimation strategies. We have conducted extensive simulation studies to compare several matching estimators and the propensity score weighting estimator for both continuous and binary outcomes. Especially, we consider three measures for binary outcomes, risk difference, relative risk and odds ratio. Our simulation results suggest that statistical methods accounting for matching structure are more advantageous and among binary effect measures, odds ratio tends to have higher power than other measures. We also apply different estimation strategies to a U.S. trauma care database to examine mortality difference between trauma centers and non-trauma centers.