Bias and variance of treatment effect estimators using propensity-score matching

Abstract

Observational studies are an indispensable complement to randomized clinical trials (RCT) for comparison of treatment effectiveness. Often RCTs cannot be carried out due to the costs of the trial, ethical questions and rarity of the outcome. When noncompliance and missing data are prevalent, RCTs become more like observational studies. The main problem is to adjust for the selection bias in the observational study. One increasingly used method is propensity-score matching. Compared to traditional multi-covariate matching methods, matching on the propensity score alleviates the curse of dimensionality. It allows investigators to balance multiple covariate distributions between treatment groups by matching on a single score. This thesis focuses on the large sample properties of the matching estimators of the treatment effect. The first part of this thesis deals with problems of the analytic supports of the logit propensity score and various matching methods. The second part of this thesis focuses on the matching estimators of additive and multiplicative treatment effects. We derive the asymptotic order of the biases and asymptotic distributions of the matching estimators. We also derive the large sample variance estimators for the treatment effect estimators. The methods and theoretical results are applied and checked in a series of simulation studies. The third part of this thesis is devoted to a comparison between propensity-score matching and multiple linear regression using simulation. iii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix CHAPTER