Statistics Colloquium

Propensity Score Estimators for Causal Inference with Complex Survey Data

Probability surveys are a major source of population representative data for policy research and program evaluation; however, the data come with the added complications of being observational as well as often being selected with unequal probabilities.  Propensity score methods, such as weighting, matching, and stratification, are an increasingly popular group of methods for inferring causal relationships from observational data.  When using complex survey data, estimates of the population level causal effect using these methods may be biased if the researcher does not adjust for the sampling design.  We propose a potential outcomes super-population framework to motivate propensity score analysis for complex survey data.  Based on the proposed framework, we develop propensity score weighted and stratified estimators and corresponding variance estimators that adjust for survey design features.  Asymptotic results of the weighted estimators are explored. Additionally, we argue that in this context the sampling weights should be used when estimating the propensity scores.The estimators are compared in a simulation study showing that the proposed estimators perform better than estimators that do not adjust for the sampling design when the treatment effects are heterogeneous.  As the treatment effects become more heterogeneous, the gains of adjusting for the survey design increase.Lastly, we demonstrate the use of the proposed estimators in an example considering the effect of health insurance coverage on self-rated health in adults.