Abstract

Much work has been devoted to estimating causal effects from observational studies. However, these studies present threats not only to internal validity due to lack of randomized assignment, but also threats to external validity if there exists treatment heterogeneity modified by the design variables in a complex sampling design. This paper investigates two “doubly-robust” (DR) estimators—Augmented Inverse Probability Weighting (AIPW) and Penalized Spline of Propensity Methods for Treatment Comparison (PENCOMP)—that consistently estimate the population average treatment effect when either the treatment assignment or outcome are modeled correctly. However, both methods assume non-informative sampling, necessitating extensions in the presence of informative sampling. We demonstrate that the DR property can be restored in PENCOMP through the integration of selection weights via the weighted finite population Bayesian bootstrap (WFPBB-PENCOMP) and in AIPW by applying selection weighted estimation components (SW-AIPW). We apply these methods to the Food Acquisition and Purchase Survey and estimate the causal impact of food assistance on household food insecurity in the United States.