It's all about balance: propensity score matching in the context of complex survey data.

Many research studies aim to draw causal inferences using data from large, nationally representative survey samples, and many of these studies use propensity score matching to make those causal inferences as rigorous as possible given the non-experimental nature of the data. However, very few applied studies are careful about incorporating the survey design with the propensity score analysis, which may mean that the results do not generate population inferences. This may be because few methodological studies examine how to best combine these methods. Furthermore, even fewer of them investigate different non-response mechanisms. This study examines methods for handling survey weights in propensity score matching analyses of survey data under different non-response mechanisms. Our main conclusions are: (i) whether the survey weights are incorporated in the estimation of the propensity score does not impact estimation of the population treatment effect, as long as good population treated-comparison balance is achieved on confounders, (ii) survey weights must be used in the outcome analysis, and (iii) the transferring of survey weights (i.e., assigning the weights of the treated units to the comparison units matched to them) can be beneficial under certain non-response mechanisms.