Optimal Use of Survey Weights for Causal Inference under Informative Sampling

Music City Center 

The increasing availability of survey data for causal inference on treatment effects presents new scopes, yet most methods assume ignorability of treatment and non-informative sampling. In practice, survey data often include survey weights, but the sampling is frequently informative-i.e., dependent on the outcome given covariates and treatment-especially when design details are undisclosed. The optimal use of survey weights for causal inference under such sampling is an open problem. We show how survey weights can enhance the efficiency of Horvitz-Thompson estimators. Specifically, we derive the efficient influence function within the class of regular asymptotically linear estimators and propose a novel estimator based on it. Using a super-population framework, we establish its doubly robust property and, via M-estimation, prove its root-N asymptotic normality under parametric nuisance modeling. To enable flexible ML methods, we extend the theory to show our estimator ensures faster-than-root-N rates when the product of nuisance function rates exceeds root-N. We support our theoretical findings through extensive simulations and analysis of the Medical Expenditure Panel Survey data.

Complex survey


Data-Adaptive Method

Doubly Robust Estimation

Empirical process

Population average treatment effect 

Survey Research Methods Section