Estimation of the average causal effect via multiple propensity score stratification

Suppose we are interested in estimating the average causal effect (ACE) for the population mean from observational study. Because of simplicity and ease of interpretation, stratification by a propensity score (PS) is widely used to adjust for influence of confounding factors in estimation of the ACE. Appropriateness of the estimation by the PS stratification relies on correct specification of the PS. We propose an estimator based on stratification with multiple PS models by clustering techniques instead of model selection. If one of them correctly specifies, the proposed estimator removes bias and thus is more robust than the standard PS stratification.