Post-stratification is often used to estimate treatment effects with higher efficiency. However, the majority of existing post-stratification frameworks depend on prior knowledge of the distributions of covariates and assume that the units are classified into post-strata without error. We propose a novel method to determine a proper stratification rule by mapping the covariates into a post-stratification factor (PSF) using predictive regression models. Inspired by the bootstrap aggregating (bagging) method, we utilize the out-of-bag delete-D jackknife to estimate strata boundaries, strata weights, and the variance of the point estimate. Confidence intervals are constructed with these estimators to take into account the additional variability coming from uncertainty in the strata boundaries and weights. Extensive simulations show that our proposed method consistently improves the efficiency of the estimates when the regression models are predictive and tends to be more robust than the regression imputation method.

翻译：事后分层常被用于提高治疗效果估计的效率。然而，现有的事后分层框架大多依赖于协变量分布的先验知识，并假设单元能够无误差地划分至各后分层。本文提出一种新颖方法：通过预测性回归模型将协变量映射为事后分层因子（PSF），从而确定合理的分层规则。受自助聚合（bagging）方法启发，我们利用离袋删除-D折刀法估计分层边界、分层权重及点估计方差，并基于这些估计量构建置信区间，以纳入分层边界与权重不确定性带来的额外变异性。大规模模拟表明：当回归模型具有预测能力时，所提方法能够持续提升估计效率，且相较于回归插补法更具稳健性。