Primary Submission Category: Matching, Weighting
Post-Stratification Using Bayesian Interpolation: Enhancing Causal Inference with Uncertainty-Aware Population Weighting
Authors: Theo Snow, Brittany Morgan Bustamante, Juliana Bartels, Simon Camponuri, Justin Remais, Alejandro Schuler, Alan Hubbard,
Presenting Author: Theo Snow*
Accurate population inferences from stratified samples often require adjusting for biases and discrepancies between sample and population distributions, commonly through post-stratification weighting. This study investigates the limitations of deterministic post-stratification weighting and explores a Bayesian framework to address these challenges. We employ a Bayesian interpolation method to estimate post-stratification weights as posterior distributions. Using demographic data from 2013-2023 American Community Surveys and sample data from a national electronic health record system, we derive strata-specific posterior distributions and compute Bayesian weights. By specifying our priors as the expected counts of patients in each stratum if the sample had the distribution of our population of interest, we assume exchangeability between sample and population distributions while incorporating uncertainty. Bayesian weights closely resembled post-stratification weights (0.56% mean difference between the point estimates from each weighting method). However, Bayesian interpolation offers the addition of posterior confidence intervals, characterizing uncertainty in the weights. This provides a robust assessment of sampling variability and population uncertainty in weighted analyses. This work demonstrates the utility of Bayesian interpolation for causal inference by providing a principled method to control for biases while propagating uncertainty through the adjustment process.