Estimator-Aligned Prospective Sample Size Determination for Designs Using Inverse Probability of Treatment Weighting

TL;DR

This paper introduces a new estimator-aligned method for prospective sample size calculation in observational studies using inverse probability weighting, improving variance estimation accuracy and power calibration.

Contribution

It develops a unified GEE-based framework that accounts for nuisance-model uncertainty and propagates variability, enhancing study planning accuracy.

Findings

Simulation shows improved power calibration over traditional RCT formulas.

Method effectively handles weight instability and outcome sparsity.

Bootstrap stabilization enhances variance estimation robustness.

Abstract

In observational studies, accurately characterizing variance is critical for sample size determination, yet unaccounted-for variability from propensity score estimation and the resulting weights limit the accuracy of standard variance approximations for design. Existing approaches often rely on heuristics or randomized controlled trial (RCT) formulas that treat weights as fixed, potentially misaligning prospective design with the causal estimator used at analysis. We propose an estimator-aligned framework for prospective sample size determination based on generalized estimating equations (GEE) and stacked M-estimation. By merging the propensity score model and marginal structural model (MSM) into a single system of estimating equations, the method propagates nuisance-model uncertainty and directly targets the large-sample variance of the IPTW estimator. For study planning, we estimate a pilot-based large-sample variance factor and introduce a bootstrap stabilization procedure that accounts for both within- and between-pilot variability. The framework applies uniformly across binary, count, and continuous outcomes through link-specific GEE representations under a common design principle. Simulation studies motivated by post-marketing safety and healthcare cost applications demonstrate that anchoring design to this variance improves power calibration relative to conventional RCT-style formulas, particularly in settings with weight instability, outcome sparsity, or heavy-tailed variability.