Optimal two-phase sampling designs for generalized raking estimators with multiple parameters of interest

TL;DR

This paper develops optimal adaptive two-phase sampling designs for generalized raking estimators with multiple parameters, improving efficiency in large observational studies with missing or error-prone data.

Contribution

It extends existing methods by deriving multiwave, adaptive sampling strategies for multiple parameters, and compares their performance to traditional approaches.

Findings

Optimized designs improve estimator efficiency over case-control sampling.

Integer-valued A-optimal allocation outperforms independent optimization.

Designs for GR differ from IPW, affecting efficiency in multi-parameter settings.

Abstract

Large observational datasets, including those derived from electronic health records, are a valuable resource for medical research but are often affected by missingness, measurement error, and misclassification. Two-phase sampling with generalized raking (GR) estimation is an efficient and robust approach to statistical inference in such settings. In this approach, variables that are unavailable or measured with error in a large phase 1 cohort are obtained with higher-quality measurements in a phase 2 subsample. Previous research has studied optimal phase 2 sampling designs for inverse probability weighted (IPW) estimators in non-adaptive, multi-parameter settings, and for GR estimators in single-parameter settings. In this work, we extend these results by deriving optimal adaptive, multiwave sampling designs for IPW and GR estimators when multiple parameters are of interest. We propose several practical allocation strategies and evaluate their performance through extensive simulations and a data example from the Vanderbilt Comprehensive Care Clinic HIV Study. Our results show that independently optimizing allocation for each parameter improves efficiency over traditional case-control sampling. We also derive an integer-valued, A-optimal allocation method that typically outperforms independent optimization. Notably, we find that optimal designs for GR can differ substantially from those for IPW, and that this distinction can meaningfully affect estimator efficiency in the multiple-parameter setting. These findings offer practical guidance for future two-phase studies involving incomplete or error-prone data.