A maximin optimal approach for sampling designs in two-phase studies

TL;DR

This paper introduces a maximin optimal sampling design for two-phase studies that enhances estimation efficiency in model-free settings, reducing estimator variance across various scenarios.

Contribution

It proposes a novel maximin criterion for designing sampling rules based on semiparametric efficiency bounds, applicable to general estimation problems.

Findings

Reduces estimator variance in simulations

Improves efficiency bounds for scalar and multi-dimensional parameters

Demonstrates effectiveness through real data analysis

Abstract

Data collection costs can vary widely across variables in data science tasks. Two-phase designs can be employed to save data collection costs. This paper considers the two-phase studies where inexpensive variables are collected for all subjects in the first phase, and expensive variables are measured for a subsample of subjects in the second phase based on a predetermined sampling rule. The estimation efficiency under two-phase designs relies heavily on the sampling rule. Existing literature primarily focuses on designing sampling rules for estimating a scalar parameter in some parametric models or specific estimating problems. However, real-world scenarios are usually model-unknown and involve two-phase designs for model-free estimation of a scalar or multi-dimensional parameter. This paper proposes a maximin criterion to design an optimal sampling rule based on semiparametric efficiency bounds. The proposed method is model-free and applicable to general estimating problems. The resulting sampling rule can minimize the semiparametric efficiency bound when the parameter is scalar and improve the bound for every component when the parameter is multi-dimensional. Simulation studies demonstrate that the proposed designs reduce the variance of the resulting estimator in various settings. The implementation of the proposed design is illustrated in a real data analysis.