Improving Estimation Efficiency for Two-Phase, Outcome-Dependent Sampling Studies

TL;DR

This paper introduces an empirical likelihood method that enhances estimation efficiency in two-phase outcome-dependent sampling by leveraging full Phase 1 data, outperforming traditional methods especially when covariates are inexpensive or surrogates are available.

Contribution

It develops a novel empirical likelihood approach that combines conditional maximum likelihood with Phase 1 data, improving efficiency without requiring covariate distribution modeling.

Findings

Significant efficiency gains over CML in simulations.

Method handles zero Phase 2 selection probabilities.

Real data application demonstrates practical benefits.

Abstract

Two-phase outcome dependent sampling (ODS) is widely used in many fields, especially when certain covariates are expensive and/or difficult to measure. For two-phase ODS, the conditional maximum likelihood (CML) method is very attractive because it can handle zero Phase 2 selection probabilities and avoids modeling the covariate distribution. However, most existing CML-based methods use only the Phase 2 sample and thus may be less efficient than other methods. We propose a general empirical likelihood method that uses CML augmented with additional information in the whole Phase 1 sample to improve estimation efficiency. The proposed method maintains the ability to handle zero selection probabilities and avoids modeling the covariate distribution, but can lead to substantial efficiency gains over CML in the inexpensive covariates, or in the influential covariate when a surrogate is available, because of an effective use of the Phase 1 data. Simulations and a real data illustration using NHANES data are presented.