Dimension Reduction Approaches for Two-Phase Subsample Selection with High-Dimensional Covariates

Introduction: Two-phase sampling is widely used to reduce the cost of studies involving expensive data collection. In phase one, inexpensive variables are observed for all individuals and a strategic subsample is selected for phase two, where costly covariates are measured. When high-dimensional auxiliary covariates (HACs) are involved, common selection methods may underperform due to overlooked nonlinearities and noise. This study investigates how dimension reduction methods can better inform phase two selection by transforming HACs into univariable predictors that retain essential signals. Methods: We investigated four-dimension reduction methods to extract low-dimensional representations of HACs—Principal Component Analysis (PCA), Uniform Manifold Approximation and Projection (UMAP), Adaptive Lasso, and a Meta-Visualization ensemble recently proposed by Ma, R. (2023). Using a simulation framework, we evaluated these methods under different data-generating scenarios. Phase two selection was informed by residual-dependent sampling, and semiparametric maximum likelihood estimation (SMLE) was applied for effect estimation. Results: Across 60 simulation scenarios, Meta-Visual consistently achieved the lowest bias and IRMSE. UMAP and PCA showed moderate performance, while Adaptive Lasso performed best in sparse settings but exhibited high variability. Nonlinear methods outperformed others under complex structures, supporting their use in high-dimensional two-phase study designs. Discussion: Dimension reduction shows promise for leveraging high-dimensional data in two-phase designs. These findings suggest that aligning reduction strategies with data complexity may support more effective subsample selection and estimation.