A two-stage dimension-reduction method for transformed responses and its applications

Abstract

Researchers in the biological sciences nowadays often encounter the curse of dimensionality. To tackle this, sufficient dimension reduction aims to estimate the central subspace, in which all the necessary information supplied by the covariates regarding the response of interest is contained. Subsequent statistical analysis can then be made in a lower-dimensional space while preserving relevant information. Many studies are concerned with the transformed response rather than the original one, but they may have different central subspaces. When estimating the central subspace of the transformed response, direct methods will be inefficient. In this article, we propose a more efficient two-stage estimator of the central subspace of a transformed response. This approach is extended to censored responses and is applied to combining multiple biomarkers. Simulation studies and data examples support the superiority of the procedure.