Response‐Adaptive Regression for Longitudinal Data

Summary We propose a response‐adaptive model for functional linear regression, which is adapted to sparsely sampled longitudinal responses. Our method aims at predicting response trajectories and models the regression relationship by directly conditioning the sparse and irregular observations of the response on the predictor, which can be of scalar, vector, or functional type. This obliterates the need to model the response trajectories, a task that is challenging for sparse longitudinal data and was previously required for functional regression implementations for longitudinal data. The proposed approach turns out to be superior compared to previous functional regression approaches in terms of prediction error. It encompasses a variety of regression settings that are relevant for the functional modeling of longitudinal data in the life sciences. The improved prediction of response trajectories with the proposed response‐adaptive approach is illustrated for a longitudinal study of Kiwi weight growth and by an analysis of the dynamic relationship between viral load and CD4 cell counts observed in AIDS clinical trials.