Dynamic Regression of Longitudinal Trajectory Features

Chronic disease studies often collect data on biological and clinical markers at follow-up visits to monitor disease progression. Viewing such longitudinal measurements governed by latent continuous trajectories, we develop a new dynamic regression framework to investigate the heterogeneity pattern of certain features of the latent individual trajectory that may carry substantive information on disease risk or status. Employing the strategy of multi-level modeling, we formulate the latent individual trajectory feature of interest through a flexible pseudo B-spline model with subject-specific random parameters, and then link it with the observed covariates through quantile regression, avoiding restrictive parametric distributional assumptions that are typically required by standard multi-level longitudinal models. We propose an estimation procedure from adapting the principle of conditional score and develop an efficient algorithm for implementation. Our proposals yield estimators with desirable asymptotic properties as well as good finite-sample performance as confirmed by extensive simulation studies. An application of the proposed method to a cohort of participants with mild cognitive impairment (MCI) in the Uniform Data Set (UDS) provides useful insights about the complex heterogeneous presentations of cognitive decline in MCI patients.