Quantile residual lifetime regression with functional principal component analysis of longitudinal data for dynamic prediction

Optimal therapeutic decisions can be made according to disease prognosis, where the residual lifetime is extensively used because of its straightforward interpretation and formula. To predict the residual lifetime in a dynamic manner, a longitudinal biomarker that is repeatedly measured during the post-baseline follow-up period should be included. In this article, we use functional principal component analysis, a powerful and flexible tool, to handle irregularly measured longitudinal data and extract the dominant features over a specific time interval. To capture the time-dependent trajectory pattern, a series of moving time windows are used to estimate window-specific functional principal component analysis scores, which are then combined with a quantile residual lifetime regression model to facilitate dynamic prediction. Estimation of this regression model can be achieved by solving estimating equations with the help of locating the minimizer of the L1-type function. Simulation studies demonstrate the advantages of our proposed method in both calibration and discrimination under various scenarios. The proposed method is applied to data from patients with chronic myeloid leukemia to illustrate its practicality, where we dynamically predict quantile residual lifetimes with longitudinal expression levels of an oncogene, BCR-ABL.