Functional principal components analysis on moving time windows of longitudinal data: dynamic prediction of times to event

Functional principal component analysis (FPCA) is a powerful approach for modelling noisy and irregularly measured longitudinal data. Similarly to principal component analysis that extracts features from multivariate random vectors, FPCA can extract features from longitudinal biomarker data. We propose to use these features to update predictions for patients’ prognoses frequently. Traditional FPCA applies only to data observed in a common time window. In the setting of time-to-event analysis, the patterns of the biomarker trajectories may change over time, which poses a challenge for the application of FPCA to dynamic prediction. We propose to use a series of moving time windows to apply FPCA techniques, and we impose smoothness constraints between parameters for these moving windows. Simulation studies show that the approach proposed can provide more robust performance than predictions based on parametric models for longitudinal biomarker data, by prediction judged by performance measures such as the root-mean-square errors and area under the curve of receiver operating characteristics. We apply the method to a longitudinal study for chronic myeloid leukaemia patients, predicting their time to disease progression by using the transcript levels of an oncogene, BCR-ABL, which is repeatedly measured during their follow-up visits.