Dynamic prediction with time-dependent marker in survival analysis using supervised functional principal component analysis

Time-varying biomarkers reflect important information on disease progression over time. Dynamic prediction for event occurrence on a real-time basis, utilizing time-varying information, is crucial in making accurate clinical decisions. Functional principal component analysis (FPCA) has been widely adopted in the literature for extracting features from time-varying biomarker trajectories. However, feature extraction via FPCA is conducted independent of the time-to-event response, which may not produce optimal results when the goal lies in prediction. With this consideration, we propose a novel supervised FPCA, where the functional principal components are determined to optimize the association between the time-varying biomarker and time-to-event outcome. The proposed framework also accommodates irregularly spaced and sparse longitudinal data. Our method is empirically shown to retain better discrimination and calibration performance than the unsupervised FPCA method in simulation studies. Application of the proposed method is also illustrated in the Alzheimer's Disease Neuroimaging Initiative database.