Abstract: Clinical studies with time-to-event outcomes often collect measurements of a large number of time-varying covariates over time (e.g., clinical assessments or neuroimaging biomarkers) in order to build a time-sensitive prognostic model. However, resource-intensive or invasive (e.g., lumbar puncture) data-collection processes mean that biomarkers may be measured infrequently and, thus, not be available at every observed event time point. Therefore, leveraging all available time-varying biomarkers is important to improving our models event occurrence. We propose a kernel smoothing-based approach that borrows information across subjects to remedy the problem of infrequent and unbalanced biomarker measurements under a time-varying hazards model. A penalized pseudo-likelihood function is proposed for estimation, and an efficient augmented penalization minimization algorithm related to the alternating direction method of multipliers is adopted for computation. Given several regularity conditions, used to control the approximation bias and stochastic variability, we show that even in the presence of ultrahigh dimensionality, the proposed method selects important biomarkers with high probability. We use simulation studies to show that our method outperforms existing methods in terms of estimation and selection performance. Finally, we apply the proposed method to real data to model time-to-disease conversion using longitudinal, whole-brain structural magnetic resonance imaging biomarkers. The results show substantial improvement in performance over that of current standards, including using baseline measures only.

Key words and phrases: Biomarker studies, high-dimensional covariates, irregular measurements, kernel-weighted estimation, neurological disorders, time-varying hazards model.