Time-varying Hazards Model for Incorporating Irregularly Measured, High-Dimensional Biomarkers

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) to build time-sensitive prognostic model. An emerging challenge is that due to resource-intensive or invasive (e.g., lumbar puncture) data collection process, biomarkers may be measured infrequently and thus not available at every observed event time point. Lever-aging all available, infrequently measured time-varying biomarkers to improve prognostic model of event occurrence is an important and challenging problem. In this paper, we propose a kernel-smoothing based approach to borrow information across subjects to remedy 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 (ADMM) is adopted for computation. Under some regularity conditions to carefully control approximation bias and stochastic variability, we show that even in the presence of ultra-high dimensionality, the proposed method selects important biomarkers with high probability. Through extensive simulation studies, we demonstrate superior performance in terms of estimation and selection performance compared to alternative methods. Finally, we apply the proposed method to analyze a recently completed real world study to model time to disease conversion using longitudinal, whole brain structural magnetic resonance imaging (MRI) biomarkers, and show a substantial improvement in performance over current standards including using baseline measures only.