UC Irvine

The proportional hazards (PH) model is widely used in time-to-event analyses, including within the nested case-control (NCC) design, an efficient sampling approach often used to reduce data collection costs in rare disease settings. By including all events and a subsample of controls, the NCC design maximizes information while reducing the number of subjects requiring full covariate information. Since the NCC design uses fewer controls compared to the full cohort analysis, however, it also reduces the number of subjects from underrepresented groups included in the sample. This further exacerbates the issue of underrepresentation in clinical research and diminishes our ability to assess potential effect modification in these subpopulations. Additionally, while the NCC design has been extensively studied for univariate outcomes, its application to multiple event data remains limited.In this dissertation, we present novel statistical methods to bridge existing gaps in current methodology for efficient sampling and robust estimation for time-to-event data. Specifically, we propose an extension of the NCC design that allows for oversampling of subpopulations, thereby maximizing precision for estimated covariate effects in these groups. The resulting estimation framework yields asymptotically valid inference in both marginal and stratified analyses while maximizing efficiency in underrepresented subpopulations. We also explore NCC sampling frameworks for multiple event settings and propose an event-specific stratified sampling design with corresponding estimation methods for marginal parameter inference. We consider the efficiency of various proposed frameworks for sampling controls, highlighting differences in performance between models assuming common and event-specific baseline hazards across recurrent events. Finally, we transition to the full cohort setting, where we assess robustness of standard proportional hazards estimators under violation of key model assumptions in the multiple event setting. We show that the estimand corresponding to the partial likelihood is dependent upon the event-specific censoring and survival distributions. The result is that commonly implemented diagnostics for multiple event survival can be shown to be misleading in situations where the baseline hazard varies by event type. The work in this dissertation is motivated by current challenges in biomarker development in the setting of Alzheimer’s disease, and applications to this area are presented.