Hierarchical models for combining nonexchangeable sources of survival and functional data

Conventional approaches to statistical inference preclude structures that facilitate incorporation of partially informative supplemental information acquired from similar circumstances. Borrowing strength from supplemental data promises to facilitate greater efficiency in the scientific investigative process, but neglecting to account for heterogeneity across the sources of information obscures understanding of the complex underlying mechanisms that produced the primary data, and may lead to biased inference. As such, inference should derive from flexible statistical models that account for inherent uncertainty while favoring the primary information as evidence for between-source heterogeneity arises. We extend existing flexible borrowing methods to settings where the estimation of a curve is of primary interest, and the amount of borrowing reflects congruence in curve shape across sources of information.;First, we propose flexible borrowing methods for time-to-event data using a piecewise exponential model construction, wherein we borrow with respect to the a parameterized baseline hazard function. We apply these methods to data assessing time to cardiac revascularization in peritoneal dialysis patients who received a heart stent. Second, we develop a piecewise log-linear hazard model using low rank thin-plate splines to model the baseline hazard and functional covariate effects possibly subject to shape restrictions. We apply these methods to data from a colorectal cancer clinical trial assessing the comparative effectiveness of three treatment regimes. Third, we propose a general methodological framework for borrowing with respect to the shape of an unknown curve that is characterized by a set of parameters. We illustrate these methods with two applications, in liver imaging and colorectal cancer clinical trials. Throughout the thesis, we conduct simulation investigations that assess the properties and advantages of the proposed methods. Last, we summarize and suggest avenues for future work.