  Conventional approaches to statistical inference preclude structures that
facilitate incorporation of supplemental information acquired from similar
circumstances. For example, the analysis of data obtained using perfusion
computed tomography to characterize functional imaging biomarkers in cancerous
regions of the liver can benefit from partially informative data collected
concurrently in noncancerous regions. This paper presents a hierarchical model
structure that leverages all available information about a curve, using
penalized splines, while accommodating important between-source features. Our
proposed methods flexibly borrow strength from the supplemental data to a
degree that reflects the commensurability of the supplemental curve with the
primary curve. We investigate our method's properties for nonparametric
regression via simulation, and apply it to a set of liver cancer data. We also
apply our method for a semiparametric hazard model to data from a clinical
trial that compares time to disease progression for three colorectal cancer
treatments, while supplementing inference with information from a previous
trial that tested the current standard of care.
