Basu, Cynthia2017-11-272017-11-272017-08https://hdl.handle.net/11299/191398University of Minnesota Ph.D. dissertation.August 2017. Major: Biostatistics. Advisor: Bradley Carlin. 1 computer file (PDF); x, 74 pages.A rare disease is defined by the Rare Diseases Act of 2002 as a disease that currently affects fewer than 200,000 patients in the USA. A pediatric population is one where the subjects are of age 18 or less. These two crucial yet underserved types of populations come with their own limitations in clinical trials. The paucity of potential trial enrollees and sensitivity of these patients, combined with a lack of sufficient natural history and experience, presents several economical, logistical and ethical challenges when designing clinical trials. An increasingly well accepted approach to address these challenges has been data extrapolation; that is, the leveraging of available data from adults or older age groups to draw conclusions for the pediatric population. Bayesian hierarchical modeling facilitates the combining (or ``borrowing") of information across disparate sources, such as adult and pediatric data. In this thesis we begin by developing, illustrating, and providing suggestions for Bayesian statistical methods that could be used to design improved clinical trials for pediatric and rare disease populations that efficiently use all available information. A variety of relevant Bayesian approaches are described, several of which are illustrated through two case studies: extrapolating adult binary efficacy data to expand the labeling for the drug Remicade to include pediatric ulcerative colitis, and a simulated continuous longitudinal dataset patterned after an evaluation of the drug cinacalcet in treating pediatric secondary hyperparathyroidism (HPT). The thesis then turns to methods useful in the study of X-linked adrenoleukodystrophy (X-ALD), a rare neurodegenerative disease for which Lorenzo’s Oil (LO) is one of the few available treatments. We offer a hierarchical Bayesian statistical approach to understanding the pharmacokinetics (PK) and pharmacodynamics (PD) of LO, linking its %We experiment with individual- and observational-level errors and various choices of prior distributions and deal with the limitation of having just one observation per administration of the drug, as opposed to the more usual multiple observations per administration. dose to the plasma erucic acid concentrations by PK modeling, and then linking this concentration to a biomarker (C26, a very long-chain fatty acid) by PD modeling. Next, we design a Bayesian Phase IIa study to estimate precisely what improvements in the biomarker can arise from various LO doses while simultaneously modeling a binary toxicity endpoint. Our Bayesian adaptive algorithm emerges as reasonably robust and efficient while still retaining good classical (frequentist) operating characteristics. Future work in this area looks toward using the results of this trial to design a Phase III study linking LO dose to actual improvements in health status, as measured by the appearance of brain lesions observed via magnetic resonance imaging. Finally, the thesis shows how to utilize the rich PK/PD data to inform the borrowing of information from adults during pediatric drug development. Here we illustrate our approaches in the context of evaluating safety and efficacy of cinacalcet for treating HPT in pediatric and adult patients. We use population PK/PD modeling of the cinacalcet data to quantitatively assess the similarity between adults and children, and in turn use this information in various hierarchical Bayesian rules for borrowing from adults, statistical properties of which can then be evaluated. In particular, we simulate the bias and mean square error performance of our approaches in settings where borrowing is and is not warranted to inform guidelines for the future use of our methods.enBayesian Hierarchical ModelsClinical TrialsData ExtrapolationPK/PDThesis or Dissertation