Title: Design and analysis of quantile equivalence bridging trials
Description: Bridging clinical trials are sometimes designed to evaluate whether a proposed dose for use in one population, e.g. , children, gives similar pharmacokinetic (PK) levels, or has similar effects on a surrogate marker as an established effective dose used in another population, e.g. , adults. For HIV bridging trials, because of the increased risk of viral resistance to drugs at low PK levels, the goal is often to determine whether the doses used in different populations result in similar percentages of patients with low PK levels. For example, it may be desired to evaluate that a proposed pediatric dose gives approximately 10% of children with PK levels below the 10 th percentile of PK levels for the established adult dose. However, the 10 th percentile for the adult dose is often imprecisely estimated in studies of relatively small size. Little attention has been given to the statistical framework for such bridging studies. This dissertation makes several contributions concerning the design and analysis of such bridging trials, which I term quantile equivalence trials. In the first chapter of the thesis, a formal statistical framework is proposed and the methodology is developed for normally distributed outcome measurements from both frequentist and Bayesian directions. Sample size and other design considerations are discussed. In the second chapter, I consider a more general situation, in which the underlying distributions are unknown. The perturbation resampling method based on asymptotically pivotal quantities is proposed. Simulation studies show that the methods provide decision error rates very close to the desired values and are a considerable improvement over the error rates obtained when the imprecision in estimating the adult quantile is ignored.

In the third chapter, I consider the situation in which bridging data are correlated, e.g. , when drug concentrations for a tested dose are evaluated in pregnant women and then for a standard dose taken by the same women several weeks after delivery. A Bayesian analysis method is proposed when antepartum and postpartum measurements are bivariate normally distributed. Some of the related practical issues are considered including the problem that arises when there are missing postpartum assessments.