University of Washington - Department of Statistics
A problem encountered across many fields in science, engineering and medicine, is finding a specific percentile of a binary-response threshold distribution (for example: finding the ED50 of a medication). Statisticians have designed two popular sequential solutions to this challenge: 'Up-and-Down' (U&D), a 1940â€™s vintage method; and Bayesian designs - most prominently 'Continual Reassessment Method' (CRM, Oâ€™Quigley et al., 1990), a design tailored to Phase I clinical trials.
U&D generates a random walk revolving around the target percentile. The theoretical properties of this walk, though relatively simple, have been seldom studied since the 1960â€™s. CRM has greater current appeal among statisticians â€“ but its convergence has not quite been proven. In my dissertation, I have attempted to tackle these two knowledge gaps and related issues, keeping in mind the needs and challenges encountered in practice. I have also tried to determine which of the two approaches is preferable under typical scenarios â€“ and whether they can be combined.