This talk on the theory and application of up-and-down designs is presented in honor of Wilfred Dixon. In an up-and-down experiment, subjects arrive sequentially or in groups, and treatment assignments and are never more than one level distant from the previous treatment. Nice theory for constructing such designs is available when treatment assignments are Markovian. In this talk, we consider two cases:

(1) assume that the probability of toxicity increases with dose, as is typical in Phase I clinical trials and toxicology studies. The goal is to estimate the MTD or the where p is a prespecified toxicity rate. We show how to control the location and spread of the treatment distributions resulting from Markovian up-and-down designs, and how to estimate the quantities of interest. (2) assume that the probability of success is unimodal as a function of dose. We describe a Markovian up-and-down design that clusters treatments around the dose with maximum success probability.

Variations inspired by the Markovian theory will be discussed.



Seminar Date:
February 28, 2007
3:30 pm