Le jeudi 17 février 2011, à 13 h 30, en la salle 2500 du pavillon Adrien-Pouliot

*Optimal Design for Clinical Trials with an Unknown Delay in Treatment Effect*

Juli Atherton, Université McGill

Sometimes clinical trials data consist, for each subject, of a sequence of baseline pre-treatment observations that are followed by a sequence of post-treatment observations. In such trials subjects serve as their own controls. Alternatively, in a randomized controlled trial with say, a control group and one or more treatment groups, a sequence of post-treatment observations is taken on each treatment group from the start of the study. In either situation, if there is an unknown delay before a treatment takes effect (assuming it does), the subject specific times-to-effect can be viewed as the unknown change-points in a multipath change-point setting. Once the data are collected, i) they may be used to estimate the size of each treatment effect and ii) to estimate the proportion of subjects that will experience a treatment effect. Before the data are collected, however, design is the main concern, and optimal timing of the observations will enhance the precision of the eventual inference.

In a broader setting, we consider, optimal design for multipath change-point problems, focusing on problems motivated by i) and ii) above. These optimal design problems are highly non-linear and a Bayesian approach is advantageous. By introducing a design measure we are able to convert a multimodal design criterion function of the design points, into one that is a concave function of the design measures over a simple region. Through this device we reduce the optimal design problem to a feasible numerical search. We carry out simulations whose results have ramifications for the design of clinical trials in which there is an unknown lag between the start of treatment and the occurrence of an effect. In particular, our results suggest that the standard practice-no doubt historically used for convenience-of having a common observation protocol for all subjects, is, in fact, under “objective modeling”, optimal. Further, in many situations, choosing equally spaced observations, which is another common and convenient practice, does not entail a substantial loss in efficiency.