Spatial Two-stage Designs for Phase II Clinical Trials.

A common endpoint in a single-arm phase II study is tumor response as a binary variable. Two widely used designs for such a study are Simon's two-stage minimax and optimal designs. The minimax design minimizes the maximal sample size and the optimal design minimizes the expected sample size under the null hypothesis. The optimal design generally has the larger total sample size than the minimax design, but its first stage's sample size is smaller than that of the minimax design. The difference in the total sample size between two types of designs can be large and so both designs can be unappealing to investigators. We develop novel designs that compromise on the two optimality criteria and avoid such occurrences using the spatial information on the first stage's required sample size and the total required sample size. We study properties of these spatial designs and show our proposed designs have advantages over Simon's designs and one of its extensions by Lin and Shih. As applications, we construct spatial designs for real-life studies on patients with Hodgkin disease and another study on effect of head and neck cancer on apnea.