We consider bivariate Phase II study designs that simultaneously monitor response and toxicity and allow a trade-off between the two. These designs are attractive in cases where an experimental treatment is of interest if it improves efficacy with some compromise in safety or if it slightly compromises efficacy with great improvement in safety. We propose single-stage and two-stage bivariate designs with trade-off in toxicity and response. The rejection rules are based on the total number of responses and toxicities observed over the course of a study. As such, they are easier to interpret and communicate to non-statisticians. Dueto the small number of patients commonly involved in Phase II clinical trials, exact distribution computation is used to obtain sample sizes. Tabulations of sample sizes for selected designs are given.

phase II trial, bivariate outcome, two-stage design, trade-off.