Estimation of the binomial probabilities in a two-stage phase II clinical trial with two co-primary endpoints

In cancer research, two-stage designs are usually used to assess the effect of a new agent in phase II clinical trials. Optimal two-stage designs with two co-primary endpoints have been proposed to assess the effects of new cancer treatments, such as cytostatic or molecularly targeted agents (MTAs), based on both response rate and early progression rate. Accurate estimation of response and early progression rates based on the data from the phase II trials conducted according to the optimal two-stage designs would be very useful for further testing of the agents in phase II trials. In this paper, we derive some estimation procedures, which include both standard and bias-corrected maximum likelihood estimates (MLE) and uniformly minimum variance unbiased estimate (UMVUE), for two binomial probabilities which are used to define the hypotheses for two co-primary endpoints tested in a two-stage phase II clinical trial. Simulation studies were performed to evaluate the performance of these procedures. These procedures are also applied to analyze the data from a phase II trial conducted by the Canadian Cancer Trials Group.