Estimation of secondary endpoints in two-stage phase II oncology trials

In the development of a new treatment in oncology, phase II trials play a key role. On the basis of the data obtained during phase II, it is decided whether the treatment should be studied further. Therefore, the decision to be made on the basis of the data of a phase II trial must be as accurate as possible. For ethical and economic reasons, phase II trials are usually performed with a planned interim analysis. Furthermore, the decision about stopping or continuing the study is usually based on a short-term outcome like tumor response, whereas secondary endpoints comprise stable disease, progressive disease, toxicity, and/or overall survival. The data obtained in a phase II trial are often analyzed and interpreted by applying the maximum likelihood estimator (MLE) without taking into account the sequential nature of the trial. However, this approach provides biased results and may therefore lead to wrong conclusions. Whereas unbiased estimators for two-stage designs have been derived for the primary endpoint, such estimators are currently not available for secondary endpoints. We present uniformly minimum variance unbiased estimators (UMVUE) for secondary endpoints in two-stage designs that allow stopping for futility (and efficacy). We compare the mean squared error of the UMVUE and the MLE and investigate the efficiency of the UMVUE. A clinical trial example illustrates the application.