| Summary: | A recently developed group-sequential response-adaptive design to compare two treatments with immediate normally distributed responses and known variances is considered. The power function of the test is the same as that under non-adaptive sampling, and significant decreases in the inferior treatment number can be achieved with only minor increases in the average sample number. Reasonably accurate corrected confidence intervals for both the treatment mean difference and the individual means are obtained by constructing approximately pivotal quantities. An approximation to the bias of the maximum likelihood estimator of the treatment mean difference is also studied. When the variances of the response variables are unknown, inaccurate estimates of these can affect the Type II error rate considerably. A new modified version of an existing sample size re-estimation method is developed for group-sequential response-adaptive designs for normal data with unknown variances. The principal modifications involve updating the required sample size at each interim analysis and calculating the test statistic based on current estimates of the variances. Simulation is used to compare the performance of this test with modified versions of two other tests from the recent literature. The power is shown to be more accurately maintained in the new test. An analogous group-sequential response-adaptive design to compare two treatments with immediate dichotomous responses is then developed. Since the variances of the response variables are unknown in binary response trials, due to their dependence on the unknown success probabilities, the new sample size re-estimation method is incorporated into the design. Two parameters of interest are considered, the log odds ratio and the simple difference between the probabilities of success. Three adaptive urn models are studied and their properties are compared to a sequential maximum likelihood estimation rule that minimises the expected number of treatment failures. Simulation results favour the drop-the-loser rule
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