Sample size re-estimation in group-sequential response-adaptive clinical trials

In clinical trials where the variances of the response variables are unknown, in accurate estimates of these can affect the type II error rate considerably. More accurate estimates of the variances may be obtained by taking a look at the data available part way through the trial and re-calculating the required sample size based on these new estimates. The main impetus for sample size re-estimation came from a two-stage procedure developed by Stein in 1945 and the literature is now replete with variations on this approach. In this paper, existing sample size re-estimation methods for both fixed sample and sequential clinical trial models will be reviewed. These will then be extended for use in group-sequential response-adaptive designs. In particular, a test for a recently developed group-sequential response-adaptive design, which compares two treatments with immediate normally distributed responses and unknown variances, is presented based on a modified version of Stein's test. The principal modifications involve updating the required sample size at each interim analysis and calculating the test statistic based on the current estimates of the variances. Hence, all the available information is used at each stage. Simulation is used to assess to what extent the updating of the required sample size at each interim analysis in the new test helps to attain the nominal error rates. The test is compared to modified versions of a simple test and a Stein-type group sequential t-test studied in the recent literature. These tests calculate the required sample sizes based on less accurate estimates of the variances. The type I error rate is close to the nominal value and the power is more accurately maintained in the new test.