Blinded sample size re-estimation in clinical trials comparing several treatments

An important question that arises in clinical trials is how many additional observations, if any, are required beyond those originally planned. This has satisfactorily been answered in the case of two-treatment double-blind clinical experiments. However, one may be interested in comparing a new treatment with its competitors, which may be more than one. This problem is addressed in this investigation involving responses from arbitrary distributions, in which the mean and the variance are not functionally related. First, a solution in determining the initial sample size for specified level of significance and power at a specified alternative is obtained. Then it is shown that when the initial sample size is large, the nominal level of significance and the power at the pre-specified alternative are fairly robust for the proposed sample size re-estimation procedure. An application of the results is made to the blood coagulation functionality problem considered by Kropf et al. Multiple comparisons of treatments with stable multivariate tests in a two-stage adaptive design, including a test for non-inferiority, Biom. J. 42(8) (2000), pp. 951–965].