Minimization of sample size when comparing two small probabilities in a non-inferiority safety trial

In clinical trials success rates of two treatments to be compared often range from 10 to 90 per cent. When the comparison probabilities are (much) smaller than 10 per cent, standard methods for sample size and power calculations may provide invalid results. This situation may occur when there is interest in safety rather than in efficacy. In such trials, no more patients should be included than strictly necessary. We compared the results of maximum likelihood methods for the computation of sample sizes in a non-inferiority trial, including exact procedures and considered unequal sample sizes for experimental and reference treatment. An exact, unequal sample size maximum likelihood procedure is advocated when the specified non-zero risk difference under the null hypothesis is not too large. Such a procedure is also indicated when the parameter of interest is the relative risk, rather than the risk difference.