A Bayesian cost-benefit approach to the determination of sample size in clinical trials

Current practice for sample size computations in clinical trials is largely based on frequentist or classical methods. These methods have the drawback of requiring a point estimate of the variance of the treatment effect and are based on arbitrary settings of type I and II errors. They also do not directly address the question of achieving the best balance between the cost of the trial and the possible benefits from using the new treatment, and fail to consider the important fact that the number of users depends on the evidence for improvement compared with the current treatment. Our approach, Behavioural Bayes (or BeBay for short), assumes that the number of patients switching to the new medical treatment depends on the strength of the evidence that is provided by clinical trials, and takes a value between zero and the number of potential patients. The better a new treatment, the more the number of patients who want to switch to it and the more the benefit is obtained. We define the optimal sample size to be the sample size that maximizes the expected net benefit resulting from a clinical trial. Gittins and Pezeshk (Drug Inf. Control 2000; 34:355-363; The Statistician 2000; 49(2):177-187) used a simple form of benefit function and assumed paired comparisons between two medical treatments and that the variance of the treatment effect is known. We generalize this setting, by introducing a logistic benefit function, and by extending the more usual unpaired case, without assuming the variance to be known.