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The choice of sample size: a mixed Bayesian / frequentist approach

¹ Center of Excellence in Biomathematics and School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran
² Department of Statistics, Allameh Tabatabaie University, Tehran, Iran
³ Department of Statistics, University of Oxford, UK

^* To whom correspondence should be addressed.

	Abstract

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parametersis taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy etal. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority,which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected netbenefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.

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