Sample sizes required for binomial trials when the true response rates are estimated

Abstract

Binomial trial sample size specification depends upon the values of the unknown response rate parameters, as well as upon the size and power of the resulting test. In practice, the values assumed for these parameters are based upon the results of previous or pilot trials, or upon the investigator's prior knowledge or belief. In either case, there is some uncertainty associated with these values that should be taken into account if the sample sizes are to be specified realistically. This paper describes a procedure for incorporating this uncertainty explicitly into the sample size determination on the basis of joint confidence distributions obtained from the pilot or prior information.