Selecting One of Two Treatments When the Responses are Dichotomous

Abstract

A decision theoretic approach to the design of a clinical trial is considered for the situation in which a total of N patients with a disease receive one of two treatments and the responses to the treatments are dichotomous. Two costs are considered: The cost of treating a patient with the inferior treatment and the cost of conducting the trial. Minimax and Bayes procedures are used to determine the optimum size of a fixed sample trial. Bayes solutions for the optimum sample size are given for a variety of beta prior distributions and various values of N. Minimax solutions are given for a variety of regions over which the minimaxing was performed, and for various values of N. The optimum sample sizes are found to be asymptotically proportional to N ^1/2 using the Bayes procedure and N ^2/3 using the minimax procedure. The consequences of erring in specifying the value of N are explored.