Optimal placebo response rates for comparing two binomial proportions.

This paper considers the problem of comparing proportions in clinical trials where two parallel groups are studied. The question of what will happen to the response rate of an active therapy if some external factor affects the placebo rate is asked and two different, but similar, answers are proposed. Assuming either a logistic or probit model has substantial influence on the sample size required to detect differences and optimal comparisons are suggested. The idea is illustrated by a clinical trial of treatment for peptic ulcer and suggestions for other possible applications are presented.