Locally optimal design for comparing two probabilities from binomial data subject to misclassification

Abstract

Optimal experimental designs are found for estimating the difference P 1− P 2 of two population probabilities, using measuring instruments possibly subject to known error rates. The available experiments considered are to measure, for i = 1 or 2, the outcome of a trial on the population i without error, or with error, or with error with the possibility of checking either positive or negative responses. Given that the cost per observation depends on which experiment is carried out, an asymptotically locally optimal allocation is derived in terms of results of Elfving which provide a simple geometrical solution which is easily generalized.