Optimal Allocation for the Comparison of Proportions

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Abstract
Optimal allocation strategies for the comparison of proportions, p1 and p2, in two groups are discussed. Allocations which (i) maximize the precision in the estimation of the difference p1-p2, (ii) maximize the precision in the estimation of the ratio p1/p2, (iii) maximize the power to detect a group difference, and (iv) minimize the total cost of a study are compared. The recommended allocation varies markedly with the desired objective. Furthermore, there is a wide range of allocation schemes which are effectively optimal with regard to each criterion considered. A study of congenital malformations occurring in pregnancies of diabetic women is used to illustrate how these considerations apply to the planning of a study.

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