Optimal allocation for the comparison of proportions.

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.