Confidence Limits for the Ratio of Two Binomial Proportions Based on Likelihood Scores: Non‐Iterative Method

The interval estimation of the ratio of two binomial proportions based on the score statistic is superior over other methods. Iterative algorithms for calculating the approximate confidence interval have been provided by, e.g., KOOPMAN (1984, Biometrics 40:513–517) and GART and NAM (1988a, Biometrics 44:323–338). This note presents the analytical solutions for upper and lower confidence limits in a closed form and gives examples for numerical illustration. The non‐iterative method is generally more desirable than the iterative method.