Review and evaluation of methods for computing confidence intervals for the ratio of two proportions and considerations for non-inferiority clinical trials

This article reviews several methods for forming confidence intervals for a risk ratio of two independent binomial proportions (which are both less than 0.50) and evaluates their statistical performance. These methods include use of a Taylor Series expansion to estimate variance, solutions to a quadratic equation, and maximum likelihood methods. In addition, for improvement of the properties of the methods based on large sample approximations, situations where either binomial count was less than or equal to 3 were managed conservatively by having an exact confidence interval for the odds ratio become the confidence interval for its risk ratio counterpart. Methods were initially evaluated by computing confidence limits for certain cases. Second, simulations were used to identify the better methods for controlling the Type I error rate while maintaining power. Last, relationships between methods were evaluated by calculating the percent of disagreement in the decision made regarding noninferiority. Methods in the group using a Taylor Series expansion in variance estimation perform similarly to the Pearson method preferred in the literature. In addition, the group of methods using a Taylor Series expansion are most easily computed. Applications of these findings are discussed for ratios that arise in randomized clinical trials that are conducted to show noninferiority of a new medical product to a reference control. Consideration is given as well to sample size calculations for noninferiority clinical trials.