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A new approach that extends the classical Clopper-Pearson procedure is proposed for the estimation of the (1–α)% confidence interval of a proportion with over-dispersion. Over-dispersion occurs when a proportion of interest shows more variation (variance inflation) than predicted by the binomial distribution. There are two steps in the approach. The first step consists of the estimation of the variance inflation factor. In the second step, an extended Clopper-Pearson procedure is applied to calculate the confidence interval after the effective sample size is obtained by adjusting with the estimated variance inflation factor. The performance of the extended Clopper-Pearson procedure is evaluated via a Monte Carlo study under the setup motivated from head lice studies. It is demonstrated that the 95% confidence intervals constructed from the new approach generally have the closest coverage rate to target (95%) when compared with those constructed from competing procedures.

The RESTORE-IMI 1 phase 3 trial demonstrated the efficacy and safety of imipenem-cilastatin (IMI) combined with relebactam (REL) for treating imipenem-nonsusceptible infections. The objective of this analysis was to compare the outcomes among patients meeting eligibility requirements based on central laboratory susceptibility versus local laboratory susceptibility. Patients with serious infections caused by imipenem-nonsusceptible, colistin-susceptible, and imipenem-REL-susceptible pathogens were randomized 2:1 to IMI-REL plus placebo or colistin plus IMI for 5 to 21 days.