Frequentist and Bayesian Pharmacometric-Based Approaches To Facilitate Critically Needed New Antibiotic Development: Overcoming Lies, Damn Lies, and Statistics

Abstract

ABSTRACTAntimicrobial drug development has greatly diminished due to regulatory uncertainty about the magnitude of the antibiotic treatment effect. Herein we evaluate the utility of pharmacometric-based analyses for determining the magnitude of the treatment effect. Frequentist and Bayesian pharmacometric-based logistic regression analyses were conducted by using data from a phase 3 clinical trial of tigecycline-treated patients with hospital-acquired pneumonia (HAP) to evaluate relationships between the probability of microbiological or clinical success and the free-drug area under the concentration-time curve from time zero to 24 h (AUC0-24)/MIC ratio. By using both the frequentist and Bayesian approaches, the magnitude of the treatment effect was determined using three different methods based on the probability of success at free-drug AUC0-24/MIC ratios of 0.01 and 25. Differences in point estimates of the treatment effect for microbiological response (method 1) were larger using the frequentist approach than using the Bayesian approach (Bayesian estimate, 0.395; frequentist estimate, 0.637). However, the Bayesian credible intervals were tighter than the frequentist confidence intervals, demonstrating increased certainty with the former approach. The treatment effect determined by taking the difference in the probabilities of success between the upper limit of a 95% interval for the minimal exposure and the lower limit of a 95% interval at the maximal exposure (method 2) was greater for the Bayesian analysis (Bayesian estimate, 0.074; frequentist estimate, 0.004). After utilizing bootstrapping to determine the lower 95% bounds for the treatment effect (method 3), treatment effect estimates were still higher for the Bayesian analysis (Bayesian estimate, 0.301; frequentist estimate, 0.166). These results demonstrate the utility of frequentist and Bayesian pharmacometric-based analyses for the determination of the treatment effect using contemporary trial endpoints. Additionally, as demonstrated by using pharmacokinetic-pharmacodynamic data, the magnitude of the treatment effect for patients with HAP is large.