A hypothesis testing framework for the ratio of means of two negative binomial distributions: classifying the efficacy of anthelmintic treatment against intestinal parasites

Over-dispersed count data typically pose a challenge to analysis using standard statistical methods, particularly when evaluating the efficacy of an intervention through the observed effect on the mean. We outline a novel statistical method for analysing such data, along with a statistically coherent framework within which the observed efficacy is assigned one of four easily interpretable classifications relative to a target efficacy: "adequate", "reduced", "borderline" or "inconclusive". We illustrate our approach by analysing the anthelmintic efficacy of mebendazole using a dataset of egg reduction rates relating to three intestinal parasites from a treatment arm of a randomised controlled trial involving 91 children on Pemba Island, Tanzania. Numerical validation of the type I error rates of the novel method indicate that it performs as well as the best existing computationally-simple method, but with the additional advantage of providing valid inference in the case of an observed efficacy of 100%. The framework and statistical analysis method presented also allow the required sample size of a prospective study to be determined via simulation. Both the framework and method presented have high potential utility within medical parasitology, as well as other fields where over-dispersed count datasets are commonplace. In order to facilitate the use of these methods within the wider medical community, user interfaces for both study planning and analysis of existing datasets are freely provided along with our open-source code via: http://www.fecrt.com/framework