Accuracy and precision of alternative estimators of ectoparasiticide efficacy

While there is consensus that the efficacy of parasiticides is properly assessed using the Abbott formula, there is as yet no general consensus on the use of arithmetic versus geometric mean numbers of surviving parasites in the formula. The purpose of this paper is to investigate the accuracy and precision of various efficacy estimators based on the Abbott formula which alternatively use arithmetic mean, geometric mean and median numbers of surviving parasites; we also consider a maximum likelihood estimator. Our study shows that the best estimators using geometric means are competitive, with respect to root mean squared error, with the conventional Abbott estimator using arithmetic means, as they have lower average and lower median root mean square error over the parameter scenarios which we investigated. However, our study confirms that Abbott estimators using geometric means are potentially biased upwards, and this upward bias is substantial in particular when the test product has substandard efficacy (90% and below). For this reason, we recommend that the Abbott estimator be calculated using arithmetic means.