Geometric means provide a biased efficacy result when conducting a faecal egg count reduction test (FECRT)

The process of conducting a faecal egg count reduction test was simulated to examine whether arithmetic or geometric means offer the best estimate of efficacy in a situation where the true efficacy is known. Two components of sample variation were simulated: selecting hosts from the general population which was modelled by the negative binomial distribution (NBD), and taking an aliquot of faeces from the selected host to estimate the worm egg count by assuming a Poisson distribution of sample counts. Geometric mean counts were determined by adding a constant (C) to each count prior to log transformation, C was set at 25, 12 or 1. Ten thousand Monte Carlo simulations were run to estimate mean efficacy, the 2.5% (lower) and the 97.5% (upper) percentile based on arithmetic or geometric means. Arithmetic means best estimated efficacy for all different levels of worm aggregation. For moderate levels of aggregation and with C = 1 the geometric mean substantially overestimated efficacy. The bias was reduced if C was increased to 25 but the results were no better than those based on arithmetic means. For very high levels of aggregation (over-dispersed populations) the geometric mean underestimated efficacy regardless of the size of C. It is recommended that the guidelines on anthelmintic resistance be revised to advocate the use of arithmetic means to estimate efficacy.