Faecal egg count reduction test

Suppose a group of ${\displaystyle n_{T}}$ animals received anthelmintic treatment and a group of ${\displaystyle n_{C}}$ animals serves as control. The percentage reduction in fecal egg counts can be calculated as

${\displaystyle {\text{Percentage reduction }}=100\times \left(1-{\frac {{\bar {x}}_{T}}{{\bar {x}}_{C}}}\right)}$

where ${\displaystyle {\bar {x}}_{T}}$ and ${\displaystyle {\bar {x}}_{C}}$ denote the mean counts of the treatment and the control group. Assuming independence, the estimated asymptotic variance of the log ratio is given by

${\displaystyle {\widehat {\text{Var}}}\left(\log {\frac {{\bar {X}}_{T}}{{\bar {X}}_{C}}}\right)={\frac {s_{T}^{2}}{n_{T}{\bar {x}}_{T}^{2}}}+{\frac {s_{C}^{2}}{n_{C}{\bar {x}}_{C}^{2}}}.}$

where ${\displaystyle {\bar {X}}_{T}}$ and ${\displaystyle {\bar {X}}_{C}}$ denote the means of random samples, ${\displaystyle s_{T}^{2}}$ and ${\displaystyle s_{C}^{2}}$ denote the sample variance of the treatment and the control group counts. The variance can be used to construct an approximate 95% CI of the log ratio using the 97.5% and the 2.5% quantile of a Student's t-distribution with ${\displaystyle n_{T}+n_{C}-2}$ degrees of freedom. The CI for the log-ratio can be then transformed back to obtain the 95% CI for the estimated reduction.

The World Association for the Advancement of Veterinary Parasitology guideline [1] states that for sheep and goats, the resistance is present if

(i) the percentage reduction in fecal egg counts is less than 95% and,

(ii) the corresponding lower 95% confidence limit is less than 90%.

If only one of these two criterion is met, then an anthelmintic resistance is suspected. Different thresholds have been suggested for other livestock.

Firstly, the conventional counting techniques such as the McMaster method introduce additional variability in the counts which is not accounted for in the fecal egg count reduction test.[2] As a result, the estimated percentage reduction are less reliable especially for low counts. Secondly, the distribution of egg counts is typically aggregated within the host population. There were several attempts to propose more elaborate statistical models in the past years.[3][4] An emerging class of statistical model, namely Bayesian hierarchical models, has been proposed to overcome these problems.[5][6][7][8][9] Easy-to-use software [10][11] and website interface [12] based on those sophisticated but reliable statistical models are available to aid veterinary researchers.