Precision of assessing anthelmintic efficacy

In counting internal helminthic parasites (the "worm burden") of domestic animals, physical restrictions often lead to sampling by small aliquots of unequal size among affected organs, among animals treated alike, and among groups of animals treated differently. We assess the impact of that type of sampling on the precision of the analyzed variable (log of estimated worm burden), derive the variance of the standard nonlinear estimator of efficacy of anthelmintic treatment, and examine the problem of number of animals required for adequate sensitivity of experiments. The standard error of sample geometric mean worm burden, for a particular anthelmintic treatment, and the standard error of estimated efficacy of a treatment, relative to control, are given for the case of log-normal burdens. Small aliquots affect precision critically only if mean burden is small, i.e., when sampling by small aliquots is unnecessary, because the physical effort required is not great. The minimal number of animals per treatment, required for at least 80% power to detect efficacy of .7 or higher, is about 4 to 6 for species of parasites constituting major burdens (where the coefficient of variation of worm burden often is near .7). However, the minimal number of animals may be as high as 15 to 20 per treatment for cases with lowly-abundant species of parasites (where the coefficient of variation may be as high as 2 or 3). An example is given to illustrate procedures.