Development of an MCMC model for analysis of FECRT data

Parasitology (Coles et al., 1992) and the “International Co-operation on Harmonisation of

technical Requirements for Registration of Veterinary Medicinal Products” (Vercruysse et al.,

2002).

It is difficult to demonstrate resistance or susceptibility within a parasite population if the

FECRT data are analysed inappropriately (Duncan et al.,2002). The use of point estimates

for the reduction in faecal egg count takes no account of variability, and results in large

confidence intervals which reduce the value of the results (Martin et al.,1989). Such methods

also fail to take into account the aggregation of parasites within the population, which not only results in potentially valuable information being lost, but can also be a source of statistical

error if not taken into account when analysing the results of FECRT (Morgan et al.,2005).

The difficulty in analysing changes in low faecal egg counts has prompted some authors to

advocate using only horses with an initial faecal egg count of greater than 150 EPG (Craven

et al., 1998; Coles et al., 2006), which in some situations drastically reduces the number of horses available for study and could potentially bias the results. The need to distinguish treatment failure due to clinical resistance from treatment failure due to other causes, such as incorrect dosage and rapid reinfection, is also important for the detection of true anthelmintic

resistance (Uhlinger,1993). However, it is essential that these factors are overcome so that

early and accurate determination of resistance can be achieved.

5.2

Development of an MCMC model for analysis of FECRT

data

There are several different ways of formulating a MCMC model to analyse FECRT data. The majority of datasets include a pre-treatment count for each animal in a similar way to the

data analysed inChapters 2to4, and so the same distribution could be fitted to these data. A

separate distribution could then be fitted to the post-treatment data, with a mean which has been scaled relative to the pre-treatment mean and a variance parameter that has been scaled relative to the pre-treatment variance parameter. This scale in mean would be used to infer the efficacy of the reduction, and most closely resembles the empirical mean reduction that is currently used to analyse such data. Either the lognormal or gamma distributions could be used to describe the distribution of mean counts, although use of the lognormal would make calculation of the change in geometric mean, equivalent to change in arithmetic mean on the log scale, simpler to calculate than the change in arithmetic mean, whereas the change in arithmetic mean is easier to calculate for the gamma distribution. Both the geometric and arithmetic means have been used by parasitologists, although often with no justification, so that either formulation could be chosen. However, it can be argued that the arithmetic mean is more useful on an epidemiological basis as it represents the pasture contamination rate more closely, and most published efficacy studies seem to be concerned with the arithmetic mean,

5.2 DEVELOPMENT OF AN MCMC MODEL FOR ANALYSIS OF FECRT DATA

so the change in arithmetic mean using a gamma formulation will be used. As before, the gamma-Poisson can be used both with and without a zero-inflated component, depending on biological reasoning with individual datasets. Typically, two counts, representing the pre- and post-treatment counts, are available from each animal from a FECRT, therefore a common group classification will be used for the two counts for each animal. This is to say that if an animal is part of the zero-inflated group at pre-treatment, then it must be part of the same group at post-treatment. Consequently, if a non-zero count is observed at either pre- or post-treatment then the animal must be classified as part of the infected group for both. This formulation allows variability to exist both within and between animals, although neither are modelled explicitly and only the combined variability is modelled. The variability is allowed to change after treatment, therefore the variation between animals may change, possibly as a result of differing efficacy between animals, and the variability within an animal may also change, possibly as a result of variation in fecundity following treatment. Again, these individual sources of variability are not explicitly modelled, and are combined into the single change in variability parameter. It is not possible to separate these sources of variability with only a single observation per animal before and after treatment, but as they are accounted for in the model the estimate of efficacy should be robust to these effects. One drawback of this formulation is that the ‘paired’ effect of animal between pre- and post- treatment data is ignored, potentially resulting in a loss of power. This could be addressed by using a different formulation, whereby the same distribution is applied to the pre-treatment counts and a distribution of efficacy is applied to the count means, resulting in the means for the post-treatment observed counts. The variability sources are addressed slightly differently with this model, with the pre-treatment within and between animal variability accounted for in the same way before, and the shape of the distribution of efficacy reflecting the variability within animals before and after treatment as well as the change in variability between animals after treatment, i.e. the ‘true’ efficacy distribution. A beta distribution could be used for this efficacy distribution, which would constrain the individual mean changes to between zero and one. However, this may not be appropriate because the true mean of the post- treatment sample may truly be higher than that of the pre-treatment sample given the affect of within animal variability on this parameter. More appropriately, a gamma or lognormal distribution could be used which would allow the individual change in mean to be above one, representing an individual efficacy of below zero, but with a prior on the mean value restricting it to values of less than one, representing a mean efficacy of greater than zero. However, in pilot tests of this model formulation using both beta and gamma distributions on simulated data with values of dataset and mean taken from real data, extremely poor convergence was observed. This may be due to model identifiably issues associated with the multiple sources of variability associated with the efficacy distribution. It is also possible that the comparatively good convergence of the first model formulation is as a result of inferring the post-treatment variability, where there is comparatively little information as a result of the lower mean counts, from the pre-treatment variability where there is more