have been used to estimate heritable traits of host resistance (Bisset et al.,1992;Vanimisetti
et al., 2004). The precision of the FEC measurement is known to be related to the number
of eggs counted (Hunter and Quenouille,1952), and therefore the mean FEC and minimum
egg detection threshold of the technique used. Attempts have been made to quantify the
observed variability between FEC using the McMasters technique (Levine et al.,1960;Dunn
and Keymer, 1986;Rossanigo and Gruner, 1991), to derive the optimal number of samples
to take (Hunter and Quenouille,1952;Gasbarre et al.,1996), and to calculate the power of
a FECRT (Gill et al.,1986). However, none of these studies have used a modelling approach
to attempt to partition the variance.
The seasonal variation in parasite burden and mean FEC has been well described in rumi-
nants (for exampleParnell,1962;Reid and Armour,1972;Eysker and Vanmeurs,1982;Smeal
et al.,1977), and has also been reported in horses (Ogbourne,1971; Herd,1986; Langrov´a,
1998; Baudena et al., 2000). However less is known about the variation in true mean FEC over a shorter period of time. It has been suggested that observed FEC vary over the course
of a day due to factors related to feed intake and gut mobility of the host (Uhlinger,1993),
although Bennett (1990) found no evidence for the diurnal variation in FEC of horses and
Keymer and Hiorns(1986) found no measurable bias in FEC in a study in mice, suggesting that observed variability is truly random. Attempts have also been made to evaluate the
use of pooled FEC samples (Eysker et al.,2008), although again without much consideration
to the statistical processes underlying the procedure. Alternative methods based on similar
principles to the McMasters technique have also been proposed (Mes,2003;Presland et al.,
2005; Cringoli, 2006), and in some cases the observed variability using the newer technique
has been shown to be less than that obtained using the McMasters technique (Mes, 2003;
Presland et al., 2005). However, none of the studies have identified the true source of the
observed variability, and some of the statistical conclusions made by Mes (2003) have been
questioned (Morrison,2004). Use of more rigorous statistical approaches to partition the ob-
served variability would therefore be of benefit. In addition, by improving the understanding of the statistical processes underlying the test, it may be possible to make recommendations that would improve the repeatability of the test.
1.4
Study objectives
The overall scope of this thesis was to use a quantitative approach to improve the analysis of faecal worm egg count data. More specific objectives were to investigate statistical issues pertaining to the analysis of FEC and FECRT data, in order to improve analysis techniques for existing data, and then to develop sample size calculation techniques with which to design future studies. In order to facilitate this, novel methods for analysis of FEC data were first developed and validated using simulated data before being applied to biological datasets.
1.4 STUDY OBJECTIVES
The progression of this thesis towards achieving these goals is outlined below.
Analysis of parasitological datasets is usually mainly concerned with providing inference on the true mean FEC, although the variability of the distribution is often also quantified using one of several possible measures. The biological relevance of each of these measures is dis- cussed, and the properties of the chosen measure demonstrated. Asymptotic assumptions are likely to be violated with FEC data, therefore methods of analysis using Bayesian MCMC were explored. Several different syntactic variations of MCMC models representing differ- ent biologically plausible distributions were compared using simulated datasets to find the parametrisation that produced the most appropriate inference for each distribution. The inference made, particularly from sparse datasets, was substantially affected by the choice of MCMC model parametrisation.
Issues pertaining to the choice of statistical technique and model selection were then explored using simulated datasets to ascertain the consequences of making incorrect asymptotic and distributional assumptions. The usefulness of model selection based on empirical fit was also examined using similar methods. As the zero-inflated and over-dispersed distributions discussed are variously nested around the Poisson distribution, the inference made using under- and over-specified models was compared, and the potential consequences were the true distribution unknown are discussed. The validated MCMC methods were then applied to FEC data obtained from horses and sheep to examine the parameter distributions and distributional fit in field data, and the inferences compared to those made using the existing methods of analysing FEC data examined in the simulation studies. The FEC data used were from parasites with completely distinct fundamental biology as well as different host species. The inference made from each type of data, including the difference in empirical fit to contrasting frequency distributions, is discussed.
A further set of models to address the specific issue of the FECRT were then developed and compared to existing methods using simulation studies, before being applied to biological datasets. The FECRT data were from diverse sources and relate specifically to screening for anthelmintic resistance within cyathostomin populations in horses. Statistical issues pertain- ing to appropriate methods of FECRT data collection and analysis were then discussed, and potential biases of the currently most widely used procedure elucidated.
Finally, a multi-level MCMC model was used to analyse FEC data obtained by repeat sam- pling of horses so that the effect of sample variability between observed FEC could be quan- tified, and recommendations to improve the repeatability of the McMasters technique are made. Using this information, methods of performing prospective precision analysis for FEC sampling, and power analysis calculations for hypothesis driven FECRT procedures, were developed and parametrised using the above inference on the variability structure of equine FEC data.