Biology Reference
In-Depth Information
chemo-expulsive treatment, residing in separate households.
76
Prior to
this, predisposition and household clustering had been studied
independently of one another. Predisposition had been demonstrated by
the statistical significance of a non-parametric measure of statistical
dependence between worm burdens from the same individual.
19,98,158
Household clustering had typically been demonstrated by dichotomizing
individuals' worm burdens as heavy or light and by determining
a statistically significant difference between the number per household
observed and the number expected by chance.
108
The recent hierarchical
modeling approach, however, revealed that individual predisposition
was very weak and almost entirely subsumed under the clustering effect
of the household.
76
Aside from quantifying the magnitude of correlation among clustered
data, hierarchical techniques permit critical adjustment for the estimated
uncertainty of regression coefficients which, if ignored, can lead to erro-
neous statistical inference. Generally, failing to account for correlation
among non-independent data leads to overoptimistic (narrow) estimates
of regression coefficient standard errors (underestimating the uncertainty
around such estimates). This can lead to erroneous rejection of a null
hypothesis (type I error). Koukounari et al.
159
highlighted the importance
of accounting for hierarchical levels of variation when analyzing the
effectiveness of mass praziquantel treatments on levels of Schistosoma
mansoni infection and morbidity in children measured pre- and post-
treatment and attending different schools. Such hierarchical structures
are common in data collected as part of protocols for the monitoring and
evaluation of interventions.
Hierarchical generalized linear models, commonly referred to as gener-
alized linear mixed models, may be fitted to data using an extension of the
generalized linear model framework
157
which is now standard in statistical
software packages. Methods for fitting hierarchical negative binomial
160
and zero-inflated models have also been developed,
161,162
although
Bayesian methods which exploit the power and versatility of Markov chain
Monte Carlo sampling may prove a more reliable means of fitting such
models.
163,164
Bayesian methods are readily accessible through software
packages such as OpenBUGS, the currently maintained and updated
version of WinBUGS,
165
and JAGS.
166
Spatial and Spatial
Temporal Models
Spatial models are hierarchical models where the clustering units are
spatially structured such that the degree of correlation between pairs of
observations depends on the Euclidean distance between them. Analo-
gously, for spatial
e
temporal models, the correlation between observa-
tions made on the same unit but at different times may depend on their
degree of temporal separation. Such correlation is termed autocorrelation;
e
