Review article Statistical modelling for clinical mastitis in the dairy cow: problems and solutions

3. MAIN TYPES OF MODELS 
FOR MODELLING CLINICAL 
MASTITIS
3.1. Generalist exploratory models
Two main modelling approaches are
performed to identify the CMAST risk fac-
tors: the first is based on a binomial distri-
bution, essentially at the lactation level,
and the second on a Poisson distribution,
used at lactation and herd levels. It is obvi-
ous that going from the herd to the lacta-
tion level, the sample selection is more
difficult and crucial, in relation with meth-
odological problems. 
3.1.1. At the herd level
At the herd level, it seems important to
consider a potential overdispersion, at least
in an empiric way, even if the causes of
overdispersion are not identified. An anal-
ysis based on the Poisson model (through a
GLM procedure) is then adapted while
including a random herd effect [13, 19, 41,
52]. Another choice is the use of a negative
binomial distribution instead of the Poisson
distribution [4, 69, 75]. The elementary

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Statistical modelling for clinical mastitis
499
estimation of the overdispersion in a Pois-
son regression [4, 5, 28] does not allow an
accurate control of the significance of the
tests concerning the factor effects. An anal-
ysis of variance, carried out from the ranks
of the herds classified according to CMAST
incidence (Kruskal-Wallis test) [34], is less
precise in terms of risk factor identification,
since independence hypotheses are still
necessary for its use.
3.1.2. At the lactation level
At the lactation level, a dichotomous
response based on a binomial distribution
allows the exclusion of a potential depend-
ence between successive CMAST cases
within a lactation. If a single lactation is
selected for each animal, a multiple logis-
tic regression model can be performed
through the GML procedure, including at
least one herd or animal effect [24, 29, 70],
or through a survival model when consid-
ering the time occurrence of the first
CMAST of the lactation [71]. If several
lactations of the same animal are selected,
a random animal or lactation effect must be
considered. An alternative method is the
use of a GEE model including the estima-
tion of within lactation correlations for one
animal, or between animal correlations
within a herd [41]. Modelling based on a
beta-binomial distribution can also be per-
formed. This takes a potential overdisper-
sion into account [75]. This is also possible
through a case-control survey, by pairing a
CMAST case with a within herd control, to
use a single lactation per animal and define
a dichotomous response for the lactation in
order to minimise the different dependence
problems [82]. But when using these meth-
ods, the numbers of analysed statistical
units are sharply decreased and conse-
quently it is not reasonable to accurately
evaluate the studied factors.
When the number of lactations including
CMAST cases is considered in the model,
the overdispersion problem is more diffi-
cult to overcome, since all the overdisper-
sion sources are potentially present for all
CMAST perception levels, and the choice
of a censoring period between successive
cases is determinant. Thus, when using gen-
eralist models, it can be recommended to
limit the number of the studied perception
levels, by selecting for example the lacta-
tions which are studied for each animal.
Such a solution was chosen in a study of
successive recurrences in the lactation
period through a logistic model (in a GEE
model), which is aimed at estimating the
correlation matrix between successive
events within a lactation [78]. Earlier meth-
odological issues have tried to solve the
problem defining indices which allow to
study successive reoccurrences [17, 65]. An
empiric approach has also been developed,
through a negative binomial distribution
including a 30-d censoring period [59]. It
nevertheless seems difficult to go on using
statistical analysis generalist methods like
random effect models with the aim to study
all potential overdispersion sources.