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

3.2.2. Specific survival models
Another method is based on distribution
mixtures in survival models. This is devel-
oped with the aim of a CMAST statistical
model by modelling the dependence between
successive events within the lactation, and
from one lactation to another (Fig. 3). Such
a method easily integrates observable bio-
logical parameters [36, 37]. This approach,
performed at the udder level, integrates the
animal and lactation levels and allows to
test individual and/or herd risk factors.
Through this work, it is possible to study the
distribution of CMAST cases per lactation
and the distribution of CMAST occurrence
periods. Nevertheless, the method does not
integrate at the present time the variability
due to mastitis risk factors at the herd level.
3.2.3. Contribution of the explanatory 
designed models
The two proposed explanatory designed
models are synthesis paths for CMAST
modelling from the results of the generalist
exploratory models. These two modelling
ways (exploratory or empirical vs. explan-
atory) are complementary [22, 58]. 
These new synthetic approaches could
help to solve previously notified problems,
such as the confounding factors and the
integration of various levels of dependence.
With such models, housing and grazing
periods, and more generally all time-
dependent variables [1, 37], can be consid-
ered at the animal level. The study of such
variables associated with that of an infec-
tion rate effect at calving allows to rule out
the lactation stage factor as one of the main
Figure 2. Diagram showing the modelling
elements making it possible to take into account
dynamically different udder-health states in the
same animal (adapted from [1]).

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Statistical modelling for clinical mastitis
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structural variables for mastitis risk from
the modelling process [37]. Consequently,
such explanatory designed models intend to
decrease the confounding problems. With
such models, the dependence between suc-
cessive cases within a lactation can explic-
itly be considered by these models [36]. In
the future, the modelling could be signifi-
cantly improved by performing the study at
the quarter level since quarter bacteriolog-
ical status could be determined. Through
this design, it would be possible to combine
the two explanatory models already pub-
lished [1, 2, 36, 37]. Such explanatory mod-
els could also help to define optimum
criteria for incidence rate definition at the
herd level, even to justify the time lag in
order to eliminate successive reoccurrences
within a lactation. The model developed
from the survival functions [36, 37] only
considers the first CMAST occurrence in a
lactation, or builds the analysis on a dichot-
omous response at the lactation level (in the
absence of recurrence parameters, more
than one clinical mastitis case per lactation
in the epidemiological context of the exper-
imental studied herds could not occur). 
But explanatory modelling techniques
require more scientific investment than the
generalist exploratory models. Neverthe-
less, they allow to add to the modelling, as
published through a dynamic discrete event
stochastic simulation model [1, 2], the
main epidemiological and experimental
knowledge concerning the CMAST risk.