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

2.2.3. Solutions for between lactation 
dependence
To study a potential dependence between
lactations, some authors consider only one
lactation per animal. The first lactation,
especially in genetic studies, is often
selected [42–44, 53, 60, 66, 70, 81, 82], or
the two first lactations when the study is
aimed at evaluating the influence of the first
lactation on the second lactation [67, 71, 72,
77]. In other cases, one lactation is ran-
domly selected among the available lacta-
tions for a given animal, which allows to
consider the lactation number as the explan-
atory variable [17, 19, 20, 51, 80].
2.2.4. Solutions for within herd 
dependence
It is also necessary to consider the ques-
tion of herd dependence in the course of
time and of animal dependence for animals
living within the same herd. As previously
presented, when a set of herds is surveyed,
the main source of overdispersion (except
the problem of following the same herd all
along a time period) is a lack of considera-
tion of significant (and generally unknown)
factors of heterogeneity in the model. To
overcome the overdispersion problem, the
models try to estimate it using a theoretic
distribution of Poisson, or a theoretic dis-
tribution yet including an overdispersion
through a negative binomial or a beta-bino-
mial distribution [75]. When the same
herds are studied in a prospective survey,
the models allow to estimate a within herd
variance through an extension of GLM pro-
cedures (Generalised Estimated Equations
or GEE) [25]. Moreover a herd fixed or ran-
dom effect is usually entered in the models,
besides the fixed effects corresponding to
other control, key or explanatory variables.
In large scale surveys, a random herd effect

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is generally entered to save the degrees of
freedom, to the detriment of an accurate
estimation of the residual variance, which
is important in order to precisely test the
factors of interest. When few and not ran-
domly selected herds are defined and used
in the model, the introduction of a fixed
effect herd factor is better. Moreover
between-study comparisons are difficult
because the control variables of the final
model are very often different according to
the study. When the analysed response at
the herd level is increasingly built from
more or less censored responses to subja-
cent levels (animal, lactation and case), the
optimal consideration of the problem is
harder.
The herd level study mainly depends
on the definition of the index, qualifying
the response variable (incidence, incidence
rate), and characterising a herd at a given
moment or in a time period. A significant