  The analysis of count data is commonly done using Poisson models. Negative
binomial models are a straightforward and readily motivated generalization for
the case of overdispersed data, i.e., when the observed variance is greater
than expected under a Poissonian model. Rate and overdispersion parameters then
need to be considered jointly, which in general is not trivial. Here we are
concerned with evidence synthesis in the case where the reporting of data is
rather heterogeneous, i.e., events are reported either in terms of mean event
counts, the proportion of event-free patients, or rate estimates and standard
errors. Either figure carries some information about the relevant parameters,
and it is the joint modeling that allows for coherent inference on the
parameters of interest. The methods are motivated and illustrated by a
systematic review in chronic obstructive pulmonary disease.
