  Tuberculosis poses a global health risk and Brazil is among the top twenty
countries by absolute mortality. However, this epidemiological burden is masked
by under-reporting, which impairs planning for effective intervention. We
present a comprehensive investigation and application of a Bayesian
hierarchical approach to modelling and correcting under-reporting in
tuberculosis counts, a general problem arising in observational count data. The
framework is applicable to fully under-reported data, relying only on an
informative prior distribution for the mean reporting rate to supplement the
partial information in the data. Covariates are used to inform both the true
count generating process and the under-reporting mechanism, while also allowing
for complex spatio-temporal structures. We present several sensitivity analyses
based on simulation experiments to aid the elicitation of the prior
distribution for the mean reporting rate and decisions relating to the
inclusion of covariates. Both prior and posterior predictive model checking are
presented, as well as a critical evaluation of the approach.
