A Hierarchical Framework for Correcting Under-Reporting in Count Data

Abstract

Tuberculosis poses a global health risk and Brazil is among the top twenty countries by absolute mortality. However, this epidemiological burden is masked by underreporting, 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. 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.

Bayesian modeling of COVID-19 cases with a correction to account for under-reported cases

“…The first is the demographic and territorial size of the country, with an estimated population of 210 million according to the Brazilian Institute for Geography and Statistics and the heterogeneity intrinsic to its extensive territory. Another problem pointed out by the past epidemics run into a recurring problem of under-reporting ( de Oliveira et al, 2017 ; Stoner et al, 2019 ).…”

Estimating the real burden of disease under a pandemic situation: The SARS-CoV2 case

“…For each time n, the new counts can be expressed in terms of the affected number of individuals introduced in the previous section. That is, for each n, the number of new individuals can be defined in terms of the number of affected individuals, as follows: new(n) = A(n) − A(n − 1), where A(n) is defined in (7). This information can be appropriately incorporated into the model to accommodate the trend present in the data using the information on the propagation of the epidemic provided by the data themselves.…”

“…A sensible way to do this is by considering that the expectation of the innovations of the latent process X n in expression (1) varies with the number of new cases at each time n, and thus that the model in (1) and (4) is not stationary anymore. Specifically, the innovations of X n will have Poisson distribution with λ n = new(n) = A(n) − A(n − 1), where A(n) is given by (7). Therefore, the unobserved process X n becomes:…”

A modelling approach for correcting reporting delays in disease surveillance data

“…As such, the true disease count is the observable count plus any cases that were never reported. In this paper, we focus on correcting reporting delay in the observable data, noting that correcting for underreporting is generally a nontrivial task, requiring additional sources of information such as prior knowledge on underreporting rates or a sample of fully observed data (ie, the truth), as discussed in the work of Stoner et al…”