A Hierarchical Framework for Correcting Under-Reporting in Count Data

TL;DR

This paper introduces a Bayesian hierarchical framework to correct under-reporting in count data, specifically applied to tuberculosis cases in Brazil, improving epidemiological estimates and informing better health interventions.

Contribution

It develops a novel Bayesian hierarchical model that accounts for under-reporting using covariates and spatio-temporal structures, with comprehensive sensitivity and model checking.

Findings

Effective correction of under-reporting in simulated data

Framework accommodates complex spatio-temporal structures

Provides guidance for prior elicitation and covariate inclusion

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 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.