A random‐censoring Poisson model for underreported data

Abstract

A major challenge when monitoring risks in socially deprived areas of under developed countries is that economic, epidemiological, and social data are typically underreported. Thus, statistical models that do not take the data quality into account will produce biased estimates. To deal with this problem, counts in suspected regions are usually approached as censored information. The censored Poisson model can be considered, but all censored regions must be precisely known a priori, which is not a reasonable assumption in most practical situations. We introduce the random-censoring Poisson model (RCPM) which accounts for the uncertainty about both the count and the data reporting processes. Consequently, for each region, we will be able to estimate the relative risk for the event of interest as well as the censoring probability. To facilitate the posterior sampling process, we propose a Markov chain Monte Carlo scheme based on the data augmentation technique. We run a simulation study comparing the proposed RCPM with 2 competitive models. Different scenarios are considered. RCPM and censored Poisson model are applied to account for potential underreporting of early neonatal mortality counts in regions of Minas Gerais State, Brazil, where data quality is known to be poor.

A Hierarchical Framework for Correcting Under-Reporting in Count Data

“…The approach can in principle be extended to include estimation of the threshold, however in many cases the threshold model may be a poor description of the under-reporting mechanism which could, for example, be related to more than one covariate. Oliveira et al (2017) presents an alternative to this approach, which treats the binary under-reporting indicator I i,t,s as unobserved and therefore random. The classification of the data is characterised by I i,t,s ∼ Bernoulli(π i,t,s ), such that π i,t,s is the probability of any data point suffering from under-reporting, which is potentially informed by covariates.…”

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 Under Reporting of Leprosy in Brazil using a Bayesian Approach

“…In disease surveillance and epidemiological studies, two main statistical approaches have been considered to deal with underreport counts. Inference under the first one is based on a censored Poisson likelihood function, allowing the estimation of both the disease rate and the probability of the observed count being underreported in each area (Bailey et al 2005; Oliveira et al, 2017). The second and potentially more flexible approach relies on the specification of a hierarchical Poisson model from which is possible to estimate both the disease rates and the proportion of reported cases in each area (Stoner et al 2019; Dvorzak and Wagner 2015; Shaweno et al 2017; Stamey et al 2006; Whittemore and Gong 1991; Papadopoulos and Silva 2012).…”