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A Hierarchical Framework for Correcting Under-Reporting in Count Data

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  • Oliver Stoner
  • Theo Economou
  • Gabriela Drummond Marques da Silva

Abstract

Tuberculosis poses a global health risk and Brazil is among the top 20 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 modeling 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. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Suggested Citation

  • Oliver Stoner & Theo Economou & Gabriela Drummond Marques da Silva, 2019. "A Hierarchical Framework for Correcting Under-Reporting in Count Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1481-1492, October.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:528:p:1481-1492
    DOI: 10.1080/01621459.2019.1573732
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    Cited by:

    1. Aghabazaz, Zeynab & Kazemi, Iraj, 2023. "Under-reported time-varying MINAR(1) process for modeling multivariate count series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    2. Maciej Berk{e}sewicz & Katarzyna Pawlukiewicz, 2020. "Estimation of the number of irregular foreigners in Poland using non-linear count regression models," Papers 2008.09407, arXiv.org.
    3. Jinjie Chen & Joon Jin Song & James D. Stamey, 2022. "A Bayesian Hierarchical Spatial Model to Correct for Misreporting in Count Data: Application to State-Level COVID-19 Data in the United States," IJERPH, MDPI, vol. 19(6), pages 1-15, March.

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