Challenges in modeling count data: Bayesian models for correction of underreporting bias and estimation of mortality schedules

• Autor(a) principal: Guilherme Lopes de Oliveira
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/37509; https://orcid.org/0000-0003-3220-6356
• topic: Bayesian inference; Censored Poisson model; Compound Poisson model; Data augmentation; Markov chain Monte Carlo methods; Model identifiability; Mortality schedules; Neonatal mortality; tuberculosis incidence; Underreporting; Estatística – Teses.; Método de Monte Carlo – Teses.; Bioestatística – Teses.; Teoria bayesiana de decisão estatística – Teses.; Poisson, Distribuição de – Teses.; Recém-nascidos – Mortalidade – Teses

In several fields, such as epidemiology and demography, count data is collected in order to assess or to monitor the risks associated with the events of interest. However, in many situations only a fraction of the true total of events is observed, characterizing the phenomenon known as underreporting, which is very common in epidemiological studies. If the underreporting occurs and it is not accounted for, the inference made from the observed counts will be biased and, consequently, the risks related to the events of interest will be underestimated. In addition to the issue of underreporting, in some studies the observed counts may be highly sparse, as usually occurs in the analysis of mortality patterns in demographic studies. In this dissertation, we address these challenging problems commonly faced when analyzing count data. Among the proposed models, there are two approaches for the correction of underreporting bias, which have been published in relevant journals in statistics, as well as an alternative methodology for estimating and smoothing mortality curves by age and sex in the presence of sparse data, which is been improved. A broader introduction to the practical problems addressed in the dissertation is provided in the opening chapter, which also provides a detailed description of the contributions related to each proposed model. The subsequent chapters corresponds to a collection of papers, which present independent methodologies with individual discussions of the problems addressed. In all cases, the inference process is made under the Bayesian paradigm. Some approaches available in the statistical literature are discussed and, in some cases, used for comparison with the proposed models. Simulated data as well as real datasets are used to explore and to illustrate the main features of the models. The final chapter summarizes the methods and results obtained throughout the dissertation, highlighting some interesting points for future research.