Modelos hierárquicos para a análise de dados de eventos recorrentes com inflação de zeros e espacialmente correlacionados

Abstract

In survival and reliability analysis, the response variable is the observed time until an event occurs, referred to as the failure time. The event of interest can range from post-release crime occurrences to electronic component failures, as well as seismic events, among other examples. However, longitudinal studies often aim to understand processes where the same individual experiences the event multiple times over an observation period. In these cases, the events are termed recurrent events. Within this context, this work proposes a new class of parametric and semi-parametric models developed for analyzing recurrent event data, characterized by the presence of excess zeros and spatial correlation. Grounded in counting methods, the proposed models are formulated based on the extension of the Non-Homogeneous Poisson Process. The inclusion of a random effects structure enables the analysis of associations arising from multiple individual-level observations. Additionally, by incorporating the structure of the Intrinsic Conditional Autoregressive model, these models facilitate the evaluation of spatial dependence patterns. To address excess zeros in the data set, the model structure of Zero-Inflated Poisson mixture is incorporated. In addition to parametric models, which assume a baseline intensity function following the Power Law process, this work also proposes more flexible semi-parametric versions. In these versions, the baseline intensity function is approximated using Bernstein Polynomials. The Bayesian approach, adopted in this thesis, offers advantages such as formally incorporating external empirical evidence and inducing specific correlations between random effects and observed data. The proposed models are evaluated for their robustness and effectiveness through a simulation study considering diverse scenarios. Furthermore, these models are applied to analyze a dataset of criminal recidivism in the Metropolitan Region of Belo Horizonte. The model results allow for a deeper analysis and a better understanding of high-risk regions for criminal incidence as well as the recurrence rate behavior over time.