Modelos conjuntos de análise de dados longitudinais censurados: aspectos computacionais e aplicação na relação do sistema de irrigação com o surgimento de manchas foliares do café

Abstract

Studies related to the characteristics of phenomena or experiments over time, such as longi- tudinal studies or investigations into the time until the occurrence of an event of interest, are

increasingly prevalent in various fields. These two phenomena can be addressed, respectively, through linear mixed models and survival models. However, there may be situations where the objective is to investigate the relationship between one or more longitudinal responses and an

event of interest, which can be achieved with the aid of joint modeling of longitudinal and survi- val data. Nevertheless, these models may encounter convergence issues and be computationally

demanding, making their use impractical in many cases. In this regard, this thesis was divided

into two stages. The first stage aims to propose the use of the cross-coverage probability mea- sure as a diagnostic tool for assessing the connection between longitudinal and survival models

to aid in the estimation of a joint model involving both processes. This objective was achieved through a Monte Carlo simulation study, comparing longitudinal and survival models based on

different censoring percentages and the covariance structure of repeated measures. In the se- cond stage, the methodology presented for the joint model of longitudinal and survival data was

applied to understand the influence of irrigation type on the time until the appearance of phoma leaf spot on coffee plants. The results of this thesis demonstrated that the procedure used to estimate cross-coverage probabilities, as a diagnostic tool for assessing the connection between longitudinal and survival models, proved to be adequate when considering the Weibull model. An increase in the censoring percentage resulted in a negative impact on numerical convergence for obtaining maximum likelihood estimates of joint models for longitudinal and survival data.

The application results provided a comprehensive analysis of the relationship between the va- riables and how time is associated with the risks of phoma leaf spot incidence in coffee plants.