Estimação Bayesiana nos modelos com respostas distais em análise de sobrevivência

Abstract

Distal outcomes models encompass methods for estimating the impact of latent variables on observed outcomes while accounting for other predictors, increasing the mathematical complexity of the models. Recent techniques aim to assess the effect of latent classes on distant outcomes in two main ways: either by directly integrating measurement errors into the model (one-step approach) or by employing classification rules to assign individuals to categories and then considering these categories as observed predictors in a structural model (three-stage approach). Although the one-step method is more robust, it is often overlooked due to its complexity, which requires re-estimating parameters whenever new variables are included. In contrast, the three-step method tends to underestimate the effects of latent predictors. A lot of research on estimating latent class effects focuses on continuous or categorical outcomes. In survival analysis, there are only a few frequentist approaches for simultaneously estimating models with distal outcomes. This work proposes an alternative approach using Bayesian inference to estimate latent variable effects in time-to-event responses. This allows for the inclusion of uncertainties and provides greater flexibility in estimation. The proposed methodology was used to analyze real data from the PrEP1519 project. The goal was to examine how HIV real-risk behaviors impact the time until the first discontinuation of HIV preventive treatment in adolescents. We conducted simulation studies to assess the properties of the estimators from the Bayesian Simplified Modal (BSM) Method and Bayesian Simultaneous (BS) Method, both of which were proposed in this dissertation for analyzing distal outcomes defined by censored failure times. The results of the simulation studies show that the Bayesian Simultaneous (BS) Method significantly reduces bias when estimating the effect of latent classes on the distal outcome. Additionally, this method allows for the inclusion of extra observed predictors in the model.