Ajuste de modelos de Cox e de florestas aleatórias em análise de sobrevivência

Abstract

This final course project explores the application and comparison of classical statistical methods and machine learning in the context of survival analysis. A detailed theoretical review of the fundamentals of time-to-event data analysis was conducted, addressing concepts such as censoring, survival and hazard functions, the non-parametric Kaplan-Meier estimator, and the Cox semiparametric proportional hazards model. In parallel, the principles of machine learning were studied, focusing on the structure of decision trees and the robustness of ensemble methods, such as random forests. To evaluate the performance of the models, consolidated metrics were used, including the C-index for discrimination, the Brier score for probabilistic accuracy, and metrics derived from the confusion matrix, such as accuracy, sensitivity, and specificity. The practical application of the methodologies was carried out through two case studies: the first, with real data from a clinical study, illustrated the workflow for the adjustment and validation of a Cox model; A second experiment, using simulated data, allowed for a direct comparison of the predictive performance between an optimized decision tree and a random forest in a controlled scenario. The results highlight the contrast between the interpretability of classical models and the predictive performance of machine learning models, discussing the scenarios in which each approach may be more advantageous.