Semiparametric transformation models in the analysis of lifetime data in presence of censored data and covariates

• Ano de defesa: 2025
• Autor(a) principal: Barili, Emerson
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertacoes da USP; Universidade de São Paulo; Faculdade de Medicina de Ribeirão Preto
• Palavras-chave em Português: Abordagem bayesiana; Saúde pública; Modelos de transformação semiparamétrico; Fração de cura; Dados médicos de tempo de vida; Dados censurados; Cure fraction; Lifetime medical data; Censored data; Public health; Bayesian approach; Semiparametric transformation models
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/17/17139/tde-17032026-141825/

The application of statistical models and methods covers studies an research in general. In this study, these tools are used in health data analysis, whereas statistical currently performence an important role in promoting the effectiveness of study results such as clinical trials, meta-analysis to obtain more accurate estimates of treatment effects, epi demiology in identifying risk factors and diseases, among others. The study introduces the idea of semiparametric regression models applied to right-censored survival data. Semiparametric models are nonlinear models that involve parametric and nonparametric components. There are situations where semiparametric models have advantages over parametric models, as they can capture complex relationships in the data without spec ifying a parametric probability distribution, providing a balance between flexibility and interpretability, that is, semiparametric models have some advantages in terms of adjust ment. The Cox model, or Cox proportional hazards model (Cox, 1972), is an example of a semiparametric model. This model is presented in the context of survival analysis, which is an essential tool in investigating phenomena where the time to the occurrence of an event of interest is the central variable. That is, it intrinsically addresses the temporal nature of the data and the possibility of incorporating censoring (Klein and Moeschberger, 2006). The principles of survival analysis are the fundamental basis of this study, where we aim to apply semiparametric transformation models to relax assumptions about the functional form of the baseline hazard, there by obtaining more robust and accurate in ference in health-related research. Semiparametric transformation models represent a f lexible class of survival analysis models that allow for modeling the effects of covariates on event times through an unspecified transformation function of the baseline hazard, while maintaining the nonparametric nature of the latter. The model fitting in the ap plications presented in this study was carried out using the Bayesian approach, since in semiparametric transformation models, Bayesian inference naturally incorporates uncer tainty in terms of the transformation function and the nonparametric baseline hazard. By specifying flexible smoothing priors, such as the Dirichlet process or splines (Ghosal and Van der Vaart, 2017; Wahba, 1990), it is possible to model the complexity of the transfor mation function without imposing rigid parametric forms. The ability to perform exact inference through computational methods such as MCMC (Markov Chain Monte Carlo) overcomes the limitations of asymptotic approximations, making the Bayesian approach a sophisticated and increasingly relevant tool in survival analysis with semiparametric transformation models. In this research, we highlight the use of survival analysis theory widely explored in medical research, where there is a high frequency of studies on patient monitoring until the occurrence of the event of interest. Therefore, the work consists of an introduction covering the literature review in Chapter 1. In Chapter 2, we present a hierarchical Bayesian analysis considering semiparametric transformation models for a dataset composed of survival times of cancer patients admitted to the intensive care unit of the National Cancer Institute (INCA) in Rio de Janeiro, Brazil. In Chapter 3, we show how to obtain inference for the parameters of semiparametric transformation models in the presence of censoring, covariates, and cure fraction under a hierarchical Bayesian approach, assuming unknown hazard rates as latent variables with a specified probability distribution. The subsequent posterior summaries of interest are obtained us ing existing MCMC simulation methods. Two applications considering survival times in medical studies illustrate the proposed methodology. In Chapter 4, we consider the use of semiparametric (transformation) models for situations in which two or more responses are associated with the same individual or unit. We assume a hierarchical Bayesian analysis for semiparametric transformation models, considering the full likelihood function derived from transformation models, treating the unknown hazard functions as latent variables, and applying MCMC methods to obtain the posterior summaries of interest. The depen dence between multivariate responses for the same individual is captured by introducing another latent variable, or frailty. Illustrations of the proposed methodology are presented by considering two multivariate medical datasets on survival times.