Semiparametric modeling for multivariate survival data via copulas

• Autor(a) principal: Walmir dos Reis Miranda Filho
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/41685
• topic: Archimedean copulas; Marginal survival functions; Baseline distributions; Regression model classes; Estatística – Teses; Análise de sobrevivência (Biometria) – Teses; Análise funcional – Teses; Análise de regressão – Teses

Clustered survival data can arise if the event of interest (the failure) is recurrent and more than one observed time is registered for each subject (which forms a cluster) under study, and the number of observed times is fixed for all subjects. Since survival data associated with the same cluster is expected to be correlated, it should be modeled in order to account for that dependence. Copula models became an appropriate framework to model clustered survival data, linking marginal survival functions to form a joint survival distribution. Much of the literature on survival copula models is concentrated on results marginally using only the Weibull model as the baseline distribution and the Proportional Hazards model as the regression structure when working with clustered survival data or supposing an informative censoring model for univariate survival data. This work proposes new survival copula models under a random and independent right-censoring assumption, addressing a variety of marginal baseline distributions (Weibull, Bernstein Polynomials, and Piecewise Exponential models) and regression model classes (Proportional Hazards, Proportional Odds, and Yang-Prentice models). Concerning the copulas themselves, each one among those treated in this work belongs to the Archimedean copula class, a family of copulas widely used in survival analysis due to some important properties. Five Archimedean copula models were addressed in this work: Ali-Mikhail-Haq; Clayton; Frank; Gumbel-Hougaard, and Joe. To evaluate and compare the proposed survival copula models, results for an extensive simulation study and a real data application were obtained. For the simulated data, variations can occur on the copula function and on the marginal baseline distribution or regression model class used for generation. Also, simulation scenarios were divided by true Kendall's tau correlation values for the copula model chosen for generation. When fitting the simulated data, better results are obtained for fitted models with the correct copula, given a specification of baseline distribution and regression structure. Moreover, even generating marginally from the Weibull model, results for fitted semiparametric models follow closely those obtained when fitting the Weibull model, being better (in general) for marginally generated data from the Exponentiated Weibull distribution, among the models fitted with the correct copula. For all survival copula models presented in this work, an R package is currently in development, containing specific functions for fitting and analysis.