Banca de DEFESA: LUCAS EBER FLORIANO DE OLIVEIRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LUCAS EBER FLORIANO DE OLIVEIRA
DATE: 11/03/2022
TIME: 09:00
LOCAL: Instituto de Matemática e Estatística (IME), Universidade Federal da Bahia (UFBA)
TITLE:

Residual analysis for the time-dependent generalized logistic model (GTDL)

KEY WORDS:

GTDL, Cox proportional hazards model, residual analysis.

PAGES: 72
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUBÁREA: Estatística
SPECIALTY: Regressão e Correlação
SUMMARY:

Several researchers have used the traditional Cox proportional hazards model, which has a simple interpretation and can be extended to incorporate time-dependent covariates; however, it is observed that in the practice, the data set does not always fit this model because they do not satisfy the usual properties of proportionality of failure rates and the effect of the covariate over time cannot be detected. In this work we have studied the modelling of survival data using the time-dependent generalized logistic model (GTDL). The use of this model is a significant alternative proposed by Mackenzie (1996) that satisfy the presupposition of non-proportionality of risks. In order to assess the goodness of fit of the model, we introduced Cox-Snell, modified Cox-Snell, martingale, deviance, randomized quantile, NMSP and NRSP residuals. We conducted a simulation study via Monte Carlo to investigate the asymptotic behaviour of the maximum likelihood estimators of the GTDL model obtained through the direct maximization of the log-likelihood function, for cases where the survival function is proper and when we have a model of cure fraction. Also, another simulation study is conducted to know the empirical distribution of residuals. Finally, we applied the methodologies studied to a set of data available in the literature involving patients with lung cancer.

BANKING MEMBERS:
Interno - 2979623 - JALMAR MANUEL FARFAN CARRASCO
Externa ao Programa - 2584511 - NIVEA BISPO DA SILVA
Externo à Instituição - EDER ANGELO MILANI