The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis

Abstract

In applications of survival analysis, the failure rate function may frequently present a unimodal shape. In such cases, the log-normal and log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the odd log-logistic Weibull distribution is proposed for modelling data with a decreasing, increasing, unimodal and bathtub failure rate function as an alternative to the log-Weibull regression model. For censored data, we consider a classic method to estimate the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals is determined and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the new regression model applied to censored data. We analyse a real data set using the log-odd log-logistic Weibull regression model.

The power-Cauchy negative-binomial: properties and regression

“…In the context of survival analysis, some distributions have been used to analyze censored data. For example, more recently, Cruz et al (2016) proposed the log-odd log-logistic Weibull regression model with censored data, Lanjoni et al (2016) defined an extended Burr XII regression model and Ortega et al (2016) introduced the odd Birnbaum-Saunders regression model with applications to lifetime data. In a similar manner, we define a location-scale regression model using the LPCNB regression model.…”

Estimation and application in log-Fréchet regression model using censored data

“…In Cruz, Ortega and Cordeiro [8], analysis has been conducted on the previous heart transplant survival time data under log-Weibull regression model. Therefore, we conduct a comparison between log-Weibull and LF regression model based on AIC and BIC criteria.…”

“…Several studies were conducted using the log-location-scale regression models. These include the log-Burr XII regression model with censored data analysis by Silva et al [2], the log-modified Weibull regression models with censored data by Carrasco, Ortega and Paula [3], the log-generalized modified Weibull regression model with censored analysis by Ortega, Cordeiro and Carrasco [4], the log-exponentiated Weibull regression model with intervalcensored analysis by Hashimoto et al [5], the log-Weibull extended regression model with censored data analysis by Silva, Ortega and Cancho [6], the log-Burr XII regression model with grouped survival data analysis by Hashimoto et al [7], log-odd log-logistic Weibull regression model with censored data by Cruz, Ortega and Cordeiro [8], log-odd log-logistic generalized half-normal regression model with censored data by Pescim et al [9]. In this paper, based on log-location-scale regression model and Fréchet distribution, the log-Fréchet (LF) regression model is proposed.…”

O modelo de regressão odd log-logística gama generalizada com aplicações em análise de sobrevivência

“…Sua importância reside na sua capacidade de modelar funções de risco monótona e não-monótona que são bastante comuns em dados de análise de sobrevivên-cia e confiabilidade, e possui alguns submodelos especiais como, a gama generalizada exponenciada, a Weibull exponenciada, a semi normal exponenciada e a semi normal generalizada, entre outros. Outros trabalhos realizados recentemente nestes temas são, Cordeiro et al (2011), Cordeiro et al (2013a), Cordeiro et al (2013b) e Cruz et al (2016).…”

“…Os autores chamam esta família de família loglogística generalizada (GLL). Recentemente, Cruz et al (2016) propuseram a odd loglogística Weibull; da Silva Braga et al (2016) estudaram a distribuição odd log-logística normal e Cordeiro et al (2016) propuseram a família beta odd log-logística generalizada. Neste sentido, é desenvolvido uma metodologia semelhante para propor um novo modelo baseado na distribuição gama generalizada (GG).…”