Modelling non-proportional hazard for survival data with different systematic components
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Modelling non-proportional hazard for survival data with different systematic components Fábio Prataviera1 · Selene M. C. Loibel2 · Kathleen F. Grego3 · Edwin M. M. Ortega1 · Gauss M. Cordeiro4 Received: 18 May 2019 / Revised: 9 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a new extended regression model based on the logarithm of the generalized odd log-logistic Weibull distribution with four systematic components for the analysis of survival data. This regression model can be very useful and could give more realistic fits than other special regression models. We obtain the maximum likelihood estimates of the model parameters for censored data and address influence diagnostics and residual analysis. We prove empirically the importance of the proposed regression by means of a real data set (survival times of the captive snakes) from a study carried out at the Herpetology Laboratory of the Butantan Institute in São Paulo, Brazil. Keywords Censored data · Generalized odd log-logistic Weibull · Maximum likelihood · Non-proportional hazard · Regression model · Survival analysis
Handling Editor: Bryan F. J. Manly.
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Edwin M. M. Ortega [email protected] Fábio Prataviera [email protected] Selene M. C. Loibel [email protected] Kathleen F. Grego [email protected] Gauss M. Cordeiro [email protected]
1
Departamento de Ciências Exatas, Universidade de São Paulo, Piracicaba, SP, Brazil
2
Universidade Estadual Paulista, Júlio de Mesquita Filho, São Paulo, SP, Brazil
3
Laboratório de Herpetologia - Instituto Butantan, São Paulo, SP, Brazil
4
Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil
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Environmental and Ecological Statistics
1 Introduction Survival analysis is one of the areas of Statistics that has grown steadily in recent decades. It is common for the response variable (time until the occurrence of the event of interest) to be related to the explanatory variables that explain its variability. We study the effects of these explanatory variables on the response variable using a regression model that is appropriate for censored data. In some practical situations, it is common to assume the property of proportional risks. For these cases, some parametric regression models (Weibull, log-normal, log-logistic, etc.) as well as the semiparametric Cox regression, can be used to model censored data. We now present a brief summary of the regression models in survival analysis. An efficient way to study the effects of explanatory variables on survival times is through regression models. For doing this, two approaches can be adopted: 1. Parametric modeling includes two regression models: (a) The first modeling considers a regression structure in the original parameters of the distribution by means of suitable link functions. In these terms, Prataviera et al. (2018) proposed a regression model based on the generalized odd loglogistic flexible Weibull (GOLLWF) distribution. (b) The second formulation refers to
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