A General Survival Regression Model with Nonconstant Shape Parameter

Josmar MAZUCHELI[1]

Jorge Alberto ACHCAR[2]

Emílio Augusto COELHO-BARROS2

Francisco LOUZADA-NETO[3]

§    ABSTRACT: In this paper we introduce a general class of survival regression models where both the scale parameters as well as the shape parameter can be modeled in terms of covariates. The advantage of such formulation is that the general framework accommodates several lifetime models usually considered in accelerated lifetime test while maximum likelihood estimators can be performed using an unique algorithm. However, classical tests to assess significance of the model parameters often have problems, since the sample sizes are small or moderate, compromising the validation of the asymptotic distributions of the test statistics. Therefore, we overcome this problem by proposing an alternative direct approach. The idea is to bootstrapping the test statistics, namely, likelihood ratio statistic, Wald and score, in order to obtain their empirical distributions. We present the results of a simulation study, which shows that the bootstrap tests perform well even for small or moderate sample sizes and in the presence of censoring. The benefit of bootstrapping is that bootstrap estimates give empirical evidence under the standard theory, providing an easy alternative method for testing. The methodology is applied on two real datasets on accelerated lifetime test.

§    KEYWORDS: Accelerated life tests; bootstrap; hypothesis tests; shape-dependent survival models; Weibull distribution.

 



[1] Departamento de Estatística, Universidade Estadual de Maringá -- UEM, CEP: 87020-900, Maringá, PR, Brazil. E-mail: jmazucheli@uem.br

[2] Departamento de Medicina Social, Faculdade de Medicina de Ribeirão Preto -- FMRP, Universidade de São Paulo -- USP, CEP: 14049-900, Ribeirão Preto, SP, Brazil. E-mail: achcar@fmrp.usp.br / eacbarros@gmail.com

[3] Departamento de Estatística, Universidade Federal de São Carlos -- UFSCar, CEP: 13565-905, São Carlos, SP, Brazil. E-mail: dfln@power.ufscar.br