Abstract
We address the issue of performing hypothesis testing in accelerated failure time models for non-censored and censored samples. The performances of the likelihood ratio test and a recently proposed test, the gradient test, are compared through simulation. The gradient test features the same asymptotic properties as the classical large sample tests, namely, the likelihood ratio, Wald and score tests. Additionally, it is as simple to compute as the likelihood ratio test. Unlike the score and Wald tests, the gradient test does require the computation of the information matrix, neither observed nor expected. Our study suggests that the gradient test is more reliable than the other classical tests when the sample is of small or moderate size.
Highlights
An important class of regression models used to assess the relationship between the response variable and the covariates in survival analysis is parametric accelerated failure time (AFT) models
We address the issue of performing hypothesis testing in accelerated failure time models for non-censored and censored samples
Given the importance of such models, several authors have extended the AFT models, for example, adding a random effect to deal with correlated survival data (Lambert, Collett, Kimber, & Johnson, 2004; Pan, 2001), allowing measurement error in the covariates (Gimenez & Bolfarine, 1997; Valenca & Bolfarine, 2006) or including a cure fraction to treat the presence of immune individuals in the sample (Yamaguchi, 1992; Peng, 1998; Ortega, 2009)
Summary
An important class of regression models used to assess the relationship between the response variable and the covariates in survival analysis is parametric accelerated failure time (AFT) models. Lemonte and Ferrari (2011a) compared the size and power properties of the four rival tests in a Birnbaum-Saunders regression model for complete samples Their simulation results suggest that the score and the gradient tests outperform the likelihood ratio and the Wald tests in small and moderate-sized samples, and are consistent with the study of Ferrari and Pinheiro (2014). They noticed that the Wald and score tests were markedly oversized and that the inverse of the observed information matrix frequently produced negative standard errors for censored samples in their simulations Their overall conclusion is in favor of the gradient test.
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