Abstract
In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.
Highlights
Cure rate models have been extensively studied in the literature for data sets where the event of interest may not occur for part of the population studied
In this paper we study the performance of the likelihood ratio and the gradient tests via simulation study, to test coefficients related to cure rate parameter in the Weibull promotion time cure model
It shows that for all considered cases, the null rejection rates of the tests exceed the corresponding nominal level. This is in agreement with liberal characteristic of the likelihood ratio test in small samples and shows the same trend of the gradient test
Summary
Cure rate models have been extensively studied in the literature for data sets where the event of interest may not occur for part of the population studied. We can mention just Sposto et al (1992), which present a small (100 samples) and restrict simulation study to compared the likelihood ratio, Wald, and score tests based on a mixture model. Among the studies that consider the statistical gradient in survival models with censored data, we can cite Lemonte and Ferrari (2011b), that consider samples with right censoring of type II to test hypotheses about the two parameters of the Birnbaum-Saunders distribution, and Medeiros et al (2014) that compare the performance of the gradient and likelihood ratio tests in accelerated failure time models under random censoring. In this paper we study the performance of the likelihood ratio and the gradient tests via simulation study, to test coefficients related to cure rate parameter in the Weibull promotion time cure model.
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