Goodness-of-fit test for a parametric survival function with cure fraction
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We consider the survival function for univariate right-censored event time data, when a cure fraction is present. This means that the population consists of two parts: the cured or non-susceptible group, who will never experience the event of interest versus the non-cured or susceptible group, who will undergo the event of interest when followed up sufficiently long. When modeling the data, a parametric form is often imposed on the survival function of the susceptible group. In this paper, we construct a simple novel test to verify the aptness of the assumed parametric form. To this end, we contrast the parametric fit with the nonparametric fit based on a rescaled Kaplan–Meier estimator. The asymptotic distribution of the two estimators and of the test statistic are established. The latter depends on unknown parameters, hence a bootstrap procedure is applied to approximate the critical values of the test. An extensive simulation study reveals the good finite sample performance of the developed test. To illustrate the practical use, the test is also applied on two real-life data sets.
KeywordsBootstrap Cramér-von Mises Cure fraction Kaplan–Meier Parametric models Weak convergence
Mathematics Subject Classification62N01 62N02 62N03
This work was supported by the European Research Council [2016-2021, Horizon 2020/ERC Grant No. 694409], by the Interuniversity Attraction Poles Program [IAP-network P7/06] of the Belgian Science Policy Office, and the Research Foundation Flanders (FWO), Scientific Research Community on ‘Asymptotic Theory for Multidimensional Statistics’ [W000817N]. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation Flanders (FWO) and the Flemish Government—department EWI.
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