Goodness-of-fit test for a parametric survival function with cure fraction
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Goodness-of-fit test for a parametric survival function with cure fraction Candida Geerdens1 · Paul Janssen1 · Ingrid Van Keilegom2 Received: 22 October 2018 / Accepted: 7 October 2019 © Sociedad de Estadística e Investigación Operativa 2019
Abstract 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. Keywords Bootstrap · Cramér-von Mises · Cure fraction · Kaplan–Meier · Parametric models · Weak convergence Mathematics Subject Classification 62N01 · 62N02 · 62N03
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11749019-00680-4) contains supplementary material, which is available to authorized users.
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Ingrid Van Keilegom [email protected] Candida Geerdens [email protected] Paul Janssen [email protected]
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Censtat, Universiteit Hasselt, Agoralaan 1, 3590 Diepenbeek, Belgium
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Orstat, KU Leuven, Naamsestraat 69 - bus 3500, 3000 Leuven, Belgium
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C. Geerdens et al.
1 Introduction In classical survival analysis, it is usually assumed that all subjects under study will eventually experience the event of interest. For instance, in an experiment that studies the lifetime of certain electronic or mechanical devices, it is clear that all devices will sooner or later fail. Likewise, when studying the survival time of a certain group of patients in which all causes of death are confounded, it is clear that all patients will eventually die. However, there are also many contexts in which subjects under study never experience the event of interest. Their survival time is considered to be infinite. A prominent example is the lifetime of cancer patients after treatment. Due to medical advances, part of the patient population will not die of cancer. Other relevant examples stem from epidemiology (e.g., in case of a disease outbreak a fraction of the population will not get infected), economy (e.g., in an employment study part of the population may never get a job) and criminology (e.g., in a recidivism study a po
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