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Goodness-of-fit test for a parametric survival function with cure fraction

Author

Listed:
  • Candida Geerdens

    (Universiteit Hasselt)

  • Paul Janssen

    (Universiteit Hasselt)

  • Ingrid Van Keilegom

    (KU Leuven)

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.

Suggested Citation

  • Candida Geerdens & Paul Janssen & Ingrid Van Keilegom, 2020. "Goodness-of-fit test for a parametric survival function with cure fraction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 768-792, September.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00680-4
    DOI: 10.1007/s11749-019-00680-4
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    References listed on IDEAS

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    1. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
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    Cited by:

    1. Mercedes Conde‐Amboage & Ingrid Van Keilegom & Wenceslao González‐Manteiga, 2021. "A new lack‐of‐fit test for quantile regression with censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 655-688, June.

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