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The nonparametric location-scale mixture cure model

Author

Listed:
  • Justin Chown

    (Ruhr-Universität Bochum)

  • Cédric Heuchenne

    (University of Liège
    Université Catholique de Louvain)

  • Ingrid Van Keilegom

    (KU Leuven)

Abstract

We propose completely nonparametric methodology to investigate location-scale modeling of two-component mixture cure models that is similar in spirit to accelerated failure time models, where the responses of interest are only indirectly observable due to the presence of censoring and the presence of long-term survivors that are always censored. We use nonparametric estimators of the location-scale model components that depend on a bandwidth sequence to propose an estimator of the error distribution function that has not been considered before in the literature. When this bandwidth belongs to a certain range of undersmoothing bandwidths, the proposed estimator of the error distribution function is root-n consistent. A simulation study investigates the finite sample properties of our approach, and the methodology is illustrated using data obtained to study the behavior of distant metastasis in lymph-node-negative breast cancer patients.

Suggested Citation

  • Justin Chown & Cédric Heuchenne & Ingrid Van Keilegom, 2020. "The nonparametric location-scale mixture cure model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1008-1028, December.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:4:d:10.1007_s11749-019-00698-8
    DOI: 10.1007/s11749-019-00698-8
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    References listed on IDEAS

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    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Zeng, Donglin & Yin, Guosheng & Ibrahim, Joseph G., 2006. "Semiparametric Transformation Models for Survival Data With a Cure Fraction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 670-684, June.
    3. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
    4. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    5. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    6. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    7. Lopez-Cheda, Ana & Cao, Ricardo & Jacome, Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," LIDAM Reprints ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Wenbin Lu, 2008. "Maximum likelihood estimation in the proportional hazards cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 545-574, September.
    9. López-Cheda, Ana & Cao, Ricardo & Jácome, M. Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 144-165.
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    Cited by:

    1. Motahareh Parsa & Ingrid Van Keilegom, 2023. "Accelerated failure time vs Cox proportional hazards mixture cure models: David vs Goliath?," Statistical Papers, Springer, vol. 64(3), pages 835-855, June.
    2. Escobar-Bach, Mikael & Van Keilegom, Ingrid, 2023. "Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).

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