IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v49y1994i2p218-241.html
   My bibliography  Save this article

Exponential Mixture Models with Long-Term Survivors and Covariates

Author

Listed:
  • Ghitany, M. E.
  • Maller, R. A.
  • Zhou, S.

Abstract

Suppose a population contains individuals who may be subject to failure with exponentially distributed failure times, or else are "immune" to failure. We do not know which individuals are immune but we can infer their presence in a data set if many of the largest failure times are censored. We also have explanatory vectors containing covariate information on each individual. Models for data with such immune or "cured" individuals are of great interest in medical and criminological statistics, for example. In this paper we provide sufficient conditions for the existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters in a useful parameterization of these models. The theory is then applied to derive the asymptotic properties of the likelihood ratio test for a difference between immune proportions in a "one-way" classification. A procedure for testing the "boundary" hypothesis, that there are in fact no immunes present in data with a one-way classification, is also discussed.

Suggested Citation

  • Ghitany, M. E. & Maller, R. A. & Zhou, S., 1994. "Exponential Mixture Models with Long-Term Survivors and Covariates," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 218-241, May.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:2:p:218-241
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(84)71023-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sean Yiu & Vernon T. Farewell & Brian D. M. Tom, 2017. "Exploring the existence of a stayer population with mover–stayer counting process models: application to joint damage in psoriatic arthritis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 669-690, August.
    2. Hirose, Hideo, 2012. "Estimation of the number of failures in the Weibull model using the ordinary differential equation," European Journal of Operational Research, Elsevier, vol. 223(3), pages 722-731.
    3. Morbiducci, Marta & Nardi, Alessandra & Rossi, Carla, 2003. "Classification of "cured" individuals in survival analysis: the mixture approach to the diagnostic-prognostic problem," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 515-529, January.
    4. Barreto-Souza, Wagner, 2015. "Long-term survival models with overdispersed number of competing causes," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 51-63.
    5. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    6. Lopez-Cheda , Ana & Cao, Ricardo & Jacome, Maria Amalia & Van Keilegom, Ingrid, 2015. "Nonparametric incidence and latency estimation in mixture cure models," LIDAM Discussion Papers ISBA 2015014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. H. Vu & R. Maller & X. Zhou, 1998. "Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 627-653, December.
    8. Pons, O. & Lemdani, M., 2003. "Estimation and test in long-term survival mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 465-479, January.
    9. Shen, Pao-sheng, 2000. "Testing for sufficient follow-up in survival data," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 313-322, October.
    10. 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.
    11. Francisco Louzada & Juliana Cobre, 2012. "A multiple time scale survival model with a cure fraction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 355-368, June.
    12. Amico, Mailis & Van Keilegom, Ingrid, 2017. "Cure models in survival analysis," LIDAM Discussion Papers ISBA 2017007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Choi, K. C. & Zhou, X., 2002. "Large Sample Properties of Mixture Models with Covariates for Competing Risks," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 331-366, August.
    14. Varadan Sevilimedu & Shuangge Ma & Pamela Hartigan & Tassos C. Kyriakides, 2021. "An Application of the Cure Model to a Cardiovascular Clinical Trial," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 402-430, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:49:y:1994:i:2:p:218-241. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.