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Nonparametric Estimation in a Cure Model with Random Cure Times

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  • Rebecca A. Betensky
  • David A. Schoenfeld

Abstract

Summary. Acute respiratory distress syndrome (ARDS) is a life‐threatening acute condition that sometimes follows pneumonia or surgery. Patients who recover and leave the hospital are considered to have been cured at the time they leave the hospital. These data differ from typical data in which cure is a possibility: death times are not observed for patients who are cured and cure times are observed and vary among patients. Here we apply a competing risks model to these data and show it to be equivalent to a mixture model, the more common approach for cure data. Further, we derive an estimator for the variance of the cumulative incidence function from the competing risks model, and thus for the cure rate, based on elementary calculations. We compare our variance estimator to Gray's (1988, Annals of Statistics16, 1140–1154) estimator, which is based on counting process theory. We find our estimator to be slightly more accurate in small samples. We apply these results to data from an ARDS clinical trial.

Suggested Citation

  • Rebecca A. Betensky & David A. Schoenfeld, 2001. "Nonparametric Estimation in a Cure Model with Random Cure Times," Biometrics, The International Biometric Society, vol. 57(1), pages 282-286, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:282-286
    DOI: 10.1111/j.0006-341X.2001.00282.x
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    References listed on IDEAS

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    1. Martin G. Larson & Gregg E. Dinse, 1985. "A Mixture Model for the Regression Analysis of Competing Risks Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 201-211, November.
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    Cited by:

    1. Guosheng Yin & Joseph G. Ibrahim, 2005. "A General Class of Bayesian Survival Models with Zero and Nonzero Cure Fractions," Biometrics, The International Biometric Society, vol. 61(2), pages 403-412, June.
    2. N. Balakrishnan & M. V. Koutras & F. S. Milienos & S. Pal, 2016. "Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 937-966, December.
    3. Wende Clarence Safari & Ignacio López-de-Ullibarri & María Amalia Jácome, 2023. "Latency function estimation under the mixture cure model when the cure status is available," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 608-627, July.
    4. Jad Beyhum & Jean-Pierre Florens & Ingrid Keilegom, 2023. "A nonparametric instrumental approach to confounding in competing risks models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 709-734, October.
    5. Guosheng Yin, 2005. "Bayesian Cure Rate Frailty Models with Application to a Root Canal Therapy Study," Biometrics, The International Biometric Society, vol. 61(2), pages 552-558, June.
    6. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    7. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    8. Guoqing Diao & Ao Yuan, 2019. "A class of semiparametric cure models with current status data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 26-51, January.
    9. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 467-495, June.
    10. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 959-989, October.
    11. Jad Beyhum & Jean-Pierre Florens & Ingrid Van Keilegom, 2021. "A nonparametric instrumental approach to endogeneity in competing risks models," Papers 2105.00946, arXiv.org.

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