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Identifiability of cure models revisited

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  • Hanin, Leonid
  • Huang, Li-Shan

Abstract

We obtained results on identifiability of mixture, mixture proportional hazards and bounded cumulative hazards (or Yakovlev) models of survival in the presence of cured (or non-susceptible) subpopulation. These results specify conditions under which model parameters can, or cannot, be estimated from the observed potentially censored survival times and thus may guide statistical modeling. The results are formulated for larger classes of models and in greater generality than previously and correct some misconceptions that exist in statistical literature on the subject. All results are supplied with rigorous self-contained proofs.

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  • Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:261-274
    DOI: 10.1016/j.jmva.2014.06.002
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    References listed on IDEAS

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    1. Peng, Yingwei & Zhang, Jiajia, 2008. "Identifiability of a mixture cure frailty model," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2604-2608, November.
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    5. Yu, Menggang & Taylor, Jeremy M.G. & Sandler, Howard M., 2008. "Individual Prediction in Prostate Cancer Studies Using a Joint Longitudinal SurvivalCure Model," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 178-187, March.
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    8. 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.
    9. 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.
    10. Mao, Meng & Wang, Jane-Ling, 2010. "Semiparametric Efficient Estimation for a Class of Generalized Proportional Odds Cure Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 302-311.
    11. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
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    Cited by:

    1. Yolanda M. Gómez & Diego I. Gallardo & Marcelo Bourguignon & Eduardo Bertolli & Vinicius F. Calsavara, 2023. "A general class of promotion time cure rate models with a new biological interpretation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 66-86, January.
    2. 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.
    3. Frederico Machado Almeida & Enrico Antônio Colosimo & Vinícius Diniz Mayrink, 2021. "Firth adjusted score function for monotone likelihood in the mixture cure fraction model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 131-155, January.
    4. Fangya Mao & Richard J. Cook, 2023. "Spatial dependence modeling of latent susceptibility and time to joint damage in psoriatic arthritis," Biometrics, The International Biometric Society, vol. 79(3), pages 2605-2618, September.
    5. 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.
    6. Olayidé Boussari & Laurent Bordes & Gaëlle Romain & Marc Colonna & Nadine Bossard & Laurent Remontet & Valérie Jooste, 2021. "Modeling excess hazard with time‐to‐cure as a parameter," Biometrics, The International Biometric Society, vol. 77(4), pages 1289-1302, December.
    7. Xiaoguang Wang & Ziwen Wang, 2021. "EM algorithm for the additive risk mixture cure model with interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 91-130, January.
    8. Reza Azimi & Mahdy Esmailian & Diego I. Gallardo & Héctor J. Gómez, 2022. "A New Cure Rate Model Based on Flory–Schulz Distribution: Application to the Cancer Data," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    9. 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).

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