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Flexible estimation in cure survival models using Bayesian P-splines

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  • Bremhorst, Vincent
  • Lambert, Philippe

Abstract

In the analysis of survival data, it is usually assumed that any unit will experience the event of interest if it is observed for a sufficiently long time. However, it can be explicitly assumed that an unknown proportion of the population under study will never experience the monitored event. The promotion time model, which has a biological motivation, is one of the survival models taking this feature into account. The promotion time model assumes that the failure time of each subject is generated by the minimum of N independent latent event times with a common distribution independent of N. An extension which allows the covariates to influence simultaneously the probability of being cured and the latent distribution is presented. The latent distribution is estimated using a flexible Cox proportional hazard model where the logarithm of the baseline hazard function is specified using Bayesian P-splines. Introducing covariates in the latent distribution implies that the population hazard function might not have a proportional hazard structure. However, the use of P-splines provides a smooth estimation of the population hazard ratio over time. The identification issues of the model are discussed and a restricted use of the model when the follow-up of the study is not sufficiently long is proposed. The accuracy of our methodology is evaluated through a simulation study and the model is illustrated on data from a Melanoma clinical trial.

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  • Bremhorst, Vincent & Lambert, Philippe, 2016. "Flexible estimation in cure survival models using Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 270-284.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:270-284
    DOI: 10.1016/j.csda.2014.05.009
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    References listed on IDEAS

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    Cited by:

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    3. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    4. Matthew McTeer & Robin Henderson & Quentin M. Anstee & Paolo Missier, 2024. "Handling Overlapping Asymmetric Data Sets—A Twice Penalized P-Spline Approach," Mathematics, MDPI, vol. 12(5), pages 1-33, March.
    5. Gressani, Oswaldo & Lambert, Philippe, 2018. "Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 151-167.
    6. Sam Efromovich & Jufen Chu, 2018. "Hazard rate estimation for left truncated and right censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 889-917, August.
    7. Michaela Kreyenfeld & Dirk Konietzka & Philippe Lambert & Vincent Jerald Ramos, 2023. "Second Birth Fertility in Germany: Social Class, Gender, and the Role of Economic Uncertainty," European Journal of Population, Springer;European Association for Population Studies, vol. 39(1), pages 1-27, December.
    8. Philippe Lambert, 2023. "Comments on: 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 506-509, June.
    9. Philippe Lambert & Vincent Bremhorst, 2020. "Inclusion of time‐varying covariates in cure survival models with an application in fertility studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 333-354, January.
    10. Vincent Bremhorst & Michaela Kreyenfeld & Philippe Lambert, 2016. "Fertility progression in Germany: An analysis using flexible nonparametric cure survival models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 35(18), pages 505-534.
    11. Minnie M. Joo & Brandon Bolte & Nguyen Huynh & Bumba Mukherjee, 2023. "Bayesian Spatial Split-Population Survival Model with Applications to Democratic Regime Failure and Civil War Recurrence," Mathematics, MDPI, vol. 11(8), pages 1-23, April.
    12. Mohamed Elamin Abdallah Mohamed Elamin Omer & Mohd Rizam Abu Bakar & Mohd Bakri Adam & Mohd Shafie Mustafa, 2020. "Cure Models with Exponentiated Weibull Exponential Distribution for the Analysis of Melanoma Patients," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    13. Lambert, Philippe & Kreyenfeld, Michaela, 2023. "Exogenous time-varying covariates in double additive cure survival model with application to fertility," LIDAM Discussion Papers ISBA 2023006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Gressani, Oswaldo & Lambert, Philippe, 2016. "Fast Bayesian inference in semi-parametric P-spline cure survival models using Laplace approximations," LIDAM Discussion Papers ISBA 2016041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Bremhorst, Vincent & Kreyenfeld, Michaela & Lambert, Philippe, 2017. "Nonparametric double additive cure survival models: an application to the estimation of the nonlinear effect of age at first parenthood on fertility progression," LIDAM Discussion Papers ISBA 2017004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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