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Inclusion of time‐varying covariates in cure survival models with an application in fertility studies

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  • Philippe Lambert
  • Vincent Bremhorst

Abstract

Cure survival models are used when we desire to acknowledge explicitly that an unknown proportion of the population studied will never experience the event of interest. An extension of the promotion time cure model enabling the inclusion of time‐varying covariates as regressors when modelling (simultaneously) the probability and the timing of the monitored event is presented. Our proposal enables us to handle non‐monotone population hazard functions without a specific parametric assumption on the baseline hazard. This extension is motivated by and illustrated on data from the German Socio‐Economic Panel by studying the transition to second and third births in West Germany.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:183:y:2020:i:1:p:333-354
    DOI: 10.1111/rssa.12501
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    References listed on IDEAS

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    1. 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.
    2. Elizabeth R. Brown & Joseph G. Ibrahim, 2003. "Bayesian Approaches to Joint Cure-Rate and Longitudinal Models with Applications to Cancer Vaccine Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 686-693, September.
    3. Li Li & Ji-Hyun Lee, 2017. "A latent promotion time cure rate model using dependent tail-free mixtures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 891-905, June.
    4. Lambert, Philippe, 2007. "Archimedean copula estimation using Bayesian splines smoothing techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6307-6320, August.
    5. Jullion, Astrid & Lambert, Philippe, 2007. "Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2542-2558, February.
    6. Bremhorst, Vincent & Kreyenfeld, Michaela & Lambert, Philippe, 2016. "Fertility progression in Germany: An analysis using flexible nonparametric cure survival models," LIDAM Reprints ISBA 2016023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. 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.
    8. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.
    9. 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.
    10. Zhou, Jie & Zhang, Jiajia & McLain, Alexander C. & Cai, Bo, 2016. "A multiple imputation approach for semiparametric cure model with interval censored data," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 105-114.
    11. Bremhorst, Vincent & Lambert, Philippe, 2016. "Flexible estimation in cure survival models using Bayesian P-splines," LIDAM Reprints ISBA 2016002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. 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.
    13. Li, Yi & Lin, Xihong, 2006. "Semiparametric Normal Transformation Models for Spatially Correlated Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 591-603, June.
    14. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    15. Yueh-Yun Chi & Joseph G. Ibrahim, 2006. "Joint Models for Multivariate Longitudinal and Multivariate Survival Data," Biometrics, The International Biometric Society, vol. 62(2), pages 432-445, June.
    16. Zhang, Jiajia & Peng, Yingwei, 2007. "An alternative estimation method for the accelerated failure time frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4413-4423, May.
    17. Zhang, Jiajia & Peng, Yingwei & Li, Haifen, 2013. "A new semiparametric estimation method for accelerated hazards mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 95-102.
    18. 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.
    19. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2004. "A new joint model for longitudinal and survival data with a cure fraction," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 18-34, October.
    20. 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.
    21. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
    22. 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).
    23. Tamás Bartus & Lívia Murinkó & Ivett Szalma & Bernadett Szél, 2013. "The effect of education on second births in Hungary," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(1), pages 1-32.
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. Kreyenfeld, Michaela & Konietzka, Dirk & Lambert, Philippe & Ramos, Vincent Jerald, 2022. "Second Birth Fertility in Germany: Social Class, Gender, and the Role of Economic Uncertainty," LIDAM Discussion Papers ISBA 2022023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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