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Exogenous time-varying covariates in double additive cure survival model with application to fertility

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  • Lambert, Philippe
  • Kreyenfeld, Michaela

Abstract

Extended cure survival models enable to separate covariates that affect the probability of an event (or long-term survival) from those only affecting the event timing (or short-term survival). We propose to generalize the bounded cumulative hazard model to handle additive terms for time-varying (exogenous) covariates jointly impacting long- and short-term survival. The selection of the penalty parameters is a challenge in that framework. A fast algorithm based on Laplace approximations in Bayesian P-spline models is proposed. The methodology is motivated by fertility studies where women’s characteristics such as the employment status and the income (to cite a few) can vary in a non-trivial and frequent way during the individual follow-up. The method is furthermore illustrated by drawing on register data from the German Pension Fund which enabled us to study how women’s time-varying earnings relate to first birth transitions.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2023006
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    References listed on IDEAS

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    1. Lambert, Philippe & Bremhorst, Vincent, 2019. "Estimation and identification issues in the promotion time cure model when the same covariates influence long- and short-term survival," LIDAM Reprints ISBA 2019027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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).
    3. 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.
    4. J. K. Lindsey, 1995. "Fitting Parametric Counting Processes by Using Log‐Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(2), pages 201-212, June.
    5. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    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. Lambert, Philippe & Bremhorst, Vincent, 2020. "Inclusion of time-varying covariates in cure survival models with an application in fertility studies," LIDAM Reprints ISBA 2020040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Lore Dirick & Tony Bellotti & Gerda Claeskens & Bart Baesens, 2019. "Macro-Economic Factors in Credit Risk Calculations: Including Time-Varying Covariates in Mixture Cure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 40-53, January.
    9. Lambert, Philippe, 2021. "Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    10. Lambert, Philippe, 2021. "Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data," LIDAM Reprints ISBA 2021057, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. 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.
    12. 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.
    13. 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.
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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.

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