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An Additive–Multiplicative Cox–Aalen Regression Model

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  • THOMAS H. SCHEIKE
  • MEI‐JIE ZHANG

Abstract

We propose an additive–multiplicative intensity model that extends the Cox regression model as well as the additive Aalen model. Instead of having a simple baseline intensity the extended model uses an additive Aalen model as its covariate dependent baseline. Approximate maximum likelihood estimators of the baseline intensity functions and the relative risk parameters of the Cox model are suggested by solving the score equations. The derived estimator is efficient. We establish the large sample properties of the estimator. The model provides a simple pragmatic way of including time‐varying covariate effects.

Suggested Citation

  • Thomas H. Scheike & Mei‐Jie Zhang, 2002. "An Additive–Multiplicative Cox–Aalen Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 75-88, March.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:1:p:75-88
    DOI: 10.1111/1467-9469.00065
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    Cited by:

    1. Peng He & Frank Eriksson & Thomas H. Scheike & Mei-Jie Zhang, 2016. "A Proportional Hazards Regression Model for the Subdistribution with Covariates-adjusted Censoring Weight for Competing Risks Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 103-122, March.
    2. Lee, Unkyung & Sun, Yanqing & Scheike, Thomas H. & Gilbert, Peter B., 2018. "Analysis of generalized semiparametric regression models for cumulative incidence functions with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 59-79.
    3. Christa Brelsford & Caterina Bacco, 2018. "Are ‘Water Smart Landscapes’ Contagious? An Epidemic Approach on Networks to Study Peer Effects," Networks and Spatial Economics, Springer, vol. 18(3), pages 577-613, September.
    4. Pablo Martínez-Camblor, 2022. "Learning the Treatment Impact on Time-to-Event Outcomes: The Transcarotid Artery Revascularization Simulated Cohort," IJERPH, MDPI, vol. 19(19), pages 1-12, September.
    5. Thomas H. Scheike & Mei-Jie Zhang, 2003. "Extensions and Applications of the Cox-Aalen Survival Model," Biometrics, The International Biometric Society, vol. 59(4), pages 1036-1045, December.
    6. Kraus, David, 2004. "Goodness-of-fit inference for the Cox-Aalen additive-multiplicative regression model," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 285-298, December.
    7. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    8. Miao Han & Liuquan Sun & Yutao Liu & Jun Zhu, 2018. "Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 523-547, July.
    9. Audrey Boruvka & Richard J. Cook, 2015. "A Cox-Aalen Model for Interval-censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 414-426, June.
    10. Christa Brelsford & Caterina De Bacco, 2018. "Are `Water Smart Landscapes' Contagious? An epidemic approach on networks to study peer effects," Papers 1801.10516, arXiv.org.
    11. Hao, Meiling & Zhao, Xingqiu & Xu, Wei, 2020. "Competing risk modeling and testing for X-chromosome genetic association," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

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