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A flexible additive multiplicative hazard model

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  • Torben Martinussen

Abstract

We present a new additive-multiplicative hazard model which consists of two components. The first component contains additive covariate effects through an additive Aalen model while the second component contains multiplicative covariate effects through a Cox regression model. The Aalen model allows for time-varying covariate effects, while the Cox model allows only a common time-dependence through the baseline. Approximate maximum likelihood estimators are derived by solving the simultaneous score equations for the nonparametric and parametric components of the model. The suggested estimators are provided with large-sample properties and are shown to be efficient. The efficient estimators depend, however, on some estimated weights. We therefore also consider unweighted estimators and describe their large-sample properties. We finally extend the model to allow for time-varying covariate effects in the multiplicative part of the model as well. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Torben Martinussen, 2002. "A flexible additive multiplicative hazard model," Biometrika, Biometrika Trust, vol. 89(2), pages 283-298, June.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:283-298
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    Cited by:

    1. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    2. Chin-Tsang Chiang, 2011. "A more flexible joint latent model for longitudinal and survival time data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 151-170, March.
    3. Xi Ning & Yinghao Pan & Yanqing Sun & Peter B. Gilbert, 2023. "A semiparametric Cox–Aalen transformation model with censored data," Biometrics, The International Biometric Society, vol. 79(4), pages 3111-3125, December.
    4. Ruixuan Liu, 2020. "A competing risks model with time‐varying heterogeneity and simultaneous failure," Quantitative Economics, Econometric Society, vol. 11(2), pages 535-577, May.
    5. Chin-Tsang Chiang & Mei-Cheng Wang, 2009. "Varying-coefficient model for the occurrence rate function of recurrent events," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 197-213, March.
    6. Zhuowei Sun & Hongyuan Cao & Li Chen, 2022. "Regression analysis of additive hazards model with sparse longitudinal covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 263-281, April.
    7. Frank Eriksson & Jianing Li & Thomas Scheike & Mei‐Jie Zhang, 2015. "The proportional odds cumulative incidence model for competing risks," Biometrics, The International Biometric Society, vol. 71(3), pages 687-695, September.
    8. Marschner, Ian C. & Gillett, Alexandra C. & O’Connell, Rachel L., 2012. "Stratified additive Poisson models: Computational methods and applications in clinical epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1115-1130.
    9. 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.
    10. Nils Lid Hjort & Emil Aas Stoltenberg, 2023. "The partly parametric and partly nonparametric additive risk model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 372-402, April.
    11. 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.
    12. Giada Adelfio & Marcello Chiodi, 2021. "Including covariates in a space-time point process with application to seismicity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 947-971, September.
    13. Torben Martinussen & Odd O. Aalen & Thomas H. Scheike, 2008. "The Mizon–Richard Encompassing Test for the Cox and Aalen Additive Hazards Models," Biometrics, The International Biometric Society, vol. 64(1), pages 164-171, March.
    14. Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
    15. Meyer, Sebastian & Held, Leonhard & Höhle, Michael, 2017. "Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i11).

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