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The partly parametric and partly nonparametric additive risk model

Author

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  • Nils Lid Hjort

    (University of Oslo)

  • Emil Aas Stoltenberg

    (BI Norwegian Business School)

Abstract

Aalen’s linear hazard rate regression model is a useful and increasingly popular alternative to Cox’ multiplicative hazard rate model. It postulates that an individual has hazard rate function $$h(s)=z_1\alpha _1(s)+\cdots +z_r\alpha _r(s)$$ h ( s ) = z 1 α 1 ( s ) + ⋯ + z r α r ( s ) in terms of his covariate values $$z_1,\ldots ,z_r$$ z 1 , … , z r . These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions $$\alpha _j(s)$$ α j ( s ) are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model’s parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:lifeda:v:29:y:2023:i:2:d:10.1007_s10985-021-09535-3
    DOI: 10.1007/s10985-021-09535-3
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    References listed on IDEAS

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    4. Martin Jullum & Nils Lid Hjort, 2019. "What price semiparametric Cox regression?," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 406-438, July.
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    6. Ørnulf Borgan & Rosemeire L. Fiaccone & Robin Henderson & Mauricio L. Barreto, 2007. "Dynamic Analysis of Recurrent Event Data with Missing Observations, with Application to Infant Diarrhoea in Brazil," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 53-69, March.
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