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What price semiparametric Cox regression?

Author

Listed:
  • Martin Jullum

    (University of Oslo)

  • Nils Lid Hjort

    (University of Oslo)

Abstract

Cox’s proportional hazards regression model is the standard method for modelling censored life-time data with covariates. In its standard form, this method relies on a semiparametric proportional hazards structure, leaving the baseline unspecified. Naturally, specifying a parametric model also for the baseline hazard, leading to fully parametric Cox models, will be more efficient when the parametric model is correct, or close to correct. The aim of this paper is two-fold. (a) We compare parametric and semiparametric models in terms of their asymptotic relative efficiencies when estimating different quantities. We find that for some quantities the gain of restricting the model space is substantial, while it is negligible for others. (b) To deal with such selection in practice we develop certain focused and averaged focused information criteria (FIC and AFIC). These aim at selecting the most appropriate proportional hazards models for given purposes. Our methodology applies also to the simpler case without covariates, when comparing Kaplan–Meier and Nelson–Aalen estimators to parametric counterparts. Applications to real data are also provided, along with analyses of theoretical behavioural aspects of our methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:3:d:10.1007_s10985-018-9450-7
    DOI: 10.1007/s10985-018-9450-7
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    References listed on IDEAS

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    1. Hjort, Nils Lid & Claeskens, Gerda, 2006. "Focused Information Criteria and Model Averaging for the Cox Hazard Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1449-1464, December.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, September.
    3. Paul Meier & Theodore Karrison & Rick Chappell & Hui Xie, 2004. "The Price of Kaplan-Meier," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 890-896, January.
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    Cited by:

    1. 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.
    2. Szilárd Nemes & Erik Bülow & Andreas Gustavsson, 2020. "A Brief Overview of Restricted Mean Survival Time Estimators and Associated Variances," Stats, MDPI, vol. 3(2), pages 1-13, May.
    3. Céline Cunen & Nils Lid Hjort, 2020. "Confidence Distributions for FIC Scores," Econometrics, MDPI, vol. 8(3), pages 1-28, July.

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