Lifetime Data Analysis

, Volume 25, Issue 3, pp 406–438 | Cite as

What price semiparametric Cox regression?

  • Martin JullumEmail author
  • Nils Lid Hjort


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.


Cox regression Focused information criteria Model selection Parametrics and semiparametrics Survival data 



Our efforts have been supported in part by the Norwegian Research Council, through the project FocuStat (Focus Driven Statistical Inference With Complex Data) and the research based innovation centre Statistics for Innovation (sfi)\(^2\). We are also grateful to the reviewers and editor Mei-Ling T. Lee for constructive comments which led to an improved presentation.

Supplementary material

10985_2018_9450_MOESM1_ESM.pdf (203 kb)
Supplementary material 1 (pdf 203 KB)


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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