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A Cox-type regression model with change-points in the covariates

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Abstract

We consider a Cox-type regression model with change-points in the covariates. A change-point specifies the unknown threshold at which the influence of a covariate shifts smoothly, i.e., the regression parameter may change over the range of a covariate and the underlying regression function is continuous but not differentiable. The model can be used to describe change-points in different covariates but also to model more than one change-point in a single covariate. Estimates of the change-points and of the regression parameters are derived and their properties are investigated. It is shown that not only the estimates of the regression parameters are \({\sqrt{n}}\) -consistent but also the estimates of the change-points in contrast to the conjecture of other authors. Asymptotic normality is shown by using results developed for M-estimators. At the end of this paper we apply our model to an actuarial dataset, the PBC dataset of Fleming and Harrington (Counting processes and survival analysis, 1991) and to a dataset of electric motors.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593, Stuttgart, Germany

    Uwe Jensen & Constanze Lütkebohmert

Authors
  1. Uwe Jensen
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  2. Constanze Lütkebohmert
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Correspondence to Constanze Lütkebohmert.

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Jensen, U., Lütkebohmert, C. A Cox-type regression model with change-points in the covariates. Lifetime Data Anal 14, 267–285 (2008). https://doi.org/10.1007/s10985-008-9083-3

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  • DOI: https://doi.org/10.1007/s10985-008-9083-3

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