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A General Approach to the Predictability Issue in Survival Analysis with Applications

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  • Enno Mammen
  • Jens Perch Nielsen

Abstract

Very often in survival analysis one has to study martingale integrals where the integrand is not predictable and where the counting process theory of martingales is not directly applicable, as for example in nonparametric and semiparametric applications where the integrand is based on a pilot estimate. We call this the predictability issue in survival analysis. The problem has been resolved by approximations of the integrand by predictable functions which have been justified by ad hoc procedures. We present a general approach to the solution of this problem. The usefulness of the approach is shown in three applications. In particular, we argue that earlier ad hoc procedures do not work in higher-dimensional smoothing problems in survival analysis. Copyright 2007, Oxford University Press.

Suggested Citation

  • Enno Mammen & Jens Perch Nielsen, 2007. "A General Approach to the Predictability Issue in Survival Analysis with Applications," Biometrika, Biometrika Trust, vol. 94(4), pages 873-892.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:4:p:873-892
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    File URL: http://hdl.handle.net/10.1093/biomet/asm062
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    Cited by:

    1. van den Berg, Gerard. J. & Janys, Lena & Mammen, Enno & Nielsen, Jens Perch, 2021. "A general semiparametric approach to inference with marker-dependent hazard rate models," Journal of Econometrics, Elsevier, vol. 221(1), pages 43-67.
    2. María Luz Gámiz & Enno Mammen & María Dolores Martínez Miranda & Jens Perch Nielsen, 2016. "Double one-sided cross-validation of local linear hazards," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 755-779, September.
    3. Janys, Lena, 2017. "A General Semiparametric Approach to Inference with Marker-Dependent Hazard Rate Models," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168077, Verein für Socialpolitik / German Economic Association.
    4. Tine Buch-Kromann & Jens Nielsen, 2012. "Multivariate density estimation using dimension reducing information and tail flattening transformations for truncated or censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 167-192, February.
    5. van den Berg, Gerard J. & Janys, Lena & Mammen, Enno & Nielsen, Jens P., 2014. "A General Semiparametric Approach to Inference with Marker-Dependent Hazard Rate Models," IZA Discussion Papers 8339, Institute of Labor Economics (IZA).

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