Nonparametric change point estimation for survival distributions with a partially constant hazard rate

  • Alessandra R. Brazzale
  • Helmut Küchenhoff
  • Stefanie Krügel
  • Tobias S. Schiergens
  • Heiko Trentzsch
  • Wolfgang Hartl


We present a new method for estimating a change point in the hazard function of a survival distribution assuming a constant hazard rate after the change point and a decreasing hazard rate before the change point. Our method is based on fitting a stump regression to p values for testing hazard rates in small time intervals. We present three real data examples describing survival patterns of severely ill patients, whose excess mortality rates are known to persist far beyond hospital discharge. For designing survival studies in these patients and for the definition of hospital performance metrics (e.g. mortality), it is essential to define adequate and objective end points. The reliable estimation of a change point will help researchers to identify such end points. By precisely knowing this change point, clinicians can distinguish between the acute phase with high hazard (time elapsed after admission and before the change point was reached), and the chronic phase (time elapsed after the change point) in which hazard is fairly constant. We show in an extensive simulation study that maximum likelihood estimation is not robust in this setting, and we evaluate our new estimation strategy including bootstrap confidence intervals and finite sample bias correction.


Change point Survival Hazard rate ICU Acute phase 



We would like to thank the Associate Editor and the two anonymous Referees for their careful reading of the paper and the most useful comments which greatly helped us improving it.


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Authors and Affiliations

  1. 1.Dipartimento di Scienze StatisticheUniversità degli Studi di PadovaPadovaItaly
  2. 2.Statistical Consulting Unit, Department of StatisticsLudwig-Maximilians-Universität MünchenMunichGermany
  3. 3.Department of StatisticsLudwig-Maximilians-Universität MünchenMunichGermany
  4. 4.Department of General, Visceral, Transplantation and Vascular Surgery, University School of Medicine, Grosshadern CampusLudwig-Maximilians-Universität MünchenMunichGermany
  5. 5.Institut für Notfallmedizin und Medizinmanagement INM, Klinikum der Universität MünchenLudwig-Maximilians-Universität MünchenMunichGermany

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