Standard Article

Smoothing Hazard Rates

  1. Jane-Ling Wang

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a11069

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Wang, J.-L. 2005. Smoothing Hazard Rates. Encyclopedia of Biostatistics. 4.

Author Information

  1. University of California, Davis, CA, USA

Publication History

  1. Published Online: 15 JUL 2005


The nonparametric approach to estimate hazard rates for lifetime data is flexible, model-free, and data-driven. No shape assumption is imposed other than that the hazard function is a smooth function. Such an approach typically involves smoothing of an initial hazard estimate, with arbitrary choice of smoother. We describe methods for grouped lifetime data observed at certain time intervals and for continuously observed lifetime data. There are some intrinsic differences between the smoothing approaches for these two types of data. More specifically, smoothing an initial hazard estimate based on the life table is adopted for grouped lifetime data; while for continuous data, smoothing is employed to increments of the Nelson–Aalen cumulative hazard estimate aiming at the derivative of the cumulative hazard function. A few nonparametric hazard regression methods are also discussed.


  • life table;
  • Nelson–Aalen estimator;
  • nonparametric smoothing methods;
  • bandwidth choices;
  • boundary effects;
  • hazard regression