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Biometrika 2006 93(2):357-366; doi:10.1093/biomet/93.2.357
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© 2006 Biometrika Trust

Confidence bands for hazard rates under random censorship

Ming-Yen Cheng1, Peter Hall2 and Dongsheng Tu3

1 Department of Mathematics, National Taiwan University, Taipei 106, Taiwan. cheng{at}math.ntu.edu.tw, 2 Centre for Mathematics and its Applications, Australian National University, Canberra ACT 0200, Australia. halpstat{at}maths.anu.edu.au, 3 NCIC Clinical Trials Group, Cancer Research Institute, Queen's University, Kingston ON K7L 3N6, Canada. dtu{at}ctg.queensu.ca

We suggest a completely empirical approach to the construction of confidence bands for hazard functions, based on smoothing the Nelsen-Aalen estimator. In particular, we introduce a local bandwidth-choice method. Our approach uses empirical information about both the survival rate and the censoring rate, and employs undersmoothing to alleviate difficulties caused by bias. We use both Edgeworth expansion and numerical simulation, the former to develop a basic formula and the latter to modify it for general use.

Key Words: Bandwidth; Censored data; Confidence band; Coverage error; Edgeworth expansion; Hazard function; Kernel methods; Survival analysis.

Received November 2004. Revised November 2005.


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