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Biometrika 1990 77(2):305-314; doi:10.1093/biomet/77.2.305
© 1990 by Biometrika Trust
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Nonparametric analysis of changes in hazard rates for censored survival data: An alternative to change-point models

HANS-GEORG MÜLLER and JANE-LINE WANG

Division of Statistics, University of California Davis, California 95616, U.S.A.

As a nonparametric estimator for the point of the most rapid change of a hazard rate we propose the location of an extremum of a nonparametric estimate of the derivative, or equivalently, of a zero of a nonparametric estimate of the second derivative. Using the kernel method for the nonparametric estimation of derivatives of the hazard rate, the asymptotic local limiting distribution and uniform consistency are applied to prove consistency and to find the limiting distribution of these estimators under random censoring and to construct confidence intervals both for the derivatives of the hazard rate and for the point of most rapid change. An application to leukaemia data illustrates this concept, and we discuss its relations to change-point modelling. The Monte Carlo method is used to assess the reliability of finite sample analyses, and in particular of the given example.

Key Words: Asymptotic distribution • Change-point • Curve estimation • Estimation of derivatives • Kernel method • Leukaemia • Lo-Singh representation • Nelson estimator


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