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Hazard function estimation with cause-of-death data missing at random

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Abstract

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, 100080, China

    Qihua Wang

  2. Department of Mathematics and Statistics, Yunnan University, Kunming, 650091, China

    Qihua Wang

  3. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong

    Qihua Wang

  4. Biostatistics Branch, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, NC, 27709, USA

    Gregg E. Dinse

  5. Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Hum, Hong Kong

    Chunling Liu

Authors
  1. Qihua Wang
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  2. Gregg E. Dinse
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  3. Chunling Liu
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Correspondence to Qihua Wang.

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Wang, Q., Dinse, G.E. & Liu, C. Hazard function estimation with cause-of-death data missing at random. Ann Inst Stat Math 64, 415–438 (2012). https://doi.org/10.1007/s10463-010-0317-2

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  • DOI: https://doi.org/10.1007/s10463-010-0317-2

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