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On Goodness‐of‐Fit Tests for Aalen's Additive Risk Model

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  • AXEL GANDY
  • UWE JENSEN

Abstract

. In this paper we propose goodness‐of‐fit tests for Aalen's additive risk model. They are based on test statistics the asymptotic distributions of which are determined under both the null and alternative hypotheses. The results are derived using martingale techniques for counting processes. An important feature of these tests is that they can be adjusted to particular alternatives. One of the alternatives we consider is Cox's multiplicative risk model. It is perhaps remarkable that such a test needs no estimate of the baseline hazard in the Cox model. We present simulation studies which give an impression of the performance of the proposed tests. In addition, the tests are applied to real data sets.

Suggested Citation

  • Axel Gandy & Uwe Jensen, 2005. "On Goodness‐of‐Fit Tests for Aalen's Additive Risk Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 425-445, September.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:3:p:425-445
    DOI: 10.1111/j.1467-9469.2005.00457.x
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    Cited by:

    1. Matthias Brueckner & Andrew Titman & Thomas Jaki, 2019. "Instrumental variable estimation in semi‐parametric additive hazards models," Biometrics, The International Biometric Society, vol. 75(1), pages 110-120, March.
    2. Ledoux, James, 2008. "On a software reliability model by Koch and Spreij," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 904-914, May.
    3. Torben Martinussen & Odd O. Aalen & Thomas H. Scheike, 2008. "The Mizon–Richard Encompassing Test for the Cox and Aalen Additive Hazards Models," Biometrics, The International Biometric Society, vol. 64(1), pages 164-171, March.
    4. RADU HERBEI & IAN W. McKEAGUE, 2009. "Hybrid Samplers for Ill‐Posed Inverse Problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 839-853, December.
    5. Jianwen Cai & Donglin Zeng, 2011. "Additive Mixed Effect Model for Clustered Failure Time Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1340-1351, December.

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