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A simulation-based goodness-of-fit test for survival data

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  • Li, Gang
  • Sun, Yanqing

Abstract

To check the validity of a parametric model for survival data, a number of supremum-type tests have been proposed in the literature using Khmaladze's (1993, Ann. Statist. 18, 582-602) transformation of a test process. However, such a transformation is usually very complicated and lacks a clear interpretation. Information could also be lost through transformation. In this note, we propose a simulation-based supremum-type test directly from the original test process using an idea originally introduced by Lin et al. (1993, Biometrika 80, 557-572). The test is developed under the framework of Aalen's (1978, Ann. Statist. 6, 701-726) multiplicative intensity counting process model, and therefore applies to a number of survival models including those with very general forms of censoring and truncation. By comparing the observed test process with a set of simulated realizations of an approximating process, our method can be used as a graphical tool as well as a formal test for checking the adequacy of the assumed parametric model. We establish consistency of the resulting test under any fixed alternative. Its performance is investigated in a simulation study. Illustrations are given using some real data sets.

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  • Li, Gang & Sun, Yanqing, 2000. "A simulation-based goodness-of-fit test for survival data," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 403-410, May.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:4:p:403-410
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    1. Nikabadze, A. & Stute, W., 1997. "Model checks under random censorship," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 249-259, March.
    2. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
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    Cited by:

    1. Paul Blanche & Thomas A. Gerds & Claus T. Ekstrøm, 2019. "The Wally plot approach to assess the calibration of clinical prediction models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 150-167, January.
    2. Li, Gang, 2003. "Nonparametric likelihood ratio goodness-of-fit tests for survival data," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 166-182, July.

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