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Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions

Author

Listed:
  • Peter Gilbert

    (Fred Hutchinson Cancer Research Center & University of Washington)

  • Ian McKeague

    (Florida State University)

  • Yanqing Sun

    (University of North Carolina at Charlotte)

Abstract

It is of interest in some applications to determine whether there is a relationship between a hazard rate function (or a cumulative incidence function) and a mark variable which is only observed at uncensored failure times. We develop nonparametric tests for this problem when the mark variable is continuous. Tests are developed for the null hypothesis that the mark-specific hazard rate is independent of the mark versus ordered and two-sided alternatives expressed in terms of mark-specific hazard functions and mark-specific cumulative incidence functions. The test statistics are based on functionals of a bivariate test process equal to a weighted average of differences between a Nelson--Aalen-type estimator of the mark-specific cumulative hazard function and a nonparametric estimator of this function under the null hypothesis. The weight function in the test process can be chosen so that the test statistics are asymptotically distribution-free.Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. Specifically, the tests are used to assess if the instantaneous or absolute risk of treatment failure depends on the amount of accumulation of drug resistance mutations in a subject's HIV virus. This assessment helps guide development of anti-HIV therapies that surmount the problem of drug resistance.

Suggested Citation

  • Peter Gilbert & Ian McKeague & Yanqing Sun, 2004. "Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions," UW Biostatistics Working Paper Series 1032, Berkeley Electronic Press.
    • Handle: RePEc:bep:uwabio:1032
    Note: oai:bepress.com:uwbiostat-1032
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    References listed on IDEAS

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    1. J. P. Fine, 1999. "Analysing competing risks data with transformation models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 817-830.
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    Cited by:

    1. Brent A. Johnson, 2017. "Nonparametric Two-Sample Tests of the Marginal Mark Distribution with Censored Marks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 545-562, June.
    2. Michal Juraska & Peter B. Gilbert, 2016. "Mark-specific hazard ratio model with missing multivariate marks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 606-625, October.
    3. Sun, Yanqing & Li, Mei & Gilbert, Peter B., 2016. "Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 348-358.
    4. Dongxiao Han & Liuquan Sun & Yanqing Sun & Li Qi, 2017. "Mark-specific additive hazards regression with continuous marks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 467-494, July.
    5. Hammou Barmi, 2022. "On comparing competing risks using the ratio of their cumulative incidence functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1067-1083, December.
    6. Michael O. Finkelstein & Bruce Levin & Ian W. McKeague & Wei‐Yann Tsai, 2006. "A Note on the Censoring Problem in Empirical Case‐Outcome Studies," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 3(2), pages 375-395, July.
    7. Yanqing Sun & Li Qi & Fei Heng & Peter B. Gilbert, 2020. "A hybrid approach for the stratified mark‐specific proportional hazards model with missing covariates and missing marks, with application to vaccine efficacy trials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 791-814, August.

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