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Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark

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  • Sun, Yanqing
  • Li, Mei
  • Gilbert, Peter B.

Abstract

Motivated by the need to assess HIV vaccine efficacy, previous studies proposed an extension of the discrete competing risks proportional hazards model, in which the cause of failure is replaced by a continuous mark only observed at the failure time. However the model assumptions may fail in several ways, and no diagnostic testing procedure for this situation has been proposed. A goodness-of-fit test procedure for the stratified mark-specific proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazards depend nonparametrically on both time and the mark is proposed. The test statistics are constructed based on the weighted cumulative mark-specific martingale residuals. The critical values of the proposed test statistics are approximated using the Gaussian multiplier method. The performance of the proposed tests is examined extensively in simulations for a variety of the models under the null hypothesis and under different types of alternative models. An analysis of the ‘Step’ HIV vaccine efficacy trial using the proposed method is presented. The analysis suggests that the HIV vaccine candidate may increase susceptibility to HIV acquisition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:348-358
    DOI: 10.1016/j.csda.2014.11.012
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    References listed on IDEAS

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    1. Yanqing Sun & Hulin Wu, 2005. "Semiparametric Time‐Varying Coefficients Regression Model for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 21-47, March.
    2. Yanqing Sun & Peter B. Gilbert, 2012. "Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 34-52, March.
    3. Han, Donghoon & Balakrishnan, N., 2010. "Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2066-2081, September.
    4. Cramer, Erhard & Schmiedt, Anja Bettina, 2011. "Progressively Type-II censored competing risks data from Lomax distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1285-1303, March.
    5. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    6. M. Juraska & P. B. Gilbert, 2013. "Mark-Specific Hazard Ratio Model with Multivariate Continuous Marks: An Application to Vaccine Efficacy," Biometrics, The International Biometric Society, vol. 69(2), pages 328-337, June.
    7. Halbo Zhou & C.‐Y. Wang, 2000. "Failure time regression with continuous covariates measured with error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 657-665.
    8. 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.
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    Cited by:

    1. Guangren Yang & Yanqing Sun & Li Qi & Peter B. Gilbert, 2017. "Estimation of Stratified Mark-Specific Proportional Hazards Models Under Two-Phase Sampling with Application to HIV Vaccine Efficacy Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 259-283, June.
    2. 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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