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Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes

Author

Listed:
  • Fei Heng

    (University of North Florida)

  • Yanqing Sun

    (University of North Carolina at Charlotte)

  • Seunggeun Hyun

    (University of South Carolina Upstate)

  • Peter B. Gilbert

    (University of Washington and Fred Hutchinson Cancer Research Center Seattle)

Abstract

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

Suggested Citation

  • Fei Heng & Yanqing Sun & Seunggeun Hyun & Peter B. Gilbert, 2020. "Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 731-760, October.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:4:d:10.1007_s10985-020-09497-y
    DOI: 10.1007/s10985-020-09497-y
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    References listed on IDEAS

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    1. 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.
    2. Kaifeng Lu & Anastasios A. Tsiatis, 2001. "Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure," Biometrics, The International Biometric Society, vol. 57(4), pages 1191-1197, December.
    3. Yanqing Sun & Seunggeun Hyun & Peter Gilbert, 2008. "Testing and Estimation of Time-Varying Cause-Specific Hazard Ratios with Covariate Adjustment," Biometrics, The International Biometric Society, vol. 64(4), pages 1070-1079, December.
    4. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
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    6. Zongwu Cai & Yanqing Sun, 2003. "Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 93-111, March.
    7. Peter B. Gilbert & Yanqing Sun, 2015. "Inferences on relative failure rates in stratified mark-specific proportional hazards models with missing marks, with application to human immunodeficiency virus vaccine efficacy trials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(1), pages 49-73, January.
    8. Yanqing Sun & Xiyuan Qian & Qiong Shou & Peter B. Gilbert, 2017. "Analysis of two-phase sampling data with semiparametric additive hazards models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 377-399, July.
    9. Daniel Nevo & Reiko Nishihara & Shuji Ogino & Molin Wang, 2018. "The competing risks Cox model with auxiliary case covariates under weaker missing-at-random cause of failure," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 425-442, July.
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    11. 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.
    12. Efromovich, Sam, 2010. "Dimension Reduction and Adaptation in Conditional Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 761-774.
    13. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
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