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Joint modeling of longitudinal and survival data with the Cox model and two-phase sampling

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  • Rong Fu

    (University of Washington)

  • Peter B. Gilbert

    (University of Washington
    Fred Hutchinson Cancer Research Center)

Abstract

A common objective of cohort studies and clinical trials is to assess time-varying longitudinal continuous biomarkers as correlates of the instantaneous hazard of a study endpoint. We consider the setting where the biomarkers are measured in a designed sub-sample (i.e., case-cohort or two-phase sampling design), as is normative for prevention trials. We address this problem via joint models, with underlying biomarker trajectories characterized by a random effects model and their relationship with instantaneous risk characterized by a Cox model. For estimation and inference we extend the conditional score method of Tsiatis and Davidian (Biometrika 88(2):447–458, 2001) to accommodate the two-phase biomarker sampling design using augmented inverse probability weighting with nonparametric kernel regression. We present theoretical properties of the proposed estimators and finite-sample properties derived through simulations, and illustrate the methods with application to the AIDS Clinical Trials Group 175 antiretroviral therapy trial. We discuss how the methods are useful for evaluating a Prentice surrogate endpoint, mediation, and for generating hypotheses about biological mechanisms of treatment efficacy.

Suggested Citation

  • Rong Fu & Peter B. Gilbert, 2017. "Joint modeling of longitudinal and survival data with the Cox model and two-phase sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 136-159, January.
    • Handle: RePEc:spr:lifeda:v:23:y:2017:i:1:d:10.1007_s10985-016-9364-1
    DOI: 10.1007/s10985-016-9364-1
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    References listed on IDEAS

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    1. 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.
    2. Haneuse, Sebastien & Saegusa, Takumi & Lumley, Thomas, 2011. "osDesign: An R Package for the Analysis, Evaluation, and Design of Two-Phase and Case-Control Studies," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i11).
    3. Weihua Cao & Anastasios A. Tsiatis & Marie Davidian, 2009. "Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data," Biometrika, Biometrika Trust, vol. 96(3), pages 723-734.
    4. Qi, Lihong & Wang, C.Y. & Prentice, Ross L., 2005. "Weighted Estimators for Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1250-1263, December.
    5. Dimitris Rizopoulos & Geert Verbeke & Emmanuel Lesaffre, 2009. "Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 637-654, June.
    6. Guo X. & Carlin B.P., 2004. "Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages," The American Statistician, American Statistical Association, vol. 58, pages 16-24, February.
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    Cited by:

    1. Yanqing Sun & Qingning Zhou & Peter B. Gilbert, 2023. "Analysis of the Cox Model with Longitudinal Covariates with Measurement Errors and Partly Interval Censored Failure Times, with Application to an AIDS Clinical Trial," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 430-454, July.

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