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Lifetime Data Anal. 2017 Jan;23(1):136-159. doi: 10.1007/s10985-016-9364-1. Epub 2016 Mar 23.

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

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Department of Biostatistics, University of Washington, Seattle, WA, 98195, USA.
Department of Biostatistics, University of Washington, Seattle, WA, 98195, USA.
Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA, 98109, USA.


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.


Case-cohort; Measurement error; Prentice surrogate endpoint evaluation; Proportional hazards model; Random effects model

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