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Review
. 2010 Jun 1;28(16):2796-801.
doi: 10.1200/JCO.2009.25.0654. Epub 2010 May 3.

Basic concepts and methods for joint models of longitudinal and survival data

Joseph G Ibrahim  1 , Haitao Chu, Liddy M Chen
Affiliations
Review

Basic concepts and methods for joint models of longitudinal and survival data

Joseph G Ibrahim et al. J Clin Oncol. .

Abstract

Joint models for longitudinal and survival data are particularly relevant to many cancer clinical trials and observational studies in which longitudinal biomarkers (eg, circulating tumor cells, immune response to a vaccine, and quality-of-life measurements) may be highly associated with time to event, such as relapse-free survival or overall survival. In this article, we give an introductory overview on joint modeling and present a general discussion of a broad range of issues that arise in the design and analysis of clinical trials using joint models. To demonstrate our points throughout, we present an analysis from the Eastern Cooperative Oncology Group trial E1193, as well as examine some operating characteristics of joint models through simulation studies.

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Conflict of interest statement

Authors' disclosures of potential conflicts of interest and author contributions are found at the end of this article.

Figures

Fig 1.
Fig 1.
Causal diagram. Y(t), observed longitudinal data; X(t), trajectory function; S, survival; Z, treatment; α, treatment effect on survival; γ, treatment effect on longitudinal process; β, effect of longitudinal process on survival.
Fig 2.
Fig 2.
Trajectory function for E1193 study. QOL, quality of life.
See this image and copyright information in PMC

References

    1. De Gruttola V, Tu XM. Modeling progression of CD4-lymphocyte count and its relationship to survival time. Biometrics. 1994;50:1003–1014. - PubMed
    1. Tsiatis AA, DeGruttola V, Wulfsohn MS. Modeling the relationship of survival to longitudinal data measured with error: Applications to survival and CD4 counts in patients with AIDS. J Am Stat Assoc. 1995;90:27–37.
    1. Faucett CJ, Thomas CC. Simultaneously modelling censored survival data and repeatedly measured covariates: A Gibbs sampling approach. Stat Med. 1996;15:1663–1685. - PubMed
    1. Faucett CJ, Schenker N, Taylor JMG. Survival analysis using auxiliary variables via multiple imputation, with applications to AIDS clinical trials data. Biometrics. 2002;58:37–47. - PubMed
    1. LaValley MP, DeGruttola V. Model for empirical Bayes estimators of longitudinal CD4 counts. Stat Med. 1996;15:2289–2305. - PubMed