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

Joseph G Ibrahim, Haitao Chu, Liddy M Chen, Joseph G Ibrahim, Haitao Chu, Liddy M Chen

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.

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.

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