Statistics and Its Interface

Volume 13 (2020)

Number 3

A Semi-parametric Joint Latent Class Model with Longitudinal and Survival Data

Pages: 411 – 422



Yue Liu (Takeda Pharmaceutical Company Limited, Cambridge, Massachusetts, U.S.A.)

Ye Lin (Department of Statistics, University of Virginia, Charlottesville, Va., U.S.A.)

Jianhui Zhou (Department of Statistics, University of Virginia, Charlottesville, Va., U.S.A.)

Lei Liu (Division of Biostatistics, School of Medicine, Washington University in St. Louis, Missouri, U.S.A.)


In many longitudinal studies, we are interested in both repeated measures of a biomarker and time to an event. When there exist heterogeneous patterns of the longitudinal and survival profiles, we propose a latent class joint model to identify subgroups of subjects and study the association between longitudinal and survival outcomes. The model is estimated by maximizing the full likelihood function. We use B-splines to approximate the baseline hazard function which involves a diverging number of parameters. Asymptotic properties of the estimator for the joint latent class model are investigated. We conduct simulation studies to assess the performance of the developed method. A real data example, Mayo Clinic Primary Biliary Cirrhosis Data, is analyzed using the joint modeling approach.


B-splines, longitudinal measurements, mixed effects model, proportional hazards model, survival outcome

This research is partly supported by the NIAAA grant RC1 AA019274 and by the AHRQ grant R01 HS020263.

Received 5 July 2019

Accepted 28 March 2020

Published 22 April 2020