Joint models for longitudinal data

Abstract

In a longitudinal study, data on different types of variables are often collected repeatedly over time. Some variables may be continuous, and some variables may be binary or times to an event of interest. Even for a single variable, data may be collected at different phases of the study with different characteristics. These different types of variables are typically associated or correlated, since they are measurements on the same individuals in the study. Analysis of data on each of these variables separately, ignoring other variables, may be inefficient and may also lead to biased results. Standard multivariate models with several correlated responses may not be easy to specify for different types of variables or when the models are nonlinear. Jointly modelling these variables simultaneously not only may be more efficient but may also reduce biases in parameter estimation. Statistical inference can then be based on the joint likelihood for all observed data. In this article, we briefly review several different types of joint models for longitudinal data. We focus on mixed effects models and likelihood methods for inference. We illustrate these joint models with datasets from HIV/AIDS studies.

Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 75-96.