Longitudinal models for AIDS marker data

Over the past decade, researchers have put a great amount of effort into developing suitable models for the analysis of longitudinal CD4 data and other markers of AIDS progression. These models must be general enough to allow for different patterns of change in the marker data. In this paper, we review the existing literature including our preferred models which involve mixed effects, stochastic terms and independent measurement error. Adding stochastic terms to standard mixed effects models gives an interpretable and parsimonious method for generalizing the covariance structure of the measurement error and short-term variability. We focus on univariate and bivariate models with integrated Ornstein-Uhlenbeck (IOU) stochastic terms. The IOU process allows for a range of biologically plausible derivative tracking that encompasses both random trajectory and Brownian motion behaviour. We illustrate these modelling techniques on longitudinal CD4 and viral RNA data.