Analyzing repeated measurements while accounting for derivative tracking varying within-subject variance and autocorrelation: the xtiou command

Linear mixed-effects models are commonly used for the analysis of longitudinal biomarkers of disease. Taylor, Cumberland, and Sy/In (1994) proposed modeling biomarkers with a linear mixed-effects model with an added integrated Ornstein–Uhlenbeck (IOU) process (linear mixed-effects IOU model). This allows for autocorrelation, changing within-subject variance, and the incorporation of derivative tracking, that is, how much a subject tends to maintain the same trajectory for extended periods of time. Taylor, Cumberland, and Sy argued that the covariance structure induced by the stochastic process in this model was interpretable and more biologically plausible than the standard linear mixed-effects model. However, their model is rarely used, partly because of the lack of available software. We present a new Stata command, xtiou, that fits the linear mixed-effects IOU model and its special case, the linear mixed-effects Brownian motion model. The model can be fit to balanced and unbalanced data, using restricted maximum-likelihood estimation, where the optimization algorithm is either the Newton–Raphson, Fisher scoring, or average information algorithm, or any combination of these. To aid convergence, the command allows the user to change the method for deriving the starting values for optimization, the optimization algorithm, and the parameterization of the IOU process. We also provide a predict command to generate predictions under the model. We illustrate xtiou and predict with an example of repeated biomarker measurements from HIV-positive patients.