Analyzing Repeated Measurements while Accounting for Derivative Tracking, Varying Within-subject Variance, and Autocorrelation: The Xtmixediou Command

Linear mixed-effects models are commonly used to model trajectories of repeated measures of biomarkers of disease. Taylor, Cumberland, and Sy (1994, Journal of the American Statistical Association 89: 727–736) proposed 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). They 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. In this article, we present the new command xtmixediou, which fits the linear mixed-effects IOU model and its special case, the linear mixed-effects Brownian motion model. The model is fit to balanced and unbalanced data using restricted maximum-likelihood estimation, where the optimization algorithm is the Newton–Raphson, Fisher scoring, or average information algorithm, or any combination of these. To aid convergence, xtmixediou 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 xtmixediou and predict with a simulated example of repeated biomarker measurements from HIV-positive patients.