Analyzing repeated measurements while accounting for derivative tracking, varying within-subject variance, and autocorrelation: The xtmixediou command
Rachael A. Hughes
Bristol Medical School
University of Bristol
Bristol, UK
[email protected]
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Michael G. Kenward
Ashkirk, UK
[email protected]
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Jonathan A. C. Sterne
Bristol Medical School
University of Bristol
Bristol, UK
[email protected]
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Kate Tilling
Bristol Medical School and
MRC Integrative Epidemiology Unit
University of Bristol
Bristol, UK
[email protected]
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Abstract. 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.
View all articles by these authors:
Rachael A. Hughes, Michael G. Kenward, Jonathan A. C. Sterne, Kate Tilling
View all articles with these keywords:
xtmixediou, xtmixediou postestimation, autocorrelation, derivative tracking, integrated Ornstein–Uhlenbeck process, repeated-measures data, within-subject variability
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