Abstract
We address the problem of estimating how different parts of the brain develop and change throughout the lifespan, and how these trajectories are affected by genetic and environmental factors. Estimation of these lifespan trajectories is statistically challenging, since their shapes are typically highly nonlinear, and although true change can only be quantified by longitudinal examinations, as follow-up intervals in neuroimaging studies typically cover less than 10% of the lifespan, use of cross-sectional information is necessary. Linear mixed models (LMMs) and structural equation models (SEMs) commonly used in longitudinal analysis rely on assumptions which are typically not met with lifespan data, in particular when the data consist of observations combined from multiple studies. While LMMs require a priori specification of a polynomial functional form, SEMs do not easily handle data with unstructured time intervals between measurements. Generalized additive mixed models (GAMMs) offer an attractive alternative, and in this paper we propose various ways of formulating GAMMs for estimation of lifespan trajectories of 12 brain regions, using a large longitudinal dataset and realistic simulation experiments. We show that GAMMs are able to more accurately fit lifespan trajectories, distinguish longitudinal and cross-sectional effects, and estimate effects of genetic and environmental exposures. Finally, we discuss and contrast questions related to lifespan research which strictly require repeated measures data and questions which can be answered with a single measurement per participant, and in the latter case, which simplifying assumptions that need to be made. The examples are accompanied with R code, providing a tutorial for researchers interested in using GAMMs.
Highlights
Large datasets with structural magnetic resonance images (MRIs) of participants whose ages span from early childhood to late adulthood provide ample opportunities to study lifespan brain trajectories
Structural equation models (SEMs) may be better able to estimate nonlinear trajectories, e.g., with a latent basis model (McArdle and Epstein, 1987; Meredith and Tisak, 1990), but structural equation models (SEMs) require that the time intervals between measurements for all participants take on a small set of unique values (Newsom, 2015; Oud and Jansen, 2000), an assumption which may be hard to satisfy with lifespan data
In contrast to the Generalized additive mixed models (GAMMs), neither of the linear mixed models (LMMs) capture the steep increase seen in early childhood, and the cubic LMM predicts an increase in cerebellum
Summary
Large datasets with structural magnetic resonance images (MRIs) of participants whose ages span from early childhood to late adulthood provide ample opportunities to study lifespan brain trajectories Important questions such data can contribute to answering include how brain structure is related to aging, how the aging effect is modified by genetics and environmental exposures, and at which age critical events like maximum volume or maximum rate of change occur. Generalized additive mixed models (GAMMs) (Lin and Zhang, 1999) offer an attractive alternative, typically yielding good fit over the full lifespan in an automated and data-driven manner This is illustrated, comparing a GAMM to LMMs with quadratic and cubic polynomials for the effect of age on cerebellum cortex volume. In contrast to the GAMM, neither of the LMMs capture the steep increase seen in early childhood, and the cubic LMM predicts an increase in cerebellum
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