  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.
