  Analyzing data from multiple neuroimaging studies has great potential in
terms of increasing statistical power, enabling detection of effects of smaller
magnitude than would be possible when analyzing each study separately and also
allowing to systematically investigate between-study differences. Restrictions
due to privacy or proprietary data as well as more practical concerns can make
it hard to share neuroimaging datasets, such that analyzing all data in a
common location might be impractical or impossible. Meta-analytic methods
provide a way to overcome this issue, by combining aggregated quantities like
model parameters or risk ratios. Most meta-analytic tools focus on parametric
statistical models, and methods for meta-analyzing semi-parametric models like
generalized additive models have not been well developed. Parametric models are
often not appropriate in neuroimaging, where for instance age-brain
relationships may take forms that are difficult to accurately describe using
such models. In this paper we introduce meta-GAM, a method for meta-analysis of
generalized additive models which does not require individual participant data,
and hence is suitable for increasing statistical power while upholding privacy
and other regulatory concerns. We extend previous works by enabling the
analysis of multiple model terms as well as multivariate smooth functions. In
addition, we show how meta-analytic $p$-values can be computed for smooth
terms. The proposed methods are shown to perform well in simulation
experiments, and are demonstrated in a real data analysis on hippocampal volume
and self-reported sleep quality data from the Lifebrain consortium. We argue
that application of meta-GAM is especially beneficial in lifespan neuroscience
and imaging genetics. The methods are implemented in an accompanying R package
\verb!metagam!, which is also demonstrated.
