Modeling Multi-Site Neuroimaging Data Using Hierarchical Bayesian Neural Networks to Study Structural Brain Variability
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2020-10-01
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en
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Abstract
Brain disorders are heterogeneous in their nature, therefore making it problematic to di er-
entiate between multiple brain disorders using a traditional case-control approach. In contrary
to case-control studies, where subjects are being classi ed into distinct groups, normative
modeling can be used to model the variation in a large population. Normative modeling is
a statistical method aiming to learn both the mean of a response variable and its normative
range, therefore being able to handle the heterogeneous nature of highly variant groups. How-
ever, large amounts of neuroimaging data are required for normative modeling. Hence, datasets
coming from di erent imaging centers need to be combined, introducing site-related variance
generated by among others variability in acquisition devices across centers. We must account
for this variability in the analysis, as these site-related variations are usually larger than those
that we are interested in when trying to detect individual outliers from the normative range.
Hierarchical Bayesian regression (HBR) models have been applied for multi-site normative
modeling previously. However, it was limited in that they only had the options to t either a
linear, or a simple parametric, form. To allow for more
exibility and make less assumptions
about the data, we will extend the HBR approach with a hierarchical Bayesian neural net-
work. Using three simulated datasets, we show the model's ability to handle site-e ects when
the estimated e ect is non-linear in both the mean and variance, while being computationally
scalable. Moreover, the model can also deal with, and hence does not over t on, sites with
limited data. Although the estimates t well to the data, the parameter sampling is unstable.
In future studies, this is something that would need to be solved rst, for example by assuming
di erent priors or experimenting with di erent chain initialization methods. Finally, we tted
and evaluated the model on image-derived phenotypes from the UK Biobank dataset. In this
test case, most brain measures showed a linear trend in their mean. Thus, we have observed
limited improvements of our model compared to the previously described linear HBR model.
However, when investigating the estimated variance, the HBNN showed a good performance in
estimating a non-linear heteroscedastic variance in the data. Nevertheless, this non-linearity in
the variance was minor, resulting in limited improvements of the neural network in comparison
to the linear HBR model. Nevertheless, our model is able to model the mean and variance
in datasets, also when there is non-linearity in the mean or variance of the data, or when the
variance follows a skew Gaussian distribution. Compared to the linear HBR model, our model
o ers additional
exibility to handle site-related variation and non-linearity in neuroimaging
datasets. Despite the limited improvements that we found, we expect that using a dataset
containing more non-linearity in the response variable would allow us to di erentiate between
both models to a greater extent.
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Faculteit der Sociale Wetenschappen