We conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease and mild cognitive impairment. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set which is obtained out-of-sample from 663 ADNI subjects having only genome-wide data. We relate longitudinal effective brain connectivity estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR). In both cases we implement a parametric bootstrap for testing SNP coefficients and make comparisons with p-values obtained from asymptotic null distributions. In both networks at an initial q-value threshold of 0.1 no effects are found. We report on exploratory patterns of associations with relatively high ranks that exhibit stability to the differing assumptions made by both FSR and LME.

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Neural networks have excelled at regression and classification problems when the input space consists of scalar variables. As a result of this proficiency, several popular packages have been developed that allow users to easily fit these kinds of models. However, the methodology has excluded the use of functional covariates and to date, there exists no software that allows users to build deep learning models with this generalized input space. To the best of our knowledge, the functional neural network (FuncNN) library is the first such package in any programming language; the library has been developed for R and is built on top of the keras architecture. Throughout this paper, several functions are introduced that provide users an avenue to easily build models, generate predictions, and run cross-validations. A summary of the underlying methodology is also presented. The ultimate contribution is a package that provides a set of general modelling and diagnostic tools for data problems in which there exist both functional and scalar covariates.