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We conduct an imaging genetics study to explore how effective brainconnectivity in the default mode network (DMN) may be related to geneticswithin the context of Alzheimer's disease and mild cognitive impairment. Wedevelop an analysis of longitudinal resting-state functional magnetic resonanceimaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects witha total of 319 rs-fMRI scans from the Alzheimer's Disease NeuroimagingInitiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRIscans to estimate effective brain connectivity within the DMN and related to aset of single nucleotide polymorphisms (SNPs) contained in an empiricaldisease-constrained set which is obtained out-of-sample from 663 ADNI subjectshaving only genome-wide data.  We examine longitudinal data in both a 4-region and an 6-region network andrelate longitudinal effective brain connectivity networks estimated usingspectral DCM to SNPs using both linear mixed effect (LME) models as well asfunction-on-scalar regression (FSR). In the former case we implement aparametric bootstrap for testing SNP coefficients and make comparisons withp-values obtained from the chi-squared null distribution. We also implement aparametric bootstrap approach for testing regression functions in FSR and wemake comparisons between p-values obtained from the parametric bootstrap top-values obtained using the F-distribution with degrees-of-freedom based onSatterthwaite's approximation.  In both networks we report on exploratory patterns of associations withrelatively high ranks that exhibit stability to the differing assumptions madeby both FSR and LME.

Spectral Dynamic Causal Modelling of Resting-State fMRI: Relating Effective Brain Connectivity in the Default Mode Network to Genetics