Bayesian longitudinal low-rank regression models for imaging genetic data from longitudinal studies

•The proposed method L2R2 jointly analyzes high-dimensional longitudinal neuroimaging responses and genetic covariates.•Modeling longitudinal SNP effects on ROI trajectories through SNP-age interactions.•L2R2 identify more longitudinal genetic effects on ROI trajectories for data from the Alzheimer's Disease Neuroimaging Initiative than the competing approaches.•Low-rank decomposition utilizes the variable structures to efficiently reduce the number of parameters for more powerful association analysis.•Modeling spatial-temporal correlations of longitudinal neuroimaging variables to increase detection power.

To perform a joint analysis of multivariate neuroimaging phenotypes and candidate genetic markers obtained from longitudinal studies, we develop a Bayesian longitudinal low-rank regression (L2R2) model. The L2R2 model integrates three key methodologies: a low-rank matrix for approximating the high-dimensional regression coefficient matrices corresponding to the genetic main effects and their interactions with time, penalized splines for characterizing the overall time effect, and a sparse factor analysis model coupled with random effects for capturing within-subject spatio-temporal correlations of longitudinal phenotypes. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations show that the L2R2 model outperforms several other competing methods. We apply the L2R2 model to investigate the effect of single nucleotide polymorphisms (SNPs) on the top 10 and top 40 previously reported Alzheimer disease-associated genes. We also identify associations between the interactions of these SNPs with patient age and the tissue volumes of 93 regions of interest from patients' brain images obtained from the Alzheimer's Disease Neuroimaging Initiative.