Effect-Size Estimation Using Semiparametric Hierarchical Mixture Models in Disease-Association Studies with Neuroimaging Data

In disease-association studies using neuroimaging data, evaluating the biological or clinical significance of individual associations requires not only detection of disease-associated areas of the brain but also estimation of the magnitudes of the associations or effect sizes for individual brain areas. In this paper, we propose a model-based framework for voxel-based inferences under spatial dependency in neuroimaging data. Specifically, we employ hierarchical mixture models with a hidden Markov random field structure to incorporate the spatial dependency between voxels. A nonparametric specification is proposed for the effect size distribution to flexibly estimate the underlying effect size distribution. Simulation experiments demonstrate that compared with a naive estimation method, the proposed methods can substantially reduce the selection bias in the effect size estimates of the selected voxels with the greatest observed associations. An application to neuroimaging data from an Alzheimer’s disease study is provided.

Empirical Bayes estimation of semi-parametric hierarchical mixture models for unbiased characterization of polygenic disease architectures

Genome-wide association studies (GWAS) suggest that the genetic architecture of complex diseases consists of unexpectedly numerous variants with small effect sizes. However, the polygenic architectures of many diseases have not been well characterized due to lack of simple and fast methods for unbiased estimation of the underlying proportion of disease-associated variants and their effect-size distribution. Applying empirical Bayes estimation of semi-parametric hierarchical mixture models to GWAS summary statistics, we confirmed that schizophrenia was extremely polygenic (∼ 40% risk variants of independent genome-wide SNPs, most within odds ratio (OR)=1.03), whereas rheumatoid arthritis was less polygenic (∼ 4 to 8% risk variants, significant portion reaching OR=1.05 to 1.1). For rheumatoid arthritis, stratified estimations revealed that expression quantitative loci in blood explained large genetic variance, and low- and high-frequency derived alleles were prone to be risk and protective, respectively, suggesting a predominance of deleterious-risk and advantageous-protective mutation. Despite genetic correlation, effect-size distributions for schizophrenia and bipolar disorder differed across allele frequency. These analyses distinguished disease polygenic architectures and provided clues for etiological differences in complex diseases.