BRAIN IMAGING GENOMICS (IEEE, 2020)

2020.09.23

TIMESTAMP
@200923
@201005

KEYWORD

• brain imaging genomics: multimodal and longitudinal neuroimaging data and high-throughput genomic data with clinical information and patient history

1. Introduction
2. Heritability estimation
   • Twin and pedigree methods
   • GWAS methods for SNP Heritability
3. Imaging genomics associations
   1. fundamentals
      • Single-SNP-Single-QT Methods
      • Polygenic risk scores
      • Multi-SNP methods
      • Multitrait methods
      • Pathway and network enrichment methods
      • Interaction methods
   2. meta-analysis
   3. multivariate regression
      • Sparse multiple regression
      • Sparse multivariate multiple regression
      • Sparse reduced-rank regression
      • Bayesian regression and neural network models
      • Summary
   4. bimultivariate correlation
      • Fundamental SCCA models
      • Enhanced SCCA models
      • Multimodal and longitudinal SCCA models
      • Other bimultivariate correlation models
      • Summary
4. Integrating imaging and genomics for outcome prediction
   • Outcome prediction
   • Joint association learning and outcome prediction
5. Conclusion and discussion
   • Summary of learning problems and reviewed methods
   • Biomedical application considerations
   • Statistical and machine learning considerations
   • Scientific and clinical impact
   • Related work and future directions

Introduction

ADNI, ENIGMA, UKB

• [4] L. Shen et al., “Genetic analysis of quantitative phenotypes in AD and MCI: Imaging, cognition and biomarkers,” Brain Imag. Behav., vol. 8, no. 2, pp. 183–207, 2014. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/24092460
• [5] A. J. Saykin et al., “Genetic studies of quantitative MCI and AD phenotypes in ADNI: Progress, opportunities, and plans,” Alzheimer’s Dement, vol. 11, no. 7, pp. 792–814, 2015. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/26194313
• [2] P. Thompson et al., “ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries,” PsyArXiv, pp. 1–41, Jul. 2019. [Online]. Available: https://psyarxiv.com/qnsh7/ doi: 10.31234/osf.io/qnsh7.
• [12] L. T. Elliott et al., “Genome-wide association studies of brain imaging phenotypes in UK Biobank,” Nature, vol. 562, no. 7726, pp. 210–216, 2018. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/30305740

Multivariate methods

• [13] J. Liu and V. D. Calhoun, “A review of multivariate analyses in imaging genetics,” Frontiers Neuroinform., vol. 8, p. 29, Mar. 2014. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/24723883
  Regression and Correlation methods
  [14] J. Yan, L. Du, X. Yao, and L. Shen, “Machine learning in brain imaging genomics,” in Machine Learning and Medical Imaging. New York, NY, USA: Academic, 2016, ch. 14, pp. 411–434. [Online]. Available: http://www.sciencedirect.com/science/article/pii/B9780128040768000141

1. Heritability estimation of brain imaging phenotypes to determine how much phenotypic variation is determined by genetics.
2. Imaging genomics associations to identify complex multi-SNP-multitrait associations.
   • fundamental strategies (SNP-based methods, polygenic risk scores (PRSs), multi-SNP methods, multitrait methods, pathway and network enrichment methods, and interaction methods)
   • meta-analysis strategies
   • multivariate regression models
   • bimultivariate correlation models
3. Integrating imaging and genomics
   to predict an outcome of interest.

• 1) a discussion of principles of method selection based on biomedical application considerations [see Fig. 1(b)] and statistical and machine learning considerations [see Fig. 1(c)]; 2) a discussion on scientific and clinical impact; and 3) a discussion on related work and future directions.

Heritability estimation

Twin and pedigree methods

• Around 2001, neuroimaging studies of twins began to report correlations in regional brain measures in identical and fraternal twins, whereby identical twins had more similar brain structure than randomly selected pairs of individuals of the same age and sex.
• Falconers heritability statistic, h2, is defined as twice the difference between the MZ and DZ intraclass correlations.
• Thompson et al. [19] reported the statistical maps of Falconers h2 statistics, for measures of gray matter density across the cortex, showing significant heritability, in a small MRI study of 80 young adult twins.
• Later studies built on this approach to fit structural equation models (SEMs) to quantify both genetic and environmental components of variance, for brain measures derived from MRI, diffusion tensor imaging (DTI), electroencephalogram (EEG), and functional MRI (fMRI), also using twin or family designs.
• A common model used for these studies was the ACE model, which estimates additive genetic (A), common (C), and unique (E) environmental contributions to trait variance (see [20] for a review of early neuroimaging studies using the ACE model).
• Brun et al. [21], for example, used a general MRI analysis method called tensor-based morphometry (TBM) to map the heritability of brain morphology in MRI scans from 23 monozygotic and 23 dizygotic twin pairs using the ACE genetic model. Significance was tested using voxelwise permutation methods.
• A similar work with other computational anatomy approaches extended the ACE model to scalar maps defined on the vertices of 3-D surface models of brain structures, such as the ventri-cles [22]. In that study, path coefficients for the ACE model that best fit the data indicated significant contributions from genetic factors (A = 7.3%), common environment (C = 38.9%), and unique environment (E = 53.8%) to lateral ventricular volume.
• Methods to estimate heritability were advanced as well. Open-source tools, such as OpenMx and SOLAR, were adapted to handle brain-derived phenotypes, including entire images. Kochunov et al. [26] examined the agreement in the heritability estimates, across a variety of data sets, for four different methods for heritability estimation which have been applied to neuroimaging data. SOLAR-Eclipse (www.solar-eclipsegenetics.org) and OpenMx (openmx.ssri.psu.edu) use iterative maximum-likelihood estimation (MLE) methods. Accelerated permutation inference for ACE (APACE) [27] and fast permutation heritability inference (FPHI) [28] use fast, noniterative approximation-based methods. Heritability estimates from the two MLE approaches closely agreed on both simulated and imaging data, but the two approximation approaches showed lower heritability estimates when running on data that deviated from normality. The authors advocated a data homogenization approach that improved agreement across packages using inverse Gaussian transformation to enforce normality on the input trait data.

• [20] P. M. Thompson, T. Ge, D. C. Glahn, N. Jahanshad, and T. E. Nichols, “Genetics of the connectome,” NeuroImage, vol. 80, pp. 475–488, Oct. 2013. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/23707675
• [26] P. Kochunov et al., “Homogenizing estimates of heritability among SOLAR-Eclipse, OpenMx, APACE, and FPHI software packages in neuroimaging data,” Frontiers Neuroinform., vol. 13, p. 16, Mar. 2019. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/30914942

GWAS methods for SNP Heritability

1. GCTA method (genome-wide complex trait analysis [29]; https://cnsgenomics.com/software/gcta/), for example, estimates heritability from general population data, and rather than requiring twins or pedigrees, it can be applied to data from individuals who are typically regarded as unrelated.
   • GCTA computes both genetic and phenotypic covariance matrices from trait data and high-density SNP data, after calculating a kinship matrix and a genotypic relatedness matrix (GRM).
   • Based on singular values of the GRM, GCTA estimates the percentage of phenotypic variance explained by all common SNPs (i.e., the SNP heritability of a trait), with a restricted maximum-likelihood linear mixed model (GREML).
   • GCTA has been used to estimate “missing” heritability—the genetic contribution from all SNPs in aggregate—without needing to know exactly which SNPs are contributing to the variance.
2. Direct application of GCTA to the heritability analysis of high-dimensional brain imaging QTs is computationally intractable. To overcome this limitation, Ge et al. [30] proposed a massively expedited genome-wide heritability analysis (MEGHA) method, which approximates GCTA and is suitable for analyzing a large number of phenotypes efficiently.
   • It was successfully used to create vertexwise heritability mapping of nearly 300000 cortical thickness QTs.
3. Ge et al. [31] proposed a moment matching method for SNP-based heritability estimation (MMHE) and further extended the GWAS-based heritabilty analysis to handle multidimensional traits (e.g., shape). It was successfully applied to the heritability estimation of the shape of a set of brain structures.
   • In a subsequent study [32], MMHE was used to complete a phenome-wide heritability analysis of the UK Biobank [3].

MEGHA & MMHE

• [30] T. Ge et al., “Massively expedited genome-wide heritability analysis (MEGHA),” Proc. Nat. Acad. Sci. USA, vol. 112, no. 8, pp. 2479–2484, 2015. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/25675487
• [31] T. Ge et al., “Multidimensional heritability analysis of neuroanatomical shape,” Nature Commun, vol. 7, Nov. 2016, Art. no. 13291. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/27845344
• [32] T. Ge, C.-Y. Chen, B. M. Neale, M. R. Sabuncu, and J. W. Smoller, “Phenome-wide heritability analysis of the UK Biobank,” PLoS Genet., vol. 13, no. 4, 2017, Art. no. e1006711. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/28388634

1. A related method—linkage disequilibrium score regression (LDSC) [33] — was also developed to estimate heritability due to all SNPs.
   • Remarkably, it does not require individual genotypes at all, but it only uses the summary statistics from a genome-wide association study. The approach exploits a feature of the genome called LD—the fact is that statistical correlations are found in a series of adjacent SNPs.
   • When applied to imaging GWAS (explained next), the LDSC method has revealed patterns of genetic correlations across brain regions, leading to the notion that the brain may be partitioned into genetic modules or sets of regions with overlapping genetic determinants.
   • Classical multivariate twin models had also reported evidence for such genetic clusters [34].
     • In [34], a multivariate model in 1038 twins identified a common genetic factor that accounted for almost all the heritability of intracranial volume (0.88) and a substantial proportion of the heritability of all subcortical structures, particularly those of the thalamus (0.71 out of 0.88), pallidum (0.52 out of 0.75), and putamen (0.43 out of 0.89).
   • LDSC has also been used to reveal an overlap between the genetic loci associated with brain structure and with schizophrenia based on the summary statistics from various published GWAS [35].
   • Similar multivariate genetic models show that genetic influences on longitudinal growth or loss rates over time significantly overlap with genetic loci associated with baseline volumes for many structures. This may be an important observation in the quest to identify loci that influence rates of brain development and degeneration [36].

LDSC in brain

• [34] M. E. Rentería et al., “Genetic architecture of subcortical brain regions: Common and region-specific genetic contributions,” Genes, Brain Behav., vol. 13, no. 8, pp. 821–830, 2014. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/25199620
• [35] P. H. Lee et al., “Partitioning heritability analysis reveals a shared genetic basis of brain anatomy and schizophrenia,” Mol. Psychiatry, vol. 21, no. 12, pp. 1680–1689, 2016. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/27725656
• [36] R. M. Brouwer et al., “Genetic influences on individual differences in longitudinal changes in global and subcortical brain volumes: Results of the ENIGMA plasticity working group,” Hum. Brain Mapping, vol. 38, no. 9, pp. 4444–4458, 2017. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/28580697

Imaging genomics associations

Fundamentals

• In some cases, heritability analysis can be used as a prescreening step to identify imaging QTs with moderate to high heritability, and subsequent genetic association studies can then be applied only to those heritable QTs (e.g., in [38]).

  [38] N. Jahanshad et al., “Genome-wide scan of healthy human connectome discovers SPON1 gene variant influencing dementia severity,” Proc.Nat. Acad. Sci. USA, vol. 110, no. 12, pp. 4768–4773, 2013. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/23471985

• A major challenge in brain imaging genomics is that both imaging and genomics data are high dimensional.

  • The ability to test over a million SNPs in the genome for associations with hundreds, thousands, or even more imaging traits in the brain induces a huge burden for multiple comparison correction.

  • While failure to properly correct for multiple comparisons leads to a high risk for false discoveries, excessive corrections greatly reduce the power to detect true signals.

  • Thus, multiple comparisons and detection power are two important topics relevant to most association studies reviewed in this article.

  • Lindquist and Mejia [39] provided an excellent review of a few major statistical approaches to address the problem of multiple comparisons using neuroimaging studies as an example.

    [39] M. A. Lindquist and A. Mejia, “Zen and the art of multiple comparisons,” Psychosomatic Med., vol. 77, no. 2, pp. 114–125, 2015. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/25647751

• The goal is to choose an appropriate threshold to balance between sensitivity (true positive rate) and specificity (true negative rate).

  • Two metrics to quantify the likelihood of obtaining false positives are often used: 1) the familywise error rate (FWER; the probability of obtaining at least one false positive in a family of tests) and 2) the false discovery rate (FDR; the proportion of false positives among all rejected tests).
    • Bonferroni correction [40], aiming to control the FWER at a user-specified level, is the most common approach for multiple comparison correction. Despite being simple to use, it is very conservative and often reduces detection power.
    • Random field theory (RFT) [41]—a popular approach for controlling the FWER in fMRI studies—considers the spatial correlation in the images and appears to be less conservative than the Bonferroni method.
    • Permutation methods are nonparametric methods that do not make assumptions on the data distribution for controlling the FWER. While they offer substantial improvements in detection power, especially in small sample sizes, they are very computationally expensive; some recent innovations have been used to accelerate permutation testing [42].
    • The FDR [43] is a newer approach that controls false positives. It is less stringent than FWER methods and thus has an increased detection power.

• While some imaging genomics studies reviewed here employ the above-mentioned methods for multiple comparison correction, others develop their own strategies for handling the issues of multiple comparisons and detection power.

  • For example, Hua et al. [44] proposed two strategies to handle multiple comparisons and increase the power of detecting imaging genomics associations.

    • On one hand, they treated the imaging QTs of the entire brain as a single multivariate response and used distance covariance to capture the association between all the QTs and each SNP, which greatly reduced the number of statistical tests.

    • On the other hand, they proposed a new FDR-based algorithm that demonstrated an increased detection power compared with two existing FDR methods.

      [44] W.-Y. Hua, T. E. Nichols, D. Ghosh, and AlzheimerŠs Disease Neuroimaging Initiative, “Multiple comparison procedures for neuroimaging genomewide association studies,” Biostatistics, vol. 16, no. 1, pp. 17–30, 2015. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/24963012

• Another critical challenge in brain imaging genomics is the relatively small effect size of SNPs on the brain.

  • Most SNPs account for under 1% of the variance in a brain QT when considered individually. Thus, the studies reviewed here all need to address this challenge, and many of these studies have aimed to develop effective strategies with increased detection power to capture interesting imaging genomics associations.
    1. For example, one strategy is to reduce the effective number of tests to alleviate the burden of multiple comparison correction (see targeted SNP/QT studies discussed in Section III-A).
    2. The second strategy is to measure combined or collective effects of multiple markers together to increase the detection power (see studies discussed in Sections III-B–III-E).
    3. The third strategy is to increase the sample size to enable the discovery of individual SNPs with small effect sizes (see studies discussed in Section IV).
    4. The fourth strategy is to apply a single multivariate model involving all the studied SNPs and QTs without needing to adjust for multiple testing (see studies discussed in Sections V and VI).

• Before covering more advanced statistical and machine learning strategies for mining brain imaging genomic associations in Sections IV–VI, we first review a few fundamental methods in this section.

  1. We start from the simplest single-SNP–single-QT approaches that search for pairwise imaging genomics associations on an SNP-by-SNP and QT-by-QT basis.
  2. Next, we discuss strategies using PRSs, which examine the aggregated effect from a set of disease-related SNPs on an imaging QT.
  3. Then, we go over basic multi-SNP or multitrait methods, which aims to learn imaging genomics associations involving either multiple SNPs or multiple traits.
  4. After that, we review enrichment analysis methods that intend to discover high-level imaging genomics associations related to biological entities, such as biological pathways, functional interaction networks, and/or brain circuits (BCs).
  5. Finally, we briefly discuss interaction methods that focus on the exploration of epistatic effects instead of main effects.

Single-SNP-Single-QT Methods

• Given a set of genetic markers such as SNPs and a set of imaging QTs, the simplest and most commonly used analytical strategy is to perform a pairwise analysis between each SNP and each QT at the individual marker level.
  • An SNP takes a value of 0, 1, or 2 (i.e., the genotype value), indicating the number of minor alleles at the corresponding chromosome location. An imaging QT typically takes a continuous value.
  • A simple linear regression model can be used to examine the additive effect of the SNP on the imaging QT. An alternative strategy is to use analysis of variance (ANOVA), which is similar to linear regression but ignores the ordering of the genotype values. It examines the trait mean differences among three genotype groups.
  • Both the strategies can be used together with hypothesis testing to obtain a p-value.
  • If multiple pairwise SNP–QT associations are examined, multiple comparison correction needs to be performed to identify significant findings.

• Fig. 2 shows three major types of SNP–QT analyses.

  1. Targeted QT Analyses: The first type is to perform genetic analysis on one or more targeted imaging QTs. For example, in Fig. 2, the bottom left (i.e., blue box) shows the Manhattan plot for the GWAS results of gray matter density of the right hippocampus.
  2. Targeted SNP Analyses: The second type is to examine the genetic effects of one or more SNPs on all the imaging QTs across the brain. For example, in Fig. 2, the right (i.e., red box) shows the voxel-based morphometry (VBM) result of mapping the genetic effect of rs6463843 (in the flanking region of the NXPH1 gene) to the brain.
  3. Brain-Wide Genome-Wide (BWGW) Analyses: The third type is to perform massive univariate analyses for all the possible SNP–QT pairs across the entire brain and the entire genome. For example, in Fig. 2, the top left summarizes all the pairwise SNP–QT association findings (only top findings are shown), where blocks labeled with “x” reach the level of p < 10 −6 . Note that, in [37], p < 10 −6 was explored as a somewhat less stringent threshold to identify imaging genomics associations showing a trend toward significance as well as examine clustering patterns of the corresponding SNP and imaging QT findings.

• In the following, we discuss a few example studies in each of these three categories.

  1. In one targeted QT study, Stein et al. [45] performed a genome-wide association study of the bilateral temporal lobe volume (TLV) as the QT. A linear regression analysis was conducted at each SNP to examine its genetic effect on the QT and covaried for age and sex. In another targeted QT study, Scelsi et al. [46] computed a novel disease progression score (DPS) from multimodal neuroimaging data and performed GWAS on it. The DPS was generated by the GRACE algorithm [47] from the longitudinal cortical amyloid burden and bilateral hippocampal volume, providing an estimate of how advanced an individual’s disease progression is in comparison with the cohort average. A linear regression analysis was conducted at each SNP to examine its genetic effect on the DPS and covaried for sex, age at first amyloid scan, education, two principal components of population structure, and number of APOE e4 alleles.

     [46] M. A. Scelsi et al., “Genetic study of multimodal imaging Alzheimer’s disease progression score implicates novel loci,” Brain, vol. 141, no. 7, pp. 2167–2180, 2018. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/29860282
     [47] M. C. Donohue et al., “Estimating long-term multivariate progression from short-term data,” Alzheimer’s Dementia, vol. 10, no. 5, pp. S400–S410, 2014. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/24656849

  2. In one targeted SNP study, Risacher et al. [48] examined the effect of the APOE e4 SNP rs429358 on several MRI and PET imaging QTs. Specifically, the effects of diagnosis, APOE e4 carrier status, and their interaction on regional amyloid deposition, regional glucose metabolism, hippocampal volume, and entorhinal cortex thickness_were examined using a two-way analysis of covariance (ANCOVA) and covaried for age and gender. In another targeted SNP study, Ho et al. [49] examined the effect of a commonly carried allele of the obesity-related FTO gene on regional brain volume measures captured by MRI. Specifically, the general linear model was used to evaluate the relation of the imaging QT at each voxel to the SNP rs3751812 controlling for _age and sex.

     [48] S. L. Risacher et al., “APOE effect on Alzheimer’s disease biomarkers in older adults with significant memory concern,” Alzheimer’s Dementia, vol. 11, no. 12, pp. 1417–1429, 2015. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/25960448

  3. In one BWGW study, Shen et al. [37] used a BWGW approach to investigate genetic effects on imaging QTs. The studied QTs included 56 volumetric and cortical thickness measures and 86 local gray matter density values for regions of interests (ROIs) across the entire brain. These imaging QTs were preadjusted to remove the effects of age, gender, education, handedness, and incracranial volume (ICV). A linear regression analysis was conducted at each SNP to examine its genetic effect on each QT. In another BWGW study, Stein et al. [57] performed the first voxel-based GWAS analysis. Using TBM to define imaging QTs, they examined genome-wide association at each voxel. A linear regression analysis was conducted at each SNP-by-voxel pair to examine the SNP genetic effect on each voxelwise QT and covaried for age and sex.

     [57] J. L. Stein et al., “Voxelwise genome-wide association study (vGWAS),” NeuroImage, vol. 53, no. 3, pp. 1160–1174, 2010. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/20171287

• Although a voxelwise GWAS enables the examination of imaging genomics associations at the finest resolution, it is facing a major computational challenge, given the huge number of univariate SNP–QT associations to test.

  • To overcome this challenge, Huang et al. [50] proposed a fast voxelwise GWAS (FVGWAS) framework to facilitate efficient BWGW study at the voxel level.

  • FVGWAS employs three components to achieve this goal.

    1. The first component is a heteroscedastic linear model that allows a very flexible covariance structure suitable for voxelwise imaging QTs.
    2. The second component is a global sure independence screening (GSIS) procedure [51] that can greatly reduce the search space size from N s N v to ∼ N 0 N v for N 0  N s . Here, N s is the number of SNPs and N v is the number of voxels.
    3. The third component is a detection procedure based on wild bootstrap methods which is computationally cheap due to no involvement of repeated analyses of simulated data sets.

  • As a result, for standard linear association, the computational complexity of FVGWAS is O((N s + N v )n 2 ), outperforming O(nN v N s ) for standard voxelwise GWAS [45], where n is the number of subjects. FVGWAS is available at https://www.nitrc.org/projects/fvgwas/.

    [50] M. Huang et al., “FVGWAS: Fast voxelwise genome wide association analysis of large-scale imaging genetic data,” NeuroImage, vol. 118, pp. 613–627, Sep. 2015. [Online]. Available:
    http://www.ncbi.nlm.nih.gov/pubmed/26025292

• One issue related to imaging genomics is that most GWAS studies (e.g., ADNI) are based on a case-control design, and the data are typically a biased sample of the target population.

  • Directly correlating imaging QTs (as secondary traits) with genotype may lead to biased inference generating misleading results.
  • Kim et al. [52] compared the standard linear regression model and disease status adjusted linear model with two models adjusting for biased case-control sample (i.e., inverse probability weighted regression [53] and retrospective likelihood [54]) on the analysis of ADNI data.
  • Zhu et al. [55] completed a similar systematic evaluation of the biased sampling issue using both simulation and ADNI data. They compared the standard linear regression model and disease status adjusted linear model with two models adjusting for biased case-control sample (i.e., retrospective likelihood [54] and reparameterization of conditional model in [56]).
  • Although the standard linear analysis was found to be generally valid on the ADNI data in [52], simulation studies in [55] showed that linear regression models without adjusting for biased sampling demonstrated severely inflated Type I error rates in some cases. In general, caution should be taken while analyzing imaging QT data as secondary phenotypes in case-control studies.

Table 1 summarizes the studies discussed earlier, where pairwise SNP–QT associations are examined on an SNPby-SNP and QT-by-QT basis. These single-SNP–single-QT methods are simple and straightforward. The findings discovered by these methods are easy to interpret since each resulting association involves only one SNP and one QT. Given the high dimensionality of both imaging and genomic data, studies examining a massive number of SNP–QT associations may face major computational and statistical challenges. In addition, multivariate associations involving multiple SNPs or multiple QTs will not be able to be identified by these methods.

Polygenic risk scores

Multi-SNP methods

Multitrait methods

Pathway and network enrichment methods

Interaction methods

2. meta-analysis

3. multivariate regression

   • Sparse multiple regression
   • Sparse multivariate multiple regression
   • Sparse reduced-rank regression
   • Bayesian regression and neural network models
   • Summary

4. bimultivariate correlation

   • Fundamental SCCA models
   • Enhanced SCCA models
   • Multimodal and longitudinal SCCA models
   • Other bimultivariate correlation models
   • Summary

Integrating imaging and genomics for outcome prediction

• Outcome prediction
• Joint association learning and outcome prediction

Conclusion and discussion

• Summary of learning problems and reviewed methods
• Biomedical application considerations
• Statistical and machine learning considerations
• Scientific and clinical impact
• Related work and future directions