4.2 Assessment of the model
Our method selects the top gene at each voxel, to reduce the amount of data. Choosing only the top gene at each voxel, however, can hinder the extensibility of our results. This may miss many genes with distributed effects, if the main effect of the gene is never the largest at any voxel. Future implementations of vGeneWAS could consider the relationship among voxels when performing association tests. Liu et al. (2009)
used parallel ICA to relate brain network data from fMRI to SNP data. They selected only a small set of 367 predefined SNPs based on a set of candidate genes for schizophrenia; this does not leverage all of the available data in the genome. Similar approaches have been attempted on voxel-based morphometry (VBM) data from structural MRI (Jagannathan et al., 2010
). However, this approach used the same subset of SNPs used by Liu et al. (2009)
. Vounou et al. (2010)
proposed a method called sparse reduced-rank regression (sRRR) which uses the sparseness of signals to simultaneously select phenotypes and genotypes. Power estimates suggest that sRRR is more powerful than using individual tests at each voxel; this may prove to be very useful in the future.
Principal components regression (PCReg) is an efficient method to test the joint association of all SNPs within a gene simultaneously. PCReg detected associations with genes missed by SNP-based regression (). By leveraging the LD in a gene, PCReg encodes variance throughout a gene to test for associations. We identified situations where SNP-based regression models may have more power (). If a single SNP has a large main effect, then testing the joint effect of all SNPs within that gene may dilute the association; the cumulative P-value from gene-based tests may be lower. However, when one considers the drastic reduction in the number of independent tests when comparing SNP-based linear regression with PCReg, gene-based testing offers advantages.
Another concern with PCReg and related regression models is that each predictor added to the regression model consumes a degree of freedom. There may then be some detection bias in the regression model, where smaller genes are found to be more significantly associated with the phenotype than larger genes, because the regression models of small genes have more degrees of freedom (Chapman and Whittaker, 2009). While we did not observe this effect, it is an important factor to consider when interpreting results. Additionally, SNPs combined into a single test statistic in PCReg could have different directions of effects, disrupting the power to detect an association. However, the situation where a gene contains SNPs with negative correlations with respect to the phenotype may be relatively rare as it requires two nearby loci to be in LD with different causal variants (Chapman and Whittaker, 2009).
Other multivariate regression methods may offer greater power to detect genetic associations than PCReg, which is used here as an example. Wang and Elston (2007)
compress genome-wide genotyping data across subjects using a Fourier transform, and assign weights to the low-frequency components in a regression model. This method is similar to PCReg, as it collapses the number of genetic tests performed while capturing much of the variance across markers. Kernel-based methods have been implemented as non-parametric gene-based tests to increase power over SNP-based methods; however, these methods have only been implemented in case-control studies (Mukhopadhyay et al., 2010
). Ridge regression (Malo et al., 2008
; Sun et al., 2009
) and lasso-based penalized regression (Zou et al., 2006
; Wu et al., 2009
) can both powerfully detect associations in genetic data. In fact, direct comparisons between ridge regression, lasso-based penalized regression, and PCReg show that the first two methods may be more powerful than PCReg depending on the underlying genetic architecture (Bovelstad et al., 2007
; Benner et al., 2010
). However, ridge regression and especially lasso-based penalized regression are extremely computationally intensive compared to PCReg. There is a huge computational requirement to complete a vGeneWAS analysis, which searches the whole image in addition to the whole genome. Due to this, we decided to strike a balance between power and computational complexity to complete the analysis in a feasible time frame. Future implementations of vGeneWAS could be improved by using additional multivariate regression methods, although they may need to be modified for speed.
A current limitation of our method, as described here, is that in its current form family-based designs (such as pedigree structures) cannot be used. The patterns in allele frequencies in a family cohort depend on kinship, and mixed-effects models would be required to control for kinship structure. Several such methods exist for SNP-based linear regression, such as Efficient Mixed-Model Association (EMMA; Kang et al., 2008
). However, to the best of our knowledge, multivariate mixed-model regression has not been attempted in a genetic context. One multivariate gene-based method called versatile gene-based association (VEGAS) avoids multivariate mixed-model regression by converting SNP-based P
-values into a multivariate gene-based test statistic (Liu et al., 2010
). As there are already many methods for SNP-based mixed-model regression, VEGAS is aptly suited to perform gene-based association tests in family-based populations. As the VEGAS test statistic is determined by SNP-based P
-values, it will not be able to detect associations where the cumulative P
-values are not significant. In this way, if a series of SNPs contribute a small amount of variance in a gene, VEGAS will miss them, because the SNP-based method will as well.
While this is one of the largest imaging genetics studies to date, our sample size still may be underpowered to detect moderate effects of genetic variants on the brain. Future studies in imaging genetics are likely to benefit from meta-analysis, which aggregates GWAS results from multiple cohorts to determine reproducible genetic associations. This aggregation of large datasets can be used to boost power to detect SNPs with smaller effects. One such effort now underway is the ENIGMA project (ENIGMA Consortium, 2011
). In cases where there is not enough data available to perform a true meta-analysis, discovery and replication datasets may be useful. In early tests using brain images, some genetic associations seen in a discovery cohort have been replicated in independent samples (e.g., Rajagopalan et al., 2011
). However, our main purpose in this study is to demonstrate a method to conduct voxelwise, gene-based analyses, which will become more powerful as imaging databases continue to grow rapidly worldwide in size and content. In assessing whether our results may generalize to new datasets, we note that we examined only a tight age range in our study (elderly subjects), and this may affect the genes found to have morphometric effects on the brain. If the genes have a varying expression pattern over time some of the top genes detected in our analysis may not be dominant during other parts of the lifespan. Although we controlled for age effects on brain structure in our analysis, it is still unknown whether the identified genetic associations with brain morphology are under some age-related influence; it is also not known if these genes are expressed in a typical/atypical age-related fashion. Datasets drawn from different parts of the lifespan would offer maximal power to detect genetic variants relevant for brain structure (as discussed in Braskie et al., 2011
; see Rajagopalan et al., 2011
, for an example).
One limitation of GWAS analyses is that they overlook rare variants, which are also emerging as key players in the genetic underpinnings of mental disorders (Bansal et al., 2010
). Our method does not consider these rare variants, but may play an important role in explaining variance in complex traits that is not accounted for by common variants. Examination of rare variants is still relatively costly (as it requires deep sequencing of large numbers of subjects). Some types of rare variant can be genotyped on SNP-chip platforms (such as copy number variants) they require separate analytical techniques from those considered in this paper (Bansal et al., 2010
). Each of these limitations will be more feasible to address when the cost of deep sequencing drops and sample sizes are large enough to reliably implicate many genes simultaneously.
Our gene-based test may be more powerful than univariate methods in certain cases, but not always. The five top genes identified in the present study do have some biological plausibility; some are known to be expressed in the brain and implicated in brain disorders. However, there are other genes missing in the short list of genes in the present findings that are frequently found using univariate approaches and strongly implicated in complex behavioral pathologies across mammalian species, such as the BDNF val66met substitution.
To explain this, we note that the analysis of currently available imaging genetics data is very underpowered. In addition, sample sizes needed to reliably detect a genetic association are even greater when multiple genes are assessed or when genome-wide search is conducted. By contrast, the BDNF
val66met substitution is often treated as a candidate gene, and if that is done, it is conventionally agreed that its effects must only satisfy a nominal significance level of P
< 0.05, if no other genes or SNPs within it are tested. In our own work on a different cohort scanned with DTI (Chiang et al., 2010a
), we were able to detect robust associations between the BDNF
val66met polymorphism and fiber integrity (fractional anisotropy) assessed with DTI. We were also able to replicate these associations in two non-overlapping (independent) samples of subjects. Even so, the significance level used (P
< 0.05) was far more lenient than the very strict thresholds required to control for false positives when the whole genome is searched. As such, false negative results in a GWAS study (e.g., not finding a significant association of the BDNF
val66met substitution when it is in fact a true association) does not mean that a gene does not affect a phenotype, just that an association was not detected at the very stringent statistical cutoff applied to account for multiple comparisons across the genome.
A review of the literature also suggests that BDNF
val66met, while a popular target of study, has a mixed history. The BDNFval66met substitution has been inconsistently implicated in mood disorders, Alzheimer’s disease, and quantitative measures of memory (Bagnoli et al., 2004
; Combarros et al., 2004
; Nacmias et al., 2004
; Nishimura et al., 2004
; Tsai et al., 2004
; Desai et al., 2005
; Matsushita et al., 2005
; Vepsalainen et al., 2005
). In a secondary, post hoc
, analysis, we tested the effect of the BDNFval66met allele in this current sample using standard univariate regression (with a dominant model, controlling for age and sex) and it did not survive correction for multiple spatial comparisons. An association test of the BDNF
val66met allele with the hippocampal volume of the 731 subjects in this dataset did not survive the nominal significance level of P
= 0.05. As such, we were not able to use BDNF
as a “gold standard” gene; arguably, there are not yet any such genes with universally replicable associations on brain structure that can be used to gauge the face validity of novel methods.
Another limitation is that any approach that stops after selecting only one gene per voxel is not biologically plausible as a model of phenotypes with complex genetic determination. As such, the development of gene-based tests should be considered as a way station towards a more sophisticated treatment of complex genetic effects, in pathway or gene-gene interaction models (Inkster et al., 2010
). However, testing gene-gene interactions in the vGeneWAS framework is computationally intractable as the number of tests quickly approaches nCk
=n!/((n−k)!k!) at each voxel in the whole brain to test for interactions among all sets of k
different genes drawn from an overall pool of N
genes. Additionally, interaction effect sizes are generally much smaller than the main effects we are searching for in this paper, so our sample size would need to be much larger to accommodate the necessary correction for multiple comparisons and smaller effect sizes (Cordell, 2009
). As genome-wide interaction analysis (GWIA; Marchini et al., 2005
) is computationally intensive and underpowered with current imaging datasets, we recently developed an alternative method (Chiang et al., 2011b,c
) to detect likely gene-gene interactions among SNPs, without having to compute all N
-1)/2 pairwise or all n!/((n-k)!k!) k
th-order interactions on the genome. Two advantages of this genetic network analysis, relative to genome-wide interaction analysis (GWIA) are apparent: (1) genetic correlation can tap into the natural latent structure of gene action in a brain image; (2) voxel clustering by genetic affinity leads to high power to find SNPs with correlated effects in genome-wide scans.
4.3 Biological significance of the findings
Gene-based tests of association across the genome and brain have not been attempted before, to our knowledge. Recently, imaging genetics studies have focused on single-locus associations with summary brain volume measures or 3D statistical parametric maps. vGeneWAS advances the burgeoning field of imaging genetics by providing the framework to perform multivariate, gene-based association tests. It does not restrict analyses by requiring prior hypotheses about a specific causal variant or ad hoc region of interest. vGeneWAS is the first attempt to apply gene-based tests to morphometric imaging data and opens up more possibilities to discover putative genetic variants that contribute to differences in brain structure. This may help when the main effect of each variant in a gene is too small to detect with traditional SNP-based methods.
Although vGeneWAS is a multivariate, gene-based method, we identified genes previously associated with brain disease using SNP-based tests. Many variants in the GAB2
gene are implicated in the development of late-onset Alzheimer’s disease (LOAD) and are thought to interact with the APOE
epsilon 4 allele. In the pattern of effects for GAB2
on the brain (), the highlighted areas are generally periventricular, and ventricular enlargement is a prominent characteristic of AD (de Leon et al., 1989
; Chou et al., 2010). As we noted in our prior papers on TBM in Alzheimer’s disease (Hua et al., 2008
), there is occasionally a ring of voxels around the lateral ventricles that show partial volume effects that mostly like reflect ventricular expansion. Clearly, the ventricular expansion itself indirectly results from the diffuse loss of brain parenchyma, so the changes detected there may also reflect, to some extent, atrophic processes more remote than the voxels singled out in the voxel-based maps. LRDD
is highly expressed in the brain and is involved with DNA repair including signaling apoptosis in tumor cells. PTPRB
is associated with addiction to drugs and alcohol and may be involved with tumor regulation (Telliez et al., 2000
; Wu et al., 2006
; Ishiguro et al., 2008
; Brown et al., 2009
). Based on gene expression and links to brain diseases, many of the genes identified in our analysis may have differential morphometric effects across the brain. In addition to some of the more well-studied genes, we identified many genes such as IGSF5
that have little research available to infer their plausibility. However, almost all of the genes identified in our analysis are highly expressed in the brain, which at least suggests that the genes may have a role in brain function. Further analysis is required to examine to what extent each gene variant identified in our analysis mediates brain differences.
Many of the associations identified here seem to have a plausible story, but we need to consider that some of the patterns of association, especially clusters of association, may be due to short-range spatial correlations in the images. Adjacent voxels in brain scans tend to covary, as do Jacobian maps used to represent a localized measure of volume difference. These methods rely on non-linear algorithms that generate spatially smooth deformations. In addition to the simulated (null) cluster size maps in this study, Stein et al. (2010a)
found that a small amount of spatial clustering is seen even if the genetic data is null. Also, voxels were down-sampled which may introduce partial volume effects. However, performing a vGeneWAS scan on non-down-sampled, original sized images is estimated to take 4,372 days (or approximately 12 years) to complete. To this end, the extent to which a gene affects regions of the brain should be interpreted cautiously; however, certain patterns of gene effects that appear in non-adjacent structures or in large clusters may signal gene effects not attributable purely to spatial smoothing or partial volume effects.
To better understand the contribution of genes to global versus local brain structure differences, we conducted association analysis on both (1) the globally normalized brain images and (2) estimates of total intracranial volume (eTIV) that contain information on overall differences in brain scale. We searched for specific gene effects on global brain volume differences using our gene-based method. We computed brain volume measures (eTIV) from our dataset using the automated FreeSurfer package (Fischl et al., 2002
). Using the eTIV measure as the phenotype we tested each of the 18,044 genes for association. Looking at the top genes that we found in our analysis of the normalized images, none of the top 20 most highly associated genes was associated with eTIV phenotype. This provides further evidence that the genetic effects we are detecting exert influences on regional brain volumes rather than simply reflecting non-specific effects on the overall volume of the brain.
Additionally, results should be interpreted cautiously when global anatomical normalization is used. By removing, as far as possible, the effects of individual brain size variation from the data, it is possible to discover genes that may have a specific effect on a particular structure, above and beyond any overall genetic effects on brain size (as brain size itself is heritable). Global normalization is commonly performed in all brain mapping studies, as many extraneous factors affect an individual’s head size, body size or height that may not be relevant for cognition or for understanding brain function. Global anatomical normalization adjusts for this source of variance in the data, to a large extent, making more localized effects easier to identify. Even so, by applying global anatomical normalization, some genes may be missed that influence the total size of the brain. In fact, if a gene were responsible for influencing brain size, but had a uniform effect on all brain regions, it would be missed in the current analysis, as global effects are discounted. As such, in addition to mapping gene effects, it makes sense to also perform genetic analyses of whole brain size, as has been performed in two recent studies (Paus et al., 2011
; ENIGMA Consortium, 2011
In conclusion, our method may be used to perform gene-based tests on any 3D brain maps, such as data from voxel-based morphometry, diffusion tensor imaging, and cortical surface data. In addition, we found a set of candidate genes that may substantially affect brain morphometry and warrant further study.