Despite advances in the genomics of complex traits, only a portion of heritability for common human diseases has been elucidated. To date, most common variant discovery approaches have relied on tests of disease association using one SNP at a time. Methods that leverage existing datasets and exploit information across multiple SNPs within a gene region are likely to yield additional information regarding the locus association with traits. We developed a novel strategy, MixMAP, that relies on well-vetted statistical principles and draws from the vast array of summary data now available from genetic association studies, to test formally for locus-level association. The primary inputs required for this approach are single SNP level p-values for tests of trait association and mapping of SNPs to locus regions while the output is locus level estimates and tests of association. Application of MixMAP to SNP summary data for a pre-defined set of genes within the GLGC meta-analysis of association with LDL-C suggest that MixMAP can provide substantial value in discovery that is complementary to single SNP testing approaches in identifying novel loci for LDL-C. In addition, MixMAP analysis of PennCAC IBC array and LDL-C data support its application in combination with traditional SNP testing to enhance the power of discovery in small dataset settings. Thus, MixMAP provides a novel strategy, based on established statistical principles, for exploiting existing and emerging genomic data to provide advances in our understanding of complex human diseases.
Over the past decade sequencing of the human genome, definition of common SNP variation in human population and advances in genotyping technology have provided the possibility to discover common genetic contributions to complex traits in human. Indeed, very large scale applications of genome SNP scans in humans combined with rigorous statistical correction for multiple testing has led to an explosion of novel validated genomic discoveries for human diseases with exciting progress in functional genomics as well as promise for novel therapeutics and disease prediction. Despite this the majority of heritability for most complex traits remains to be discovered. Current statistical approaches for testing single SNP associations with disease are designed to protect against excess false positives but may be excessively conservative. Further, single SNP approaches to analysis do not draw strength from information gained by assessing simultaneously trends of association across a locus. These observations suggest that false negatives are a significant feature of existing association analysis and that additional genomic discovery should be possible in existing data if appropriate statistical methodologies are applied. Indeed, recent research suggests that common variants with individual level effects that are too small to be considered statistically significant using stringent significance thresholds account for a substantial proportion of this missing heritability for complex traits 
. However, differentiating the true signals within the vast amount of SNP data with moderate p-values remains an unsolved problem.
We chose to analyze genetic contributors to LDL-C for several reasons. First, LDL-C is an important complex trait that is causal for a substantial portion of CVD death and morbidity in our society. Second, LDL-C has a well described heritability and large rigorously performed meta-analyses have been performed and summary data are publicly available (GLGC). Third, although many loci for LDL-C have been identified through association studies at
, only a modest portion of its heritability (approximately
of genetic variability 
) has been defined. Fourth, the basic biology of plasma lipids and LDL-C has been extensively studied in animal models and cell systems providing some additional mechanistic reference for any novel discoveries we might make. We hypothesized that we would identify novel loci for LDL-C, beyond the existing single SNP-based discoveries, through application of MixMAP in the large GLGC meta-analysis summary data. As an informative example, we chose to focus on the set of SNPs for CVD candidate genes included on the ITMAT-Broad-CARe (IBC) SNP array which was designed to provide dense SNP coverage in putative candidate CVD genes as well as some coverage of emerging loci at the time of its design 
. This approach allowed us to focus on a defined set of SNPs within candidate loci and to perform direct comparison of findings for this subset of SNPs within the GLGC data-set to those in the smaller PennCAC sample application.
In GLGC data, MixMAP confirmed association for over
of the loci identified through single SNP testing of the 31827 SNPs in 2960 genes examined. Failure to detect more of the loci established by single SNP testing should not be surprising because MixMAP loses information for extremely low individual SNP p-values and is not designed for finding association when SNP coverage of a gene region is poor, as is the case for some loci that reached significance in the GLGC. Further, from a biological perspective, almost all clinically important LDL-C genes/loci were detected by MixMAP (e.g., LDLR, APOB, APOE, HMGCR, PCSK9, LPA, SORT1, ABCG5/8, TRIB1, ABCA1, APOA5-A4-C3-A1 and CETP). MixMAP, however, did provide evidence for
new loci (corresponding to
interrogated genes) for LDL-C in GLGC data that did not reach genome wide significance in single SNP testing. This may be an under estimate because we applied conservative criteria for our selection of novel loci (greater than 500kb from known GLGC locus, pairwise
with top SNP at GLGC established LDL-C locus, and outside of region with multiple candidate genes). For example, interrogated SNPs in C2, which MixMAP identifies as a gene associated with LDL-C, have
with the top GLGC SNP at the HLA locus in Teslovich et al. 
A more detailed description of the 12 genes/loci detected by MixMAP alone is provided in Supplementary Materials. For many of these 12 loci (FN1, UGT1A1, PPARG, GAB2 and APOH) the GLGC single SNP test p-value provided suggestive evidence of association (
) and published data in mice and human support specific biological processes and plausible mechanisms of association with LDL-C for some of the index genes (UGT1A1, PPARG and APOH) at these loci 
. Notably, a recent meta-analysis of IBC array data for plasma lipids across 66,240 individuals also supports an association of APOH with LDL-C and suggests that UGT1A1 is a locus for total cholesterol levels 
. For some MixMAP significant loci with suggestive GLGC single SNP tests, there is no or limited published biology or mechanism for association with LDL-C (e.g. FN1 and GAB2). On the other hand, some loci that are significant by MixMAP have quite modest statistical support in GLGC single SNP analysis, but have strong published data supporting mechanisms by which genes at the locus may modulate LDL-C (e.g NPC1 and PPARD) 
. Finally, a few MixMAP loci have neither suggestive single SNP support from GLGC nor reported biological plausibility for gene-lipid associations (e.g. PKN2 and CDK) and such loci require further focus and validation. Overall, these data support the utility of MixMAP, when used in combination with traditional single SNP testing, in discovery of true loci for LDL-C and other complex traits particularly.
A specific challenge in the genomics of complex traits is identifying loci for such a trait when power is low due to limited availability of human data. We chose to illustrate this issue in a small sample (PennCAC, n
2096) using LDL-C as an example in part because the large GLGC dataset for LDL-C provides an external reference for any MixMAP findings. In PennCAC, no individual SNPs meet criteria for association with LDL-C using the conservative genome-wide Bonferroni correction (
) or the less conservative IBC array-wide Bonferroni correction (
). At a less stringent, suggestive single SNP criteria (
loci (represented by
genes) are identified. At one of these loci,
interrogated genes (APOA5 and BUD13) contain SNPs with genome-wide significant signals in the independent GLGC dataset. As expected at this less conservative threshold, however, most SNPs lack supporting signals in GLGC data and lack supporting biology for genes at the locus () suggesting that several may be false positives. Using MixMAP
independent loci, were suggested for LDL-C. Of these,
(SORT1 and LPA) have genome-wide significant signals in the independent GLGC data and one (VPS13B) had a significant MixMAP signal in GLGC data. Furthermore,
loci (IL1R2 and VP13B) have some support for modulation of lipids in animal models 
. Overall, these PennCAC LDL-C analyses suggest that application of MixMAP in small sample settings may provide complementary value to single SNP tests and other strategies to maximize genetic inference in settings where sample size is limited. Although in these small sample settings false positives will remain a challenge, MixMAP should enhance findings for prioritization and further follow-up.
We recognize that independent replication of findings is essential for complete validation of novel findings in genetic studies. Because the GLGC data represent the largest published lipids GWAS meta-analysis to date, we believe a comprehensive replication for LDL-C beyond these GLGC data is not possible at the current time. However, we will pursue this for lipid genes/loci in additional GLGC data when these data become available (e.g., Metabochip project data expected 2013 
). We also acknowledge that for common SNP variation, a single gene often can not specifically be assigned to the disease-associated variant. Further, simple proximity to a variant and even incorporation of expression QTL knowledge are not always correct in selecting causal genes. This problem can lead to incorrect assumptions of causal genes and raise concerns for validity of gene-based inference. However, this limitation is not unique to our illustration of MixMAP and is common to current gene and pathway analyses leveraging common SNP datasets (e.g. 
). The challenge can be addressed in part by leveraging the maximum amount of linkage disequilibrium, eQTL, fine mapping and biological data when assigning genes to the associated SNPs. In the present investigation, we use gene as the cluster to which SNPs belong, though MixMAP is not limited by this specification. Importantly, the user can employ alternative and newly evolved classifications, as the primary input to the MixMAP algorithm.
The results of the simulation study further support the application of MixMAP as a complementary strategy to single-SNP based testing, particularly in the context of moderate gene level effects and adequate SNP coverage. Our on-going research is exploring calibrating the variance coefficient in the prediction interval, as an alternative to using
, to obtain desired control of the FDR in specific well-defined settings. Because a first stage ranking of
-values is applied prior to inverse normally transforming the data for model fitting, the implications of using p-values from a single cohort study (PennCAC) versus a meta-analysis (GLGC) are limited to the varying degrees of precision in each setting. That is, the full range of the quantitative data, and specifically the fact that p-values from a meta-analysis tend to be substantially smaller than those from a single cohort study, is not being incorporated into the analysis presented herein. We expect additional knowledge can be gained through a mixture modeling extension of MixMAP that can accommodate the quantitative nature of the summary data, and this is currently under investigation. The present investigation is based on common variants, and while incorporating the results of rare variant analysis poses an additional challenge as these variants tend to be grouped a priori
for analysis, such an extension would also likely be informative.
Further extensions of MixMAP would also allow application to gene set and/or pathway-based analysis of association data. Specifically, through inclusion of multiple nested random effects, the MixMAP framework could be applied using both locus level and pathway information simultaneously. Through fully parametric modeling, this may offer advantages over gene set enrichment analysis, which similarly involves a first stage rank ordering 
. This extension of MixMAP would be notably distinct from the hierarchical modeling approach of 
that similarly includes random gene specific effects, but separately models each gene set and focuses testing on fixed intercepts representing pathway effects rather than latent variables. Additional future work includes a specific evaluation of the influence of linkage disequilibrium, minor allele frequencies, gene size and numbers of recombinant hotspots as potential covariates in the models, as well as comprehensive evaluation of the complex statistical power considerations across a range of applications and conditions, including candidate gene studies, GWAS, pathway analysis and partial or whole-exome sequencing studies. Additional characterization of MixMAP may facilitate applications to summary findings from Metabochip and exome sequencing, as well in interrogation of gene sets and pathways utilizing such data. In conclusion, the approach we have described is intended to complement single SNP analysis and should provide a useful tool to potentiate existing summary data and reveal important novel loci, pathways and causal factors for complex diseases at little additional cost.