Existing methods for functional enrichment

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The methods discussed here are concerned with finding the enrichment of GWAS signals in specific functional annotations or cell types/ tissues, either as an intermediate step in solving a different biological question or as the ultimate goal of the method. For example, finding that Crohn’s disease associated variants are enriched in open chromatin regions in a specific blood cell type. This may help with finding disease relevant cell types/ tissues for the development of therapeutic targets or in fine-mapping whereby association statistics can be reweighted (e.g. using enrichment information to define prior probabilities of causality in Bayesian fine-mapping).

The most basic functional enrichment methods estimate enrichment of association P values on the basis of comparisons of the full set of GWA variants (or a subset of those reaching genome wide significance). This yields two sets of P values; those from variants overlapping the annotation and those from variants not overlapping the annotation. Standard statistical tests (e.g. Kolmogorov-Smirnov test) can then be used to infer the probability that the two sets of P values were drawn from the same distribution, and thus infer enrichment. This method highlights some valid findings, but statistical concerns (e.g. not controlling for confounders) make it hard to trust unexpected results.

Due to these confounding effects, the P values need to be adjusted using a well specified null distribution of the test statistic. For example, if the method does not take into account the non-random distribution of SNPs and annotations across the genome then this may lead to spurious results. The existing methods vary with how they define this null distribution and deal with potential confounding. For example, GoShifter uses random permutations to estimate the empirical enrichment under the null, GREGOR uses 500 matched SNPs (by (i) number of variants in LD, (ii) MAF and (iii) distance to nearest gene) to assess enrichment and GARFIELD uses feature matching (by (i) nearest TSS and (ii) LD proxies) in logistic regression to quantify enrichment.

The existing methods discussed can be broadly grouped into:

1. Matched SNP set methods (SNPs matched by confounding features and analysis repeated several times to compute matched null enrichment statistics which are then used to adjust observed P value for these confounders).

2. Circularised permutation methods (originally based on LD block subsampling methods, circularise SNPs and annotation overlap to generate a set of empirically derived null statistics, the empirical P value is computed as the proportion of null statistics exceeding the observed overlap proportion).

3. Statistical modelling methods

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The main existing methods that leverage GWAS findings with functional annotations are:

1. GPA (2014):

• Statistical modelling method
• Primarily used to prioritise GWAS variants using multiple GWAS data sets (pleiotropy - diseases are related and often share underlying genetic variants) and functional annotations, but an intermediate result is the enrichment of functional annotations.
• Does not account for LD between variants. I.e. assume independence between SNPs in the model.

2. fgwas (2014):

• Statistical modelling method
• Used to find enrichment of annotations in GWAS SNPs by fitting a model across the whole genome. But to do this, the genome is segmented and at most 1 CV is assumed in each segment.
• Defines a full hierarchical model and uses penalised regression to estimate the parameters. Uses cross validation, forward and backward selection and conditional analysis to find final model.
• Implies the resulting empirically estimated prior probabilities can be used in Maller et al.’s method to reweight GWAS statistics.
• See detailed review here: https://annahutch.github.io/PhD/fGWAS.html

3. (Stratified) LD score regression (2015):

• Statistical modelling method
• Regress LD scores (sum of r^2) against GWAS summary statistics. Expect positive correlation between LD and association statistics because the more things you tag the more likely you are to tag the CV. This means that CV effect sizes are inflated due to LD.
• Used to account for confounding (population stratification and cryptic relatedness) to ensure that the null SNPs P values follow the uniform distribution.
• Stratified LD score regression is used for identifying functional enrichment from GWAS summary statistics (using genome-wide info from all SNPs and explicitly modelling LD).
• In this paper they compare with GoShifter, fgwas, top SNPs and PICS.
• See detailed review here: https://annahutch.github.io/PhD/LD-score-regression.html

4. GoShifter (2015):

• Circularised permutation method
• Developed to see whether enriched annotations were able to prioritise causal variation.
  1. Find SNP set consisting of index SNPs and friends.
  2. Overlay the SNP set to annotation data.
  3. Circularise the SNP set and annotations and do random permutations to estimate the empirical enrichment under the null (this takes into account LD between SNPs and the non-random distribution of annotations relative to each other).
  4. Derive P values using this estimated empirical null distribution.
• USP: Can assess independent effects from colocalising annotations using the stratified enrichment method (i.e. identify important annotations from those that merely appear in similar regions to the important annotation possibly due to wet-lab experiments querying the same genomic functional process to find the annotations).

5. GREGOR (2015):

• Matched SNP set method
• “Genomic Regulatory Elements and Gwas Overlap algoRithm”.
• Used to evaluate enrichment of any set of genetic variants with any set of regulatory features. * 3 aims:
  1. Elucidate the important tissue/cell type in which genetic variation impacts transcription for a particular trait.
  2. NArrow focus of the regulatory features underlying transcription distributed by trait-associated variants.
  3. Use positional overlap with selected regulatory domains to identify potential functional candidates at trait-associated loci.
• See detailed review here: https://annahutch.github.io/PhD/GREGOR.html

6. GARFIELD (2019):

• Matched SNP set method
• Obtain OR of annotations for SNPs exceeding some P value threshold basically through:
  1. Finding a set of independent SNPs and overlaying these (and LD friends of these) to annotations to get a binary indicator of that SNP in that association.
  2. Put this in a logistic regression model, regressing a binary SNP P<T indicator against the binary annotation vector and categorical covariants on LD (quantile of how many “friends”) and TSS distance to account for confounding.
  3. Build up the model using simple forward selection.
• In the paper they compare their method to GPA, LDSC, fgwas, GREGOR and GoShifter.
• See detailed review here: https://annahutch.github.io/PhD/garfield.html

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Limitations

• GPA doesn’t account for LD.

• fgwas assumes a single CV per region.

• GoShifter paper finds that matched SNP methods do not control for type 1 errors well and that the choice of matching parameters affect results.

• GoShifter involves thresholding (choosing SNPs above some LD threshold with index SNP) and tends to favor high-resolution annotations (those with small average size). It was found to be the most conservative out of the 6 methods in the GARFIELD paper.

• Statistical modelling methods are more complex and computationally intensive.