GENOME-WIDE ANALYSIS OF 102,084 MIGRAINE CASES IDENTIFIES 123 RISK LOCI AND SUBTYPE-SPECIFIC RISK ALLELES 167 8 Stratified LD Score regression We used stratified LD Score regression (S-LDSC) to partition the SNP heritability by functional genomic annotations.54 We used the baseline-LD model55 that contains 75 annotations, including conserved, coding and regulatory regions of the genome and different histone modifications. Baseline-LD model adjusts for MAF- and LD-related annotations, such as recombination rate and predicted allele age, which decreases the risk of model misspecification.54-56 We used the same QC as with the univariate LDSC, and the baseline LDv1.1 European LD scores estimated from the 1000 Genomes Project Phase 3, downloaded from https://data.broadinstitute.org/alkesgroup/ LDSCORE/. We set the significance threshold for enrichment of individual binary functional annotations to α = 0.05/24, as we considered only 24 unique functional annotations without the flanking regions. Results are listed in Supplementary Table 8. Subtype analyses of migraine with and without aura First, we combined new MA and MO data (Table 2) with the previously used migraine subtypespecific meta-analysis data,13 and estimated migraine subtype-specific effect sizes for the 123 lead variants from the migraine meta-analysis. We tested how often the direction of allelic effects was similar between the IHGC MA/MO and the new cohorts using a binomial test (Supplementary Table 12B). Next, we stratified the lead variants by using the information from the migraine subtype-specific analyses. For each of the variants, we estimated probabilities between four possible explanations of the observed data that we call ‘NULL’, ‘MO’, ‘MA’ and ‘BOTH’. Under model NULL, the effect is not present in either of the migraine subtypes (i.e., the effect is zero); under model MO or MA, the effect is present only in MO or only in MA but not in both; and under model BOTH, a non-zero effect is shared by both MO and MA. We used a Bayesian approach for model comparison that combines a bivariate Gaussian prior distribution on the two effect sizes with a bivariate Gaussian approximation to the likelihood using GWAS summary statistics.57 Across all models, the prior standard deviation for the effect is 0.2 on the log-odds scale for non-zero effects and 0 for a zero effect. The bivariate priors for the four models are as follows: NULL assumes a zero effect in both migraine subtypes, MO and MA assume a non-zero effect for one subtype and a zero effect for the other subtype, and BOTH combines the fixed-effect model (exactly the same effect in both subtypes) with the independent-effects model (the two effect sizes are non-zero but uncorrelated with each other) with equal weights. Finally, we assumed that each of the four models (NULL, MO, MA, BOTH) is equally probable a priori, which we considered an appropriate assumption since all these variants show a convincing association to overall migraine (P < 5 × 10-8). Then we used the Bayes formula to work out the posterior probability on each model. The results are shown in Figure 3A, thresholded by a probability cutoff of 95% and in Supplementary Table 12A. The correlation parameter between MO and MA GWAS statistics needed in the bivariate likelihood approximation was estimated to be 0.148 using the empirical Pearson correlation of the effect size estimates of the common variants (MAF > 0.05) that did not show a strong association to either of the migraine subtypes (P > 1 × 10-4).58
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