Mejora del factor de potencia en circuitos trifásicos equilibrados

We used the software program METAL (Willer et al., 2010) to conduct sample-size-weighted meta-analysis of all SNPs that passed the quality-control thresholds. Prior to running the

meta-analyses, we applied a single correction for genomic control to the cohort-level sum- mary statistics. A total of 9,256,490 autosomal SNPs were meta-analyzed using data in the 64 filtered EduYears files, and 9,280,749 autosomal SNPs were meta-analyzed using data in the 52 filtered College files.14

A. EDUYEARS (N = 293,723)

We used sample-size-weighted meta-analysis in our primary analyses because the method is more robust to errors in variable scaling at the cohort level. As a robustness check, we also conducted a secondary meta-analysis of EduYears with inverse-variance weighting. Con- sistent with the results from our many diagnostic tests, the results were highly similar, sug- gesting that the scale of measurement was successfully harmonized across cohorts. The cor- relation between the two sets of P-values obtained using the two methods was 0.91. We conducted sample-size-weighted sex-stratified meta-analyses of EduYears as another robust- ness check to see whether the results differ for men and women. Figure 4.1 and Figure 4.14a- b provide Manhattan plots for the pooled-sex, women-only, and men-only analyses of

EduYears.

To select independent genome-wide significant SNPs from our primary EduYears results, we first grouped the GWAS results into “clumps” as follows. The SNP with the smallest P- value was chosen as the lead SNP in its clump. All SNPs less than 500 kb away from this lead SNP, in LD with it to the extent r2 _{> 0.1, and with an association P-value smaller than}

10-6 _{were assigned to this clump. The next clump was greedily formed around the SNP with}

the next smallest P-value not already assigned to the first clump. This process was iterated until no SNPs remained with P-value < 5×10-8_{. The end result was 77 approximately inde-}

pendent clumps, each centered around, and represented by, a genome-wide significant SNP. Next, we checked the long-range LD between these 77 approximately independent SNPs without imposing any restriction on distance (except for residing on the same chromosome). If the r2 _{between two SNPs is greater than 0.5, we merged the corresponding clumps and}

assigned the SNP with smaller P-value to represent that locus. This step resulted in 74 ap- proximately independent loci, each represented by a genome-wide significant SNP. The PLINK tool version 1.9 (Chang et al., 2015) and 1000 Genomes Project phase 1 genotyping data (Abecasis et al., 2012) (from 268 individuals with European ancestry) was used to per- form clumping and calculating r2 _{between a pair of SNPs. Table B5 shows the EduYears}

14 _{SNPs with a sample size less than 100,000 (3,074,494 SNPs in EduYears, and 3,161,722 SNPs in College) were} excluded from the meta-analyses.

124 GWASIDENTIFIES 74LOCI ASSOCIATED WITH EDUCATIONAL ATTAINMENT

pooled-sex and sex-stratified association results for these 74 approximately-independent ge- nome-wide significant SNPs.

As in the earlier GWAS of EA (Rietveld, Medland, et al., 2013) and other large GWAS of polygenic traits (Locke et al., 2015; Ripke et al., 2014; Wood et al., 2014), the Q-Q plot of the meta-analysis (Figure 4.2) exhibits inflation (λGC = 1.28), consistent with a polygenic

architecture. Forest plots of the EduYears-associated SNPs (not shown) provide little evi- dence that the estimated effects are driven by a small number of outlier cohorts, cohorts from a given region, or by one of the sexes (see Table B5 for the heterogeneity P-values for the lead SNPs).

Figure 4.14. Manhattan plots from the sex-stratified analyses of EduYears.

a.

b.

Note: In each plot, the x-axis is chromosomal position, and the y-axis is the P-value on a –log10 scale. The black line shows the genome-wide significance level (5×10-8_{). The red x’s are the approximately 74 independent ge-} nome-wide significant associations (“lead SNPs”) from the EduYears pooled results. The black dots labeled with rs numbers are the 3 Rietveld, Medland, et al. (2013) SNPs.

To help gauge the magnitude of the estimated effects, we used a well-known approximation to compute unstandardized regression coefficients from the METAL output obtained from the sample-size-weighted meta-analysis:

(4.10) 𝛽̂𝑗≈ 𝑧𝑗

𝜎̂𝑌

√2𝑁𝑗 𝑀𝐴𝐹𝑗 (1 − 𝑀𝐴𝐹𝑗)

for SNP j with minor allele frequency MAFj, sample size Nj, METAL z-statistic zj, and stand-

ard deviation of the phenotype 𝜎̂𝑌. For a derivation, see the SOM in Rietveld, Medland, et

al. (2013). Figure 4.3a shows effects in standard-deviation units of the SNP with lowest P- value in each of the 74 loci, ordered from largest to smallest. As a benchmark for the mag- nitudes, the figure also shows corresponding estimates for the three phenotypes studied by the GIANT consortium in similarly large samples to ours (hereafter, the “GIANT pheno- types”): height (Wood et al., 2014), body mass index (Locke et al., 2015) (BMI), and waist- to-hip ratio adjusted for BMI (Shungin et al., 2015) (WHR). Consistent with the findings in Rietveld, Medland, et al. (2013), the EduYears estimates are in the range 0.014 to 0.048 standard deviations per allele (2.7 to 9.0 weeks of schooling), with incremental R2 _{in the}

range 0.01% to 0.035%. The EduYears effects are smaller than those for height and BMI and more similar to those for WHR. The minor allele frequency of the SNP with the largest effect size in SD-units is 0.04.

B. COLLEGE (N = 280,007)

The Manhattan plot for the College analysis is shown in Figure 4.15. Overall, the results are similar to those from the EduYears analyses, but with higher P-values (consistent with the hypothesis that the College variable is a noisier measure of educational attainment than the

EduYears variable). If we apply the procedure described previously to determine the number

of approximately independent SNPs reaching genome-wide significance, we find 34 such SNPs (compared to 74 in the EduYears meta-analysis). Of these, 24 reach genome-wide significance in the EduYears analyses, and 27 are within 500kb distance and in LD with an

EduYears lead SNP to the extent r2 _{> 0.1. Supplementary Table 1.12 in Okbay, Beauchamp,}

et al. (2016) shows the association results for these 34 approximately independent genome- wide significant SNPs from the College meta-analysis and the EduYears lead SNPs in the same locus, if any.

126 GWASIDENTIFIES 74LOCI ASSOCIATED WITH EDUCATIONAL ATTAINMENT