Per-allele disease and complex trait effect sizes are predominantly African MAF-dependent in European populations

Understanding genetic architectures of disease is fundamental to partitioning heritability, polygenic risk prediction, and statistical fine-mapping. Genetic architectures of disease in European populations have been shown to depend on European minor allele frequency (MAF): SNPs with lower MAF have larger per-allele effects, due to the action of negative selection. However, we hypothesized that African MAF (defined using African-ancestry segments in African Americans), which is not distorted by the out-of-Africa bottleneck, might better predict per-allele effect sizes of common genetic variation in European populations; we note that common variants explaining most disease heritability are typically much older than the split between African and non-African populations. To demonstrate this, we first analyze the proportion of non-synonymous SNPs, which are strongly impacted by negative selection. The proportion of non-synonymous SNPs is much better predicted by African MAF than European MAF; a mixture of African MAF with weight <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>w</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.95</mml:mn></mml:math> (95% CI: (0.93, 0.96)) and European MAF with weight ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>w</mml:mi></mml:math> ) is a more powerful predictor than either European MAF (<i>P</i><10^-15, 3.65x greater increase in log-likelihood relative to a null model without MAF dependence) or African MAF (<i>P</i><10^-15). Next, we consider the widely used <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> model, in which per-allele GWAS effect size variance is proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>E</mml:mi></mml:mrow> </mml:msub> <mml:mfenced><mml:mrow><mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>E</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow><mml:mi>α</mml:mi></mml:mrow> </mml:msup> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>E</mml:mi></mml:mrow> </mml:msub> </mml:math> is the European MAF. We propose a different model in which per-allele effect size variance is proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> <mml:mfenced><mml:mrow><mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:msup> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>w</mml:mi> <mml:mi>*</mml:mi> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>A</mml:mi></mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:mrow><mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>w</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:mi>*</mml:mi> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>E</mml:mi></mml:mrow> </mml:msub> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>A</mml:mi></mml:mrow> </mml:msub> </mml:math> is the African MAF. We fit the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> </mml:math> model by extending the baseline-LD model used in S-LDSC to include a grid of bivariate African and European MAF bins and identifying values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>w</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> </mml:math> that best fit mean effect size variance estimates from S-LDSC across bivariate MAF bins. We demonstrate that our approach provides conservative estimates of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>w</mml:mi></mml:math> in simulations. We applied this approach to summary statistics for 50 diseases/complex traits in European populations (average <i>N</i>=483K) and estimated best-fit parameters of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>w</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.96</mml:mn></mml:math> (95% CI: (0.76, 1.16)) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:mrow><mml:mi>mix</mml:mi></mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>0.34</mml:mn></mml:math> (95% CI: (-0.67, -0.02)), attaining a far better fit than the standard <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> model using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow> <mml:mrow><mml:mi>E</mml:mi></mml:mrow> </mml:msub> </mml:math> only (<i>P<</i>10^-15, 4.53x greater decrease in mean-squared error relative to a null model without MAF dependence). We conclude that per-allele disease and complex trait effect sizes are predominantly African MAF-dependent in European populations.