Influence of filtering threshold on the power to detect GxS.

<p>Shown is the power to detect GxS for the same approaches as in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#pone.0181038.g002" target="_blank">Fig 2</a></b> (<i>n</i>_<i>1</i> = 100,000, <i>n</i>_<i>2</i> = 100,000), but here with varying filtering thresholds and fixed relative to for different types of GxS: A. qualitative GxS with small stratum-specific effects ( into opposite direction), B. pure GxS with medium sized stratum 1 effect (), and C. quantitative GxS with large stratum 1 and smaller stratum 2 effect ( into the same direction). The effect sizes for stratum 1 are chosen as those observed for the WHRadjBMI loci around <i>STAB1</i>, <i>PPARG</i>, <i>or LYPLAL1</i>. The power of [Diff_5e-8] is constant due to the lack of any filtering.</p

Recommended stratified GWAMA approaches to detect GxS.

<p>Shown are the recommended approaches to detect GxS when there is no prior hypothesis on the type of GxS (<i>H</i>_<i>0</i>: <i>No GxS</i>) and when there is a prior hypothesis on the type of GxS (<i>H</i>_<i>0</i>: <i>No qualitative GxS</i>; or <i>H</i>_<i>0</i>: <i>No pure GxS</i>; or <i>H</i>_<i>0</i>: <i>No quantitative GxS</i>). The recommendations vary on the degree to which the strata sample sizes differ (<i>f</i> being the proportion of stratum 2 sample size over stratum 1 sample size, <i>f</i> = <i>n</i>_<i>2</i><i>/n</i>_<i>1</i> with stratum 1 being the stratum with the larger absolute value of the genetic effect).</p

Simulation-based Type I error for the seven stratified GWAMA approaches to detect GxS.

<p>Shown is the type I error at a 5% significance level derived from simulated data as the proportion of variants with nominally significant difference test (<i>P</i>_<i>Diff</i><0.05) relative to the number of variants tested for difference (1,000,000 in the difference test without filtering, number of filtered variants in the approaches with filtering). The simulation results are based on a <u>balanced strata</u> design (<i>n</i>_<i>1</i> = 100,000, <i>n</i>_<i>2</i> = 100,000; split in half for two-stage approaches), variants with <i>MAF</i> = 0.05 or 0.30, and phenotypes simulated under the null hypothesis of no GxS, i.e. no difference between stratum-specific effects (<i>H</i>₀: <i>β</i>₁ = <i>β</i>₂ = <i>β</i>). We present the results for <i>β</i> = 0 and <i>β</i> ≠ 0. For the second setting, we set <i>β</i> as the minimum effect size detectable at 80% power for the given <i>MAF</i> and the given sample size for the difference test (<i>n</i> = 200 000 for one-stage approaches, β = 0.029, 0.014 for <i>MAF</i> = 0.05, <i>MAF</i> = 0.30, respectively; <i>n</i>_<i>Stage</i> = 100,000 for the two-stage approaches, β = 0.041, 0.019 for <i>MAF</i> = 0.05, <i>MAF</i> = 0.30, respectively). Marked in bold are violated type 1 error rates.</p

Power of stratified GWAMA approaches to identify GxS for balanced strata design.

<p>Shown is the power to detect GxS in equally sized strata (<i>n</i>_<i>1</i> = 100,000, <i>n</i>_<i>2</i> = 100,000) for each of the considered approaches, for varying effect sizes in stratum 2, , with a fixed genetic effect in stratum 1, , that is (A) small (), (B) medium (), or (C) large (). The effect sizes for are chosen as those observed for WHRadjBMI near <i>STAB1</i>, <i>PPARG</i> or <i>LYPLAL1</i>, respectively. The modeled GxS are visualized on the left side (red bar: , blue arrows: varying ). For the difference test without filtering, we assume a significance level at 5 x 10⁻⁸; for approaches with filtering, the filtering threshold is 1 x 10⁻⁵ and the significance level applied for the consecutive difference test is <i>α</i>_<i>Diff</i> = <i>M</i>/0.05, with M being the number of filtered lead variants (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#sec002" target="_blank">Methods</a>).</p

Application to real sex-stratified GWAMA data for WHRadjBMI from the GIANT GENDER project.

<p>Shown are the 10 identified loci with GxSex by each approach (‘x’ indicating that the locus was identified by the respective approach) at a Bonferroni-corrected significance level, based on the GIANT data for WHRadjBMI (up to 77,000 men and 98,000 women) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#pone.0181038.ref012" target="_blank">12</a>]. Detailed association results are provided in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#pone.0181038.s009" target="_blank">S2 Table</a></b> for the one-stage approaches and in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#pone.0181038.s010" target="_blank">S3 Table</a></b> for the two-stage approaches.</p

Power of stratified GWAMA approaches to identify GxS for unbalanced strata design.

<p>Shown is the power to detect GxS for the same approaches as in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#pone.0181038.g002" target="_blank">Fig 2</a></b>, but here for unbalanced strata designs with varying proportion of stratum sample sizes, <i>f = n</i>_<i>2</i><i>/n</i>_<i>1</i>, with stratum 1 being the one with the larger effect. Effect sizes are chosen as <b>in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181038#pone.0181038.g003" target="_blank">Fig 3</a></b> (fixed relative to as observed for WHRadjBMI loci around <i>STAB1</i>, <i>PPARG</i>, <i>or LYPLAL1</i>): A. qualitative GxS with small (, into opposite direction), B. pure GxS with medium (), and C. quantitative GxS with large ().</p

Data flow-chart.

<p>Three sources of genome-wide results were used: i) meta-analysis of Levene’s test results for between-genotype heterogeneity of phenotypic variances; ii) published results for marginal effects genome-wide association studies undertaken by the GIANT and GLGC consortia; iii) published results for SNP <b>×</b> physical activity and SNP <b>×</b> smoking in BMI (from the GIANT consortium).</p

Spearman correlations between <i>P</i>_<i>int</i> in <i>SNP × Physical Activity</i> and <i>SNP × Smoking</i> on BMI analyses and marginal effects <i>P</i>_m or heterogeneity of variance from Levene's test <i>P</i>_<i>v</i>.

<p>Spearman correlations between <i>P</i>_<i>int</i> in <i>SNP × Physical Activity</i> and <i>SNP × Smoking</i> on BMI analyses and marginal effects <i>P</i>_m or heterogeneity of variance from Levene's test <i>P</i>_<i>v</i>.</p

Enrichment of variance and gene <i>×</i> environment interaction nominally significant results with GWAS-derived loci.

<p>Enrichment of variance and gene <i>×</i> environment interaction nominally significant results with GWAS-derived loci.</p

Comparison of Levene's test <i>P</i>_v ranks from different centiles of the <i>P</i>_m rank-ordered distribution for the index traits.

<p>Comparison of Levene's test <i>P</i>_v ranks from different centiles of the <i>P</i>_m rank-ordered distribution for the index traits.</p