Forest plot of <i>M</i> statistics summarizing systematic patterns of heterogeneity among studies in the CARDIOGRAMplusC4D GWAS meta-analysis.

<p>Sorted <i>M</i> statistics are presented for individual studies represented by filled squares with their 95% confidence intervals shown by horizontal lines; the sizes of the squares are proportional to each studies’ inverse-variance weighting. Studies showing weaker (<i>M</i> < 0) than average genetic effects can be distinguished from those showing stronger (<i>M</i> > 0) than average effects.</p

Heterogeneity in the CARDIoGRAMplusC4D meta-analysis can be explained by differences in age of CAD onset, family history and ancestry.

<p><i>M</i> statistics for each study in the CARDIoGRAMplusC4D meta-analysis (Y- axis) are plotted against the average variant effect size (expressed as odds ratios) (X-axis) in each study. Panel A shows the ancestry of each study, panel B distinguishes early-onset from late-onset studies and panel C identifies studies ascertained with a positive family history of coronary artery disease. Panel D is a composite plot showing the degree of genetic enrichment among the studies in the meta-analysis, which ranged from non-enriched (late-onset studies without a positive family history of coronary artery disease) to doubly enriched (early-onset studies with a positive family history of coronary artery disease). The dashed lines indicate the Bonferroni corrected 5% significance threshold (<i>M</i> = ±0.483) to allow for multiple testing of 48 studies.</p

Empirical type- 1 error rates and power to detect an outlier study for <i>M</i> at threshold α = 0.05.

<p>Empirical type- 1 error rates and power to detect an outlier study for <i>M</i> at threshold α = 0.05.</p

A comparative power analysis of <i>M</i> and Cochran’s Q to detect systematic heterogeneity.

<p>The nine panels show (from left to right) simulations for 10, 15 and 30 studies, examined at 50, 25 and l0 variants; Data points for the <i>M</i> statistic are represented by filled circles whilst those for Cochran’s Q are denoted by filled triangles. Each data point represents a meta-analysis scenario where effect sizes for the non-outlier studies were held constant (log_e(odds ratio) = 0.182 i.e. odds ratio = 1.2) to model homogeneous effects. The effect sizes of variants in the outlier study were the product of the non-outlier effect size (i.e. log_e(odds ratio) = 0.182) and a parameter (fold-change) to model a continuous series of systematic heterogeneity patterns. All studies were equally weighted (standard error of log_e(odds ratio) = 0.1).</p

The power of the <i>M</i> statistic to detect systematic outlier studies.

<p>A power analysis of the <i>M</i> statistics for meta-analysis scenarios with varying numbers of studies and variants. The three panels show (from left to right) simulations for 10, 15 and 30 studies; 50, 25 and 10 variant simulations are shown by filled diamonds, filled circles, or open squares respectively. Each data point represents a meta-analysis simulation with 1,000 replicates, where an outlier study was assigned genetic effects that are x-fold stronger than the effects assigned to the remaining studies showing typical effects. Effect sizes for variants in the studies showing typical effects were allocated from an L—shaped distribution (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1006755#pgen.1006755.s011" target="_blank">S2 Table</a>) whilst effect sizes for variants in the outlier study were calculated as a multiple of the typical effect size. For example, effect sizes for variants in an outlier study 2-fold-stronger than studies showing typical effects would be computed as (2 x ({0.04, 0.12, 0.2, 0.28, 0.4}, σ = 0.10).</p