P-M plots of the type 2 diabetes meta-analysis results of Scott <i>et al.</i>[<b>10</b>].

<p>Two associated loci showing high heterogeneity are plotted. The dashed horizontal line shows the genome-wide significance threshold. The dotted vertical lines show the prediction regions based on m-value.</p

Power of FE, RE, and BE method when the number of studies having an effect varies.

<p>We assume 5 studies and gradually decrease the number of studies having an effect from 5 to 2. We assume an equal sample size of 1,000. We increase the odds ratio as the number of studies decreases to show the relative performance between methods. The power is estimated as the proportion of the simulated 10,000 meta-analysis sets whose meta-analysis p-value calculated by each method exceeds the genome-wide threshold ().</p

Application of FE, RE, and BE to the Crohns disease meta-analysis results of Franke <i>et al.</i>[13].

<p>The boldface denotes the top p-value among the three methods. Only six associated loci are presented that were shown to have more significant RE p-values than FE p-values <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002555#pgen.1002555-Han1" target="_blank">[23]</a>.</p

False positive rate of FE, RE, and BE at increasing significance thresholds.

<p>The values in the parentheses are the ratio between the false positive rate and the threshold. The estimates are obtained from 100 million null panels assuming 5 studies of an equal sample size 1,000.</p

P-M plots of the Crohns disease meta-analysis results of Franke <i>et al.</i>[<b>13</b>].

<p>Two of six associated loci showing high heterogeneity are plotted. See <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002555#pgen.1002555.s001" target="_blank">Figure S1</a> for the plots of all six loci. The names of the studies follow Franke <i>et al. </i><a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002555#pgen.1002555-Franke1" target="_blank">[13]</a>. The dashed horizontal line shows the genome-wide significance threshold. The dotted vertical lines show the prediction regions based on m-value.</p

Power of FE, RE, and BE method when the effect size varies between studies in the pattern following a normal distribution.

<p>The -axis denotes heterogeneity where we simulate the standard deviation of the effect size (log of relative risk) to be times the effect size. We assume the mean relative risk of 1.3 and assume 5 studies of an equal sample size 1,000. The power is estimated as the proportion of the simulated 10,000 meta-analysis sets whose meta-analysis p-value calculated by each method exceeds the genome-wide threshold ().</p

Accuracy of importance sampling depending on the number of samples.

<p>For each given number of samples used for the importance sampling, we measure the variance of the p-value estimate of BE by running the importance sampling 100 different times for the same dataset. We use the 69 associated loci from the Crohns disease data of Franke <i>et al.</i><a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002555#pgen.1002555-Franke1" target="_blank">[13]</a>. The ratio between the standard deviation of the estimate and the target p-value is reported, which is averaged over 69 loci.</p

Comparison of prediction accuracies of p-value, m-value, and BF.

<p>We simulate 1,000 meta-analysis of 10 studies with varying sample sizes where only a subset of the studies have an effect. Given 10,000 studies, we threshold each statistic to predict the studies having an effect and the studies not having an effect, and vary the threshold to draw the ROC curves. In A, true prediction rate is the proportion of the studies actually having an effect that are correctly predicted to have an effect and false prediction rate is the proportion of the studies actually not having an effect that are incorrectly predicted to have an effect. In B, true and false prediction rates are similarly defined but in the direction of predicting studies not having an effect. For BF, we use the asymptotic BF of Wakefield <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002555#pgen.1002555-Wakefield1" target="_blank">[39]</a> with prior where .</p

A figure depicting the interpretations based on a P-M plot.

<p>A figure depicting the interpretations based on a P-M plot.</p

Histograms of m-values of different types of studies.

<p>We assume four types of studies which is the all four combinations of large sample () and small sample (), and effect () and no effect (). We repeatedly simulate a meta-analysis of eight studies, two studies per each type, and calculate the m-values of the studies.</p