Epistasis Test in Meta-Analysis: A Multi-Parameter Markov Chain Monte Carlo Model for Consistency of Evidence

<div><p>Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The “missing heritability” has been suggested to be due to lack of studies focused on epistasis, also called gene–gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called “Epistasis Test in Meta-Analysis” (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene–gene interactions in the renin–angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione <i>S</i>-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at <a href="https://cran.r-project.org/web/packages/etma/index.html" target="_blank">https://cran.r-project.org/web/packages/etma/index.html</a>].</p></div

Inconsistent estimates of interaction effects in the same data.

<p>This figure describes a meta-regression analysis based on the data from Fang et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0152891#pone.0152891.ref027" target="_blank">27</a>] (detailed data are shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0152891#pone.0152891.s004" target="_blank">S1 Table</a>). The upper plot describes an investigation of the association between proportions of null/null GSTT1 in cases and the odds ratios of GSTM1 in cancer, and the lower plot describes an investigation of the association between proportions of null/null GSTM1 in cases and the odds ratios of GSTT1 in cancer. The solid lines denote unbiased estimators of odds ratios, and the dashed lines show 95% confidence intervals of odds ratios. According to a previous article, the slopes in meta regression approximate interaction effects [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0152891#pone.0152891.ref016" target="_blank">16</a>]. However, the estimates of interaction effect were inconsistent when we exchanged the independent and moderator variables (0.1377 and 0.2338, respectively). This phenomenon does not occur in individual data analysis and leads to problems in interpretation.</p

The result of real data analysis using ETMA.

<p>The result of real data analysis using ETMA.</p

Type I error of individual data analysis, ETMA and conventional meta-regression.

<p>Type I error of individual data analysis, ETMA and conventional meta-regression.</p

A typical analysis pipeline of ETMA function in 'etma' package.

<p>This figure summarized the pipeline of ETMA function. The main input is a meta-analysis dataset, which including the number of wild/mutation type of SNP1/SNP2 in case/control group. The main options include the length of chains in step 1/2, the maximum number of iterations, and the start seed. Main outputs include three matrixes. Matrix b includes the beta values (logarithmic ORs) of each SNP and interaction term, and VCOV is the variance covariance matrix of beta value. <i>P</i> is an n by 3 matrix describing three study-specific parameters (p1 = Disease risk in subjects with wild-type alleles of SNP1 and SNP2; p5 = Mutation frequency of SNP1; p6 = Mutation frequency of SNP2)</p

Summary of simulation conditions.

<p>Summary of simulation conditions.</p

The proportion of individual with different status of disease/SNP1/SNP2 could be calculated by <i>p</i>_baseline, <i>MAF</i>₁, <i>MAF</i>₂, OR_y,SNP1, OR_y,SNP2 and OR_interaction.

<p>The proportion of individual with different status of disease/SNP1/SNP2 could be calculated by <i>p</i>_baseline, <i>MAF</i>₁, <i>MAF</i>₂, OR_y,SNP1, OR_y,SNP2 and OR_interaction.</p

The statistical power of individual data analysis, ETMA and conventional meta-regression.

<p>The <i>x</i>-axis describes three levels of interaction effect (OR_interaction = 1.2, 1.5 or 2.0), and the <i>y</i>-axis indicates the statistical power provided by individual data analysis (black), ETMA (red) and conventional meta-regression (blue), respectively. The details of these methods are described in the Method. The different subplots present comparisons using different simulation parameters, and the titles of these subplots show their detailed settings. Each data point was based on 1,000 simulations.</p

Gene-Gene and Gene-Environment Interactions in Meta-Analysis of Genetic Association Studies

<div><p>Extensive genetic studies have identified a large number of causal genetic variations in many human phenotypes; however, these could not completely explain heritability in complex diseases. Some researchers have proposed that the “missing heritability” may be attributable to gene–gene and gene–environment interactions. Because there are billions of potential interaction combinations, the statistical power of a single study is often ineffective in detecting these interactions. Meta-analysis is a common method of increasing detection power; however, accessing individual data could be difficult. This study presents a simple method that employs aggregated summary values from a “case” group to detect these specific interactions that based on rare disease and independence assumptions. However, these assumptions, particularly the rare disease assumption, may be violated in real situations; therefore, this study further investigated the robustness of our proposed method when it violates the assumptions. In conclusion, we observed that the rare disease assumption is relatively nonessential, whereas the independence assumption is an essential component. Because single nucleotide polymorphisms (SNPs) are often unrelated to environmental factors and SNPs on other chromosomes, researchers should use this method to investigate gene–gene and gene–environment interactions when they are unable to obtain detailed individual patient data.</p></div

Summary of the population parameters.

<p><i>β</i>₀ is the logit-transformation prevalence of the outcome disease in people with homozygous major and the moderators in the study population. <i>β</i>₁ is the log-transformation OR of the allele effect in people without moderators. <i>β</i>₂ is the log-transformation OR of moderators on the disease in people with homozygous major, and <i>β</i>₃ is the log-transformation moderator effect. <i>F</i>_st is the frequency difference among various studies, and <i>P</i>₇, <i>P</i>₈, and <i>P</i>₉ are the proportions of moderators status in people with homozygous major [<i>p</i>(<i>x</i>₂ = 1|<i>x</i>₁ = 0)], people with heterozygous genotype [<i>p</i>(<i>x</i>₂ = 1|<i>x</i>₁ = 1)], and people with homozygous minor [<i>p</i>(<i>x</i>₂ = 1|<i>x</i>₁ = 2)], respectively.</p><p>Summary of the population parameters.</p