Interpreting meta-analyses of genome-wide association studies

Meta-analysis is an increasingly popular tool for combining multiple genome-wide association studies in a single analysis to identify associations with small effect sizes. The effect sizes between studies in a meta-analysis may differ and these differences, or heterogeneity, can be caused by many factors. If heterogeneity is observed in the results of a meta-analysis, interpreting the cause of heterogeneity is important because the correct interpretation can lead to a better understanding of the disease and a more effective design of a replication study. However, interpreting heterogeneous results is difficult. The standard approach of examining the association p-values of the studies does not effectively predict if the effect exists in each study. In this paper, we propose a framework facilitating the interpretation of the results of a meta-analysis. Our framework is based on a new statistic representing the posterior probability that the effect exists in each study, which is estimated utilizing cross-study information. Simulations and application to the real data show that our framework can effectively segregate the studies predicted to have an effect, the studies predicted to not have an effect, and the ambiguous studies that are underpowered. In addition to helping interpretation, the new framework also allows us to develop a new association testing procedure taking into account the existence of effect.     

Assessing and managing risk when sharing aggregate genetic variant data

Access to genetic data across studies is an important aspect of identifying new genetic associations through genome-wide association studies (GWASs). Meta-analysis across multiple GWASs with combined cohort sizes of tens of thousands of individuals often uncovers many more genome-wide associated loci than the original individual studies; this emphasizes the importance of tools and mechanisms for data sharing. However, even sharing summary-level data, such as allele frequencies, inherently carries some degree of privacy risk to study participants. Here we discuss mechanisms and resources for sharing data from GWASs, particularly focusing on approaches for assessing and quantifying the privacy risks to participants that result from the sharing of summary-level data.     

Endothelial nitric oxide synthase gene polymorphisms and essential hypertension in Han Chinese

We examined the effect of polymorphisms in the endothelial nitric oxide synthase gene on the risk for essential hypertension in a Han Chinese population through a meta-analysis of data from 15 studies. Associations between increased risk for essential hypertension and 4b/a were obtained in a dominant model and allele contrast (aa + ab vs bb: odds ratio (OR)(FE) = 1.26, 95% confidence interval (CI) = 1.10-1.44; a vs b allele: OR(FE) = 1.23, 95%CI: 1.09-1.40). Four studies with sample sizes over 500 produced similar results. No evidence of publication bias was found. Also, no significant heterogeneity was observed among these studies. When we examined the G894T polymorphism, we found a marginally significant association for allele contrast and the recessive model when all the eligible studies were pooled together. However, there was no evidence for a significant association after the exclusion of two studies deviating from Hardy-Weinberg equilibrium in the control group. Heterogeneity among studies was observed. Results of cumulative and recursive cumulative meta-analysis indicated that more studies are needed to objectively determine the effects of these two polymorphisms.     

Effectively Identifying eQTLs from Multiple Tissues by Combining Mixed Model and Meta-analytic Approaches

Gene expression data, in conjunction with information on genetic variants, have enabled studies to identify expression quantitative trait loci (eQTLs) or polymorphic locations in the genome that are associated with expression levels. Moreover, recent technological developments and cost decreases have further enabled studies to collect expression data in multiple tissues. One advantage of multiple tissue datasets is that studies can combine results from different tissues to identify eQTLs more accurately than examining each tissue separately. The idea of aggregating results of multiple tissues is closely related to the idea of meta-analysis which aggregates results of multiple genome-wide association studies to improve the power to detect associations. In principle, meta-analysis methods can be used to combine results from multiple tissues. However, eQTLs may have effects in only a single tissue, in all tissues, or in a subset of tissues with possibly different effect sizes. This heterogeneity in terms of effects across multiple tissues presents a key challenge to detect eQTLs. In this paper, we develop a framework that leverages two popular meta-analysis methods that address effect size heterogeneity to detect eQTLs across multiple tissues. We show by using simulations and multiple tissue data from mouse that our approach detects many eQTLs undetected by traditional eQTL methods. Additionally, our method provides an interpretation framework that accurately predicts whether an eQTL has an effect in a particular tissue.     

Meta-analysis of studies with missing data

Summary .  Consider a meta-analysis of studies with varying proportions of patient-level missing data, and assume that each primary study has made certain missing data adjustments so that the reported estimates of treatment effect size and variance are valid. These estimates of treatment effects can be combined across studies by standard meta-analytic methods, employing a random-effects model to account for heterogeneity across studies. However, we note that a meta-analysis based on the standard random-effects model will lead to biased estimates when the attrition rates of primary studies depend on the size of the underlying study-level treatment effect. Perhaps ignorable within each study, these types of missing data are in fact not ignorable in a meta-analysis. We propose three methods to correct the bias resulting from such missing data in a meta-analysis: reweighting the DerSimonian–Laird estimate by the completion rate; incorporating the completion rate into a Bayesian random-effects model; and inference based on a Bayesian shared-parameter model that includes the completion rate. We illustrate these methods through a meta-analysis of 16 published randomized trials that examined combined pharmacotherapy and psychological treatment for depression.     

A Multi-SNP Locus-Association Method Reveals a Substantial Fraction of the Missing Heritability

There are many known examples of multiple semi-independent associations at individual loci; such associations might arise either because of true allelic heterogeneity or because of imperfect tagging of an unobserved causal variant. This phenomenon is of great importance in monogenic traits but has not yet been systematically investigated and quantified in complex-trait genome-wide association studies (GWASs). Here, we describe a multi-SNP association method that estimates the effect of loci harboring multiple association signals by using GWAS summary statistics. Applying the method to a large anthropometric GWAS meta-analysis (from the Genetic Investigation of Anthropometric Traits consortium study), we show that for height, body mass index (BMI), and waist-to-hip ratio (WHR), 3%, 2%, and 1%, respectively, of additional phenotypic variance can be explained on top of the previously reported 10% (height), 1.5% (BMI), and 1% (WHR). The method also permitted a substantial increase (by up to 50%) in the number of loci that replicate in a discovery-validation design. Specifically, we identified 74 loci at which the multi-SNP, a linear combination of SNPs, explains significantly more variance than does the best individual SNP. A detailed analysis of multi-SNPs shows that most of the additional variability explained is derived from SNPs that are not in linkage disequilibrium with the lead SNP, suggesting a major contribution of allelic heterogeneity to the missing heritability.     

Random-Effects,Fixed-Effects and the within-between Specification for Clustered Data in Observational Health Studies: A Simulation Study

Background

When unaccounted-for group-level characteristics affect an outcome variable, traditional linear regression is inefficient and can be biased. The random- and fixed-effects estimators (RE and FE, respectively) are two competing methods that address these problems. While each estimator controls for otherwise unaccounted-for effects, the two estimators require different assumptions. Health researchers tend to favor RE estimation, while researchers from some other disciplines tend to favor FE estimation. In addition to RE and FE, an alternative method called within-between (WB) was suggested by Mundlak in 1978, although is utilized infrequently.

Methods

We conduct a simulation study to compare RE, FE, and WB estimation across 16,200 scenarios. The scenarios vary in the number of groups, the size of the groups, within-group variation, goodness-of-fit of the model, and the degree to which the model is correctly specified. Estimator preference is determined by lowest mean squared error of the estimated marginal effect and root mean squared error of fitted values.

Results

Although there are scenarios when each estimator is most appropriate, the cases in which traditional RE estimation is preferred are less common. In finite samples, the WB approach outperforms both traditional estimators. The Hausman test guides the practitioner to the estimator with the smallest absolute error only 61% of the time, and in many sample sizes simply applying the WB approach produces smaller absolute errors than following the suggestion of the test.

Conclusions

Specification and estimation should be carefully considered and ultimately guided by the objective of the analysis and characteristics of the data. The WB approach has been underutilized, particularly for inference on marginal effects in small samples. Blindly applying any estimator can lead to bias, inefficiency, and flawed inference.     

Do animals living in larger groups experience greater parasitism? A meta-analysis

Parasitism is widely viewed as the primary cost of sociality and a constraint on group size, yet studies report varied associations between group size and parasitism. Using the largest database of its kind, we performed a meta-analysis of 69 studies of the relationship between group size and parasite risk, as measured by parasitism and immune defenses. We predicted a positive correlation between group size and parasitism with organisms that show contagious and environmental transmission and a negative correlation for searching parasites, parasitoids, and possibly vector-borne parasites (on the basis of the encounter-dilution effect). Overall, we found a positive effect of group size (r = 0.187) that varied in magnitude across transmission modes and measures of parasite risk, with only weak indications of publication bias. Among different groups of hosts, we found a stronger relationship between group size and parasite risk in birds than in mammals, which may be driven by ecological and social factors. A metaregression showed that effect sizes increased with maximum group size. Phylogenetic meta-analyses revealed no evidence for phylogenetic signal in the strength of the group size-parasitism relationship. We conclude that group size is a weak predictor of parasite risk except in species that live in large aggregations, such as colonial birds, in which effect sizes are larger.     

整合分析中结合效应值和总异质性的介绍

整合分析(meta-analysis)是对同一主题下多个独立实验结果进行综合的统计学方法,被认为是到目前为止最好的数量综合方法,其统计量为效应值。结合效应值(cumulative effect size)和总异质性(total heterogeneity)分别是整合分析中描述效应值中心趋向和变异程度的两个指标,是在整合分析中最重要的两个参数。在整合分析中随数据结构的不同又有多种求结合效应值和总异质性的方法。介绍了与三种数据结构(无结构数据、分类数据、连续数据)相对应的这两个指标的计算方法。     

How Many Genetic Variants Remain to Be Discovered?

A great majority of genetic markers discovered in recent genome-wide association studies have small effect sizes, and they explain only a small fraction of the genetic contribution to the diseases. How many more variants can we expect to discover and what study sizes are needed? We derive the connection between the cumulative risk of the SNP variants to the latent genetic risk model and heritability of the disease. We determine the sample size required for case-control studies in order to achieve a certain expected number of discoveries in a collection of most significant SNPs. Assuming similar allele frequencies and effect sizes of the currently validated SNPs, complex phenotypes such as type-2 diabetes would need approximately 800 variants to explain its 40% heritability. Much smaller numbers of variants are needed if we assume rare-variants but higher penetrance models. We estimate that up to 50,000 cases and an equal number of controls are needed to discover 800 common low-penetrant variants among the top 5000 SNPs. Under common and rare low-penetrance models, the very large studies required to discover the numerous variants are probably at the limit of practical feasibility. Under rare-variant with medium- to high-penetrance models (odds-ratios between 1.6 and 4.0), studies comparable in size to many existing studies are adequate provided the genotyping technology can interrogate more and rarer variants.     

Environmental determinants of food-chain length: a meta-analysis

Food-chain length is an important character of ecological communities that affects many of their functional aspects. Recently, an increasing number of studies have tested the effects of productivity, disturbance, or ecosystem size on food-chain length in a variety of natural systems. Here we conduct a formal meta-analysis to summarize findings from these empirical studies. We found significant positive mean effects of productivity and ecosystem size but no significant mean effect of disturbance on food-chain length. The strength of mean effect sizes was not significantly different between productivity and ecosystem size. These results lend general support to previous theories predicting the effect of productivity and ecosystem size, but fail to support the prediction that disturbance shortens food chains. In addition, our meta-analysis found that the effect sizes of primary studies were significantly heterogeneous for ecosystem size and disturbance, but not for productivity. This pattern might reflect that ecosystem size and disturbance can affect food-chain length through multiple different mechanisms, while productivity influences food-chain length in a simple manner through energy limitation.     

Comparison of random-effects meta-analysis models for the relative risk in the case of rare events: A simulation study

Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta-analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta-analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random-effects [RE] Poisson regression, RE zero-inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta-binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta-analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between-study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta-binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta-analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations is provided.     

A Powerful Pathway-Based Adaptive Test for Genetic Association with Common or Rare Variants

In spite of the success of genome-wide association studies (GWASs), only a small proportion of heritability for each complex trait has been explained by identified genetic variants, mainly SNPs. Likely reasons include genetic heterogeneity (i.e., multiple causal genetic variants) and small effect sizes of causal variants, for which pathway analysis has been proposed as a promising alternative to the standard single-SNP-based analysis. A pathway contains a set of functionally related genes, each of which includes multiple SNPs. Here we propose a pathway-based test that is adaptive at both the gene and SNP levels, thus maintaining high power across a wide range of situations with varying numbers of the genes and SNPs associated with a trait. The proposed method is applicable to both common variants and rare variants and can incorporate biological knowledge on SNPs and genes to boost statistical power. We use extensively simulated data and a WTCCC GWAS dataset to compare our proposal with several existing pathway-based and SNP-set-based tests, demonstrating its promising performance and its potential use in practice.     

On individual genome-wide association studies and their meta-analysis

Individual genome-wide association (GWA) studies and their meta-analyses represent two approaches for identifying genetic loci associated with complex diseases/traits. Inconsistent findings and non-replicability between individual GWA studies and meta-analyses are commonly observed, hence posing the critical question as to how to interpret their respective results properly. In this study, we performed a series of simulation studies to investigate and compare the statistical properties of the two approaches. Our results show that (1) as expected, meta-analysis of larger sample size is more powerful than individual GWA studies under the ideal setting of population homogeneity among individual studies; (2) under the realistic setting of heterogeneity among individual studies, detection of heterogeneity is usually difficult and meta-analysis (even with the random-effects model) may introduce elevated false positive and/or negative rates; (3) despite relatively small sample size, well-designed individual GWA study has the capacity to identify novel loci for complex traits; (4) replicability between meta-analysis and independent individual studies or between independent meta-analyses is limited, and thus inconsistent findings are not unexpected.     

The Impact of Phenotypic and Genetic Heterogeneity on Results of Genome Wide Association Studies of Complex Diseases

Phenotypic misclassification (between cases) has been shown to reduce the power to detect association in genetic studies. However, it is conceivable that complex traits are heterogeneous with respect to individual genetic susceptibility and disease pathophysiology, and that the effect of heterogeneity has a larger magnitude than the effect of phenotyping errors. Although an intuitively clear concept, the effect of heterogeneity on genetic studies of common diseases has received little attention. Here we investigate the impact of phenotypic and genetic heterogeneity on the statistical power of genome wide association studies (GWAS). We first performed a study of simulated genotypic and phenotypic data. Next, we analyzed the Wellcome Trust Case-Control Consortium (WTCCC) data for diabetes mellitus (DM) type 1 (T1D) and type 2 (T2D), using varying proportions of each type of diabetes in order to examine the impact of heterogeneity on the strength and statistical significance of association previously found in the WTCCC data. In both simulated and real data, heterogeneity (presence of “non-cases”) reduced the statistical power to detect genetic association and greatly decreased the estimates of risk attributed to genetic variation. This finding was also supported by the analysis of loci validated in subsequent large-scale meta-analyses. For example, heterogeneity of 50% increases the required sample size by approximately three times. These results suggest that accurate phenotype delineation may be more important for detecting true genetic associations than increase in sample size.     

Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

Network-Based Meta-Analyses of Associations of Multiple Gene Expression Profiles with Bone Mineral Density Variations in Women

Background

Existing microarray studies of bone mineral density (BMD) have been critical for understanding the pathophysiology of osteoporosis, and have identified a number of candidate genes. However, these studies were limited by their relatively small sample sizes and were usually analyzed individually. Here, we propose a novel network-based meta-analysis approach that combines data across six microarray studies to identify functional modules from human protein-protein interaction (PPI) data, and highlight several differentially expressed genes (DEGs) and a functional module that may play an important role in BMD regulation in women.

Methods

Expression profiling studies were identified by searching PubMed, Gene Expression Omnibus (GEO) and ArrayExpress. Two meta-analysis methods were applied across different gene expression profiling studies. The first, a nonparametric Fisher’s method, combined p-values from individual experiments to identify genes with large effect sizes. The second method combined effect sizes from individual datasets into a meta-effect size to gain a higher precision of effect size estimation across all datasets. Genes with Q test’s p-values < 0.05 or I² values > 50% were assessed by a random effects model and the remainder by a fixed effects model. Using Fisher’s combined p-values, functional modules were identified through an integrated analysis of microarray data in the context of large protein–protein interaction (PPI) networks. Two previously published meta-analysis studies of genome-wide association (GWA) datasets were used to determine whether these module genes were genetically associated with BMD. Pathway enrichment analysis was performed with a hypergeometric test.

Results

Six gene expression datasets were identified, which included a total of 249 (129 high BMD and 120 low BMD) female subjects. Using a network-based meta-analysis, a consensus module containing 58 genes (nodes) and 83 edges was detected. Pathway enrichment analysis of the 58 module genes revealed that these genes were enriched in several important KEGG pathways including Osteoclast differentiation, B cell receptor signaling pathway, MAPK signaling pathway, Chemokine signaling pathway and Insulin signaling pathway. The importance of module genes was replicated by demonstrating that most module genes were genetically associated with BMD in the GWAS data sets. Meta-analyses were performed at the individual gene level by combining p-values and effect sizes. Five candidate genes (ESR1, MAP3K3, PYGM, RAC1 and SYK) were identified based on gene expression meta-analysis, and their associations with BMD were also replicated by two BMD meta-analysis studies.

Conclusions

In summary, our network-based meta-analysis not only identified important differentially expressed genes but also discovered biologically meaningful functional modules for BMD determination. Our study may provide novel therapeutic targets for osteoporosis in women.     

CALENDAR OF EVENTS

A synopsis and meta-analysis of studies that investigated the association between genetic variants involved in the homocysteine/folate metabolism pathway and risk of inflammatory bowel disease (IBD) were conducted. Four variants (MTHFR C6TTT, MTHFR A1298C, MTR A2756G and MTRR A66G) showed significant associations in individual studies. In meta-analyses, only the variant MTR A2756G indicated an association with the risk of IBD for the allele contrast and the dominant model (odds ratio (OR) 1.48 (1.12–1.97) and OR 1.55 (1.12–2.15), respectively). The effect sizes for Crohn’s disease and ulcerative colitis were similar to IBD. Cumulative meta-analysis for C677T indicated a downward trend of association as information accumulates.     

Principal Component Analysis Characterizes Shared Pathogenetics from Genome-Wide Association Studies

Genome-wide association studies (GWASs) have recently revealed many genetic associations that are shared between different diseases. We propose a method, disPCA, for genome-wide characterization of shared and distinct risk factors between and within disease classes. It flips the conventional GWAS paradigm by analyzing the diseases themselves, across GWAS datasets, to explore their “shared pathogenetics”. The method applies principal component analysis (PCA) to gene-level significance scores across all genes and across GWASs, thereby revealing shared pathogenetics between diseases in an unsupervised fashion. Importantly, it adjusts for potential sources of heterogeneity present between GWAS which can confound investigation of shared disease etiology. We applied disPCA to 31 GWASs, including autoimmune diseases, cancers, psychiatric disorders, and neurological disorders. The leading principal components separate these disease classes, as well as inflammatory bowel diseases from other autoimmune diseases. Generally, distinct diseases from the same class tend to be less separated, which is in line with their increased shared etiology. Enrichment analysis of genes contributing to leading principal components revealed pathways that are implicated in the immune system, while also pointing to pathways that have yet to be explored before in this context. Our results point to the potential of disPCA in going beyond epidemiological findings of the co-occurrence of distinct diseases, to highlighting novel genes and pathways that unsupervised learning suggest to be key players in the variability across diseases.     

A meta-analysis of CDH1 C-160A genetic polymorphism and gastric cancer risk

We explored the role of the C-160A single-nucleotide polymorphism (SNP) of CDH1 in susceptibility to gastric cancer through a systematic review and meta-analysis. Fourteen studies were included, the original groups collapsed, and re-grouped in accordance with the most appropriate genetic model. Potential sources of heterogeneity were sought out via subgroup analyses and sensitivity analyses, and publication biases were estimated. No significant association of C-160A was found with the overall risk of developing gastric cancer, but the apparently opposite tendency was noted between Caucasians and Asians, and a statistically significant association was found among Asians. The seemingly opposite tendency of associations was also seen between noncardia and cardia types or between sporadic diffuse and intestinal types of gastric cancer, but no statistically significant findings were noted. Genotyping techniques, sample size, quality appraisal scores, or article publication time did not constitute the source of heterogeneity across studies; and no publication biases were found in our meta-analysis.