A general framework for meta-analyzing dependent studies with overlapping subjects in association mapping

Meta-analyses of genome-wide association studies (GWASs) have become essential to identifying new loci associated with human diseases. We recently developed a novel framework that improves the accuracy and power of meta-analyses, which we describe in our recent Human Molecular Genetics paper. This framework can be applied to the fixed effects (FE) model, which assumes that effect sizes of genetic variants are constant across studies, and the random effects (RE) model, which assumes that effect sizes can be different among studies.

Almost all GWAS publications today employ meta-analysis methodologies, the majority of which assume that component studies are independent and that individuals among studies are unrelated. Yet many studies today use shared controls to reduce genotyping or sequencing cost. These “shared control” individuals can inadvertently overlap between multiple studies and, if not accounted for in the methodology, induce false associations in GWAS results. Most meta-analysis tools, including the RE model, cannot account for these overlapping subjects.

In our paper, we propose a general framework for adjusting association statistics to account for overlapping subjects within a meta-analysis. The key idea of our method is to transform the covariance structure of the data so it can be used in methods that strictly assume independence between studies. Specifically, our method decouples dependent studies into independent studies and adjusts association statistics to account for uncertainties in dependent studies. As a result, our approach enables general meta-analysis methods, including the FE and RE models, to account for overlapping subjects. Existing pipelines implementing these models can be reused for dependent studies if our framework is applied at the front end of the analysis procedure.

schema

A simple example of our decoupling approach. Ω and ΩDecoupled are the covariance matrices of the statistics of three studies A, B and C before and after decoupling, respectively. The thickness of the edges denotes the amount of correlation between the studies. After decoupling, the size of the nodes reflects the information that the studies contain in terms of the inverse variance.

We tested our framework for accuracy and power with five simulated datasets, each containing 1000 to 5000 individuals and 10,000 shared controls. A standard approach produced an inflated number of false positive. Our decoupling method, which systemically accounts for overlapping individuals in meta-analysis, and a standard splitting method, which splits controls into individual studies, both correctly controlled for type 1 errors. The advantage of our framework is apparent when assessing power; in one scenario, we gained 25% power in accounting for overlapping subjects with the decoupling when compared to the splitting method.

Next, we assessed the potential of our framework in identifying casual loci shared by multiple diseases and leveraging information from multiple tissues to increase power for eQTL identification. The decoupling and splitting methods controlled false-positive rates and produced significant p-values at several previously identified candidate shared loci among the three autoimmune conditions present in the Wellcome Trust Case Control Consortium (WTCCC) data. In comparison to the splitting method, our decoupling framework increased the significance of p-values in the shared loci test and increased the number of discovered eQTLs by 19%.

Our approach is flexible and allows many meta-analysis methods, such as the RE model, to account for dependency between studies and overlapping subjects. We developed this approach to complement standard software packages in the meta-analysis of GWAS. This project was led by Buhm Han and involved Dat Duong and Jae Hoon Sul. The article is available at:
https://www.ncbi.nlm.nih.gov/pubmed/26908615

The full citation to our paper is:

Han, Buhm; Duong, Dat; Sul, Jae Hoon; de Bakker, Paul I W; Eskin, Eleazar; Raychaudhuri, Soumya

A general framework for meta-analyzing dependent studies with overlapping subjects in association mapping. Journal Article

In: Hum Mol Genet, 2016, ISSN: 1460-2083.

Abstract | Links | BibTeX

Genes, Environments and Meta-Analysis

Figure 1. Application of Meta-GxE to Apoa2 locus. The forest plot (A) shows heterogeneity in the effect sizes across different studies. The PM- plot (B) predicts that 7 studies have an effect at this locus, even though only 1 study (HMDP-chow(M)) is genome-wide significant with P-value. doi:10.1371/journal.pgen.1004022.g001

It is well known that both genetic factors and environmental factors contribute to traits and specifically disease risk. In addition, an area of great interest in the research community is the interaction between genetic factors and environmental factors and their contribution to disease risk and other traits. Genetic variants that are involved in gene by environment interactions (denoted GxE) have a different effect on the trait spending on the environment. For example, some variants can have an effect on cholesterol levels only in the presence of a high fat diet. Discovering variants involved in GxE has been tremendously difficult and even though thousands of variants have been implicated in disease related traits using genome wide association studies, very few variants have been implicated in GxEs. Part of the difficulty in detecting GxEs is that the traditional approach requires analyzing studies which contain individuals with multiple environments.

We have recently published a paper with the A. Jake Lusis group in PLoS Genetics which presents a novel approach to discovering GxEs. In our approach, many different studies, each which was performed in different environments, are combined to identify GxEs. The key idea is that if variants have a different genetic effect in different environments, then these variants are candidates for being involved in GxEs. Combining studies together is a statistical technique called meta-analysis which has been a major focus of our lab the past few years. We show in the paper, the mathematically, searching for GxEs using the traditional approach and a type of meta-analysis framework called the random effects model(21565292) are very closely related.

We applied our approach to identify GxEs affected mouse HDL cholesterol by combining 17 mouse studies collected by A. Jake Lusis’ group containing almost 5,000 animals. Our approach discovered 26 loci involved in HDL, many of which appear to be involved in GxE. Virtually all of these loci were not previously discovered in any of the individual studies, but many of them map to genes known to affect HDL. Our approach also includes a visualization framework called a PM-plot which helps interpret the associated loci to help identify GxE interactions(22396665).

From the paper:

Discovering environmentally-specific loci using meta-analysis
The Meta-GxE strategy uses a meta-analytic approach to identify gene-by-environment inter- actions by combining studies that collect the same phenotype under different conditions. Our method consists of four steps. First, we apply a random effects model meta-analysis (RE) to identify loci associated with a trait considering all of the studies together. The RE method explicitly models the fact that loci may have different effects in different studies due to gene-by- environment interactions. Second, we apply a heterogeneity test to identify loci with significant gene-by-environment interactions. Third, we compute the m-value of each study to identify in which studies a given variant has an effect and in which it does not. Forth, we visualize the result through a forest plot and PM-plot to understand the underlying nature of gene-by-environment interactions.
We illustrate our methodology by examining a well-known region on mouse chromosome 1 harboring the Apoa2 gene, which is known to be strongly associated with HDL cholesterol (8332912). Figure 1 shows the results of applying our method to this locus. We first compute the effect size and its standard deviation for each of the 17 studies. These results are shown as a forest plot in Figure 1 (a). Second we compute the P-value for each individual study also shown in Figure 1 (a). If we were to follow traditional methodology and evaluate each study separately, we would declare an effect present in a study if the P-value exceeds a predefined genome-wide significance threshold (P < 1.0×10−6). In this case, we would only identify the locus as associated in a single study, HMDP-chow(M) (P = 6.84×10−9). On the other hand, in our approach, we combine all studies to compute a single P-value for each locus taking into account heterogeneity between studies. This approach leads to increased power over the simple approach considering each study separately. The combined meta P-value for the Apoa2 locus is very significant (4.41 × 10−22), which is consistent with the fact that the largest individual study only has 749 animals compared to 4,965 in our combined study.
We visualize the results through a PM-plot, in which P-values are simultaneously visualized with the m-values, which estimates the posterior probability of an effect being present in a study given the observations from all other studies, at each tested locus. These plots allow us to identify in which studies a given variant has an effect and in which it does not. M-values for a given variant have the following interpretation: a study with a small m-value(≤ 0.1) is predicted not to be affected by the variant, while a study with a large m-value(≥ 0.9) is predicted to be affected by the variant.
The PM-plot for the Apoa2 locus is shown in Figure 1 (b). If we only look at the separate study P-values (y-axis), we can conclude that this locus only has an effect in HMDP-chow(M). However, if we look at m-value (x-axis), then we find 8 studies (HMDPxB-ath(M), HMDPxB- ath(F), HMDP-chow(M), HMDP-fat(M), HMDP-fat(F), BxD-db-5(M), BxH-apoe(M), BxH- apoe(F)), where we predict that the variation has an effect, while in 3 studies (BxD-db-12(F), BxD-db-5(F), BxH-wt(M)) we predict there is no effect. The predictions for the remaining 6 studies are ambiguous.
From Figure 1, we observe that differences in effect sizes among the studies are remarkably consistent when considering the environmental factors of each study as described in Table 1. For example, when comparing study 1 – 4, the effect size of the locus decreases in both the male and female HMDPxB studies in the chow diet (chow study) relative to the fat diet (ath study). Thus we can see that when the mice have Leiden/CETP transgene, which cause high total cholesterol level and high LDL cholesterol level, effect size of this locus on HDL cholesterol level in blood is affected by the fat level of diet. Similarly, when comparing study 12 – 15, the knockout of the Apoe gene affects the effect sizes for both male and female BxH crosses. However, in the BxD cross (study 8 – 11), where each animal is homozygous for a mutation causing a deficiency of the leptin receptor, the effect of the locus is very strong in the young male animals, while as animals get older and become fatter, the effect becomes weaker. However in the case of female mice, the effect of the locus is nearly absent at both 5 and 12 weeks of age. Thus we can see that sex plays an important role in affecting HDL when the leptin receptor activity is deficient .

The full citation of our paper is:

Kang, Eun Yong; Han, Buhm; Furlotte, Nicholas; Joo, Jong Wha J; Shih, Diana; Davis, Richard C; Lusis, Aldons J; Eskin, Eleazar

Meta-Analysis Identifies Gene-by-Environment Interactions as Demonstrated in a Study of 4,965 Mice Journal Article

In: PLoS Genet, 10 (1), pp. e1004022, 2014, ISSN: 1553-7404.

Abstract | Links | BibTeX

Bibliography

Thesis Defense: Dr. Jae Hoon Sul

Dr. Jae Hoon Sul with his committee.

Dr. Jae Hoon Sul with his committee.

Jae Hoon Sul successfully defended his thesis on Wednesday September 19th.  His talk is posted on our YouTube Channel ZarlabUCLA.  Jae Hoon’s talk discusses several projects including using mixed model to correct for population structure, rare variant association studies and a meta-analysis approach for detecting multi-tissue eQTLs.  Fortunately for the lab, Jae Hoon is staying at UCLA for another year as a post-doc.

More details about what he talks about in his talk are available in the papers he discusses:

Sul, Jae Hoon; Han, Buhm ; Ye, Chun ; Choi, Ted ; Eskin, Eleazar

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

In: PLoS Genet, 9 (6), pp. e1003491, 2013, ISSN: 1553-7404.

Abstract | Links | BibTeX

Sul, Jae Hoon; Han, Buhm ; He, Dan ; Eskin, Eleazar

An Optimal Weighted Aggregated Association Test for Identification of Rare Variants Involved in Common Diseases. Journal Article

In: Genetics, 188 (1), pp. 181-188, 2011, ISSN: 1943-2631.

Abstract | Links | BibTeX

Kang, Hyun Min; Sul, Jae Hoon ; Service, Susan K; Zaitlen, Noah A; Kong, Sit-Yee Y; Freimer, Nelson B; Sabatti, Chiara ; Eskin, Eleazar

Variance component model to account for sample structure in genome-wide association studies. Journal Article

In: Nat Genet, 42 (4), pp. 348-54, 2010, ISSN: 1546-1718.

Abstract | Links | BibTeX