Multi-trait analysis of genome-wide association summary statistics using MTAG methods
Show snapshot details
On this page
This experiment, in seven questions
Jump straight to the part of the recipe you need. Data and provenance labels stay close to the action they support.
Shopping and prep list
What do I need before I start?
Biological model pending
Subject model for the experiment.
- Use
- confirm full cohort details in the source paper
Before you run
What should be confirmed before execution?
First confirmation
Species or subject information is missing.
Confirm before execution
Protocol does not list structured equipment.
Confirm before execution
This page shows passages quoted from the paper. Equipment, materials, times, and temperatures are hidden until the page is rebuilt from the full paper and checked by a reviewer. Check the paper before using this method.
Confirm before execution
Open the source paper before finalizing run-specific details.
Procurement checkpoint
Use source-stated vendors where present. Treat mapped products as sourcing options unless the page marks an exact source match.
Open quote workflowStep-by-step procedure
What do I do, in order?
MTAG Framework
In the framework that follows, all traits and genotypes are standardized to have mean zero and variance one. For SNP j, we denote the vector of marginal (i.e., not controlling for other SNPs), true effects on each of the T traits by β j. We treat these true effects as random effects with E ( β j ) = 0 and Var ( β j ) = Ω. If the true effects are correlated across traits, then the off-diagonal elements of Ω are non-zero. MTAG's key assumption is that Ω is homogeneous across SNPs, i.e., it does not depend on j.
Polygenic Prediction
We measure the predictive power of each polygenic score by its incremental R 2, defined as the increase in coefficient of determination ( R 2 ) as we move from a regression of the trait only on a set of controls (year of birth, year of birth squared, sex, their interactions, and 10 principal components of the genetic data) to a regression that additionally includes the polygenic score as an independent variable.
Biological Annotation
For a final comparison, we analyze both the GWAS and MTAG results using the bioinformatics tool DEPICT. We present the prioritized genes, enriched gene sets, and enriched tissues identified by DEPICT at the standard FDR threshold of 5%.
ONLINE METHODS
There are T traits, which may be binary or quantitative. We standardize each trait and the genotype for each single-nucleotide polymorphism (SNP) j so that they all have mean zero and variance one. The length- T vector of marginal (i.e., not controlling for other SNPs), true effects of SNP j on each of the traits is denoted β j. We assume that these are random effects with mean 0 and variance-covariance matrix Ω that is the same across j. The mean is zero because we treat the choice of reference allele as arbitrary. We make the common assumption,, that the β j 's are identically distributed across j. The assumption implies that the expected amount of phenotypic variance explained is equal for each SNP, regardless of SNP characteristics such as allele frequency.
Perfect genetic correlation and equal heritabilities
This special case corresponds to the "traits" being (the same measure of) a single trait; in other words, applying MTAG instead of inverse-variance-weighted meta-analysis to T GWAS results. Doing so can be useful if there is sample overlap in the GWAS results. In this case, as noted in the main text, MTAG specializes to β ^ MTAG, j, t = 1 ′ ∑ j - 1 1 ′ ∑ j - 1 1 β ^ j for all t, and it is no longer necessary to estimate Ω.
Measurement outputs
What raw and processed outputs should exist?
Analysis plan
How should the outputs become interpretable results?
Acquisition
Collect raw experimental outputs with enough metadata to preserve sample identity, condition, and timing.
inferred from protocolPreprocessing / cleaning
Review raw outputs for quality, remove unusable captures, and organize the data into a comparison-ready table or image set.
inferred from protocolScoring or quantification
Quantify the primary endpoint described in the methods before moving into any statistical comparison.
inferred from protocolStatistical comparison
Statistical method not yet structured for this page.
inferred from protocolReporting output
Report representative outputs alongside the summary comparison used to support the conclusion.
inferred from protocolSource and audit
What supports the facts on this page?
Evidence quotes (5)
In the framework that follows, all traits and genotypes are standardized to have mean zero and variance one. For SNP j, we denote the vector of marginal (i.e., not controlling for other SNPs), true effects on each of the T traits by β j. We treat these true effects as random effects with E ( β j ) = 0 and Var ( β j ) = Ω. If the true effects are correlated across traits, then the off-diagonal elements of Ω are non-zero. MTAG's key assumption is that Ω is homogeneous across SNPs, i.e., it does not depend on j.
We measure the predictive power of each polygenic score by its incremental R 2, defined as the increase in coefficient of determination ( R 2 ) as we move from a regression of the trait only on a set of controls (year of birth, year of birth squared, sex, their interactions, and 10 principal components of the genetic data) to a regression that additionally includes the polygenic score as an independent variable.
For a final comparison, we analyze both the GWAS and MTAG results using the bioinformatics tool DEPICT. We present the prioritized genes, enriched gene sets, and enriched tissues identified by DEPICT at the standard FDR threshold of 5%.
There are T traits, which may be binary or quantitative. We standardize each trait and the genotype for each single-nucleotide polymorphism (SNP) j so that they all have mean zero and variance one. The length- T vector of marginal (i.e., not controlling for other SNPs), true effects of SNP j on each of the traits is denoted β j. We assume that these are random effects with mean 0 and variance-covariance matrix Ω that is the same across j. The mean is zero because we treat the choice of reference allele as arbitrary. We make the common assumption,, that the β j 's are identically distributed across j. The assumption implies that the expected amount of phenotypic variance explained is equal for each SNP, regardless of SNP characteristics such as allele frequency.
This special case corresponds to the "traits" being (the same measure of) a single trait; in other words, applying MTAG instead of inverse-variance-weighted meta-analysis to T GWAS results. Doing so can be useful if there is sample overlap in the GWAS results. In this case, as noted in the main text, MTAG specializes to β ^ MTAG, j, t = 1 ′ ∑ j - 1 1 ′ ∑ j - 1 1 β ^ j for all t, and it is no longer necessary to estimate Ω.
Machine-readable layer
[
{
"@context": "https://schema.org",
"@type": "HowTo",
"name": "Multi-trait analysis of genome-wide association summary statistics using MTAG methods",
"description": "Protocol for Multi-trait analysis of genome-wide association summary statistics using MTAG methods",
"step": [
{
"@type": "HowToStep",
"position": 1,
"name": "MTAG Framework",
"text": "In the framework that follows, all traits and genotypes are standardized to have mean zero and variance one. For SNP j, we denote the vector of marginal (i.e., not controlling for other SNPs), true effects on each of the T traits by β j. We treat these true effects as random effects with E ( β j ) = 0 and Var ( β j ) = Ω. If the true effects are correlated across traits, then the off-diagonal elements of Ω are non-zero. MTAG's key assumption is that Ω is homogeneous across SNPs, i.e., it does not depend on j."
},
{
"@type": "HowToStep",
"position": 2,
"name": "Polygenic Prediction",
"text": "We measure the predictive power of each polygenic score by its incremental R 2, defined as the increase in coefficient of determination ( R 2 ) as we move from a regression of the trait only on a set of controls (year of birth, year of birth squared, sex, their interactions, and 10 principal components of the genetic data) to a regression that additionally includes the polygenic score as an independent variable."
},
{
"@type": "HowToStep",
"position": 3,
"name": "Biological Annotation",
"text": "For a final comparison, we analyze both the GWAS and MTAG results using the bioinformatics tool DEPICT. We present the prioritized genes, enriched gene sets, and enriched tissues identified by DEPICT at the standard FDR threshold of 5%."
},
{
"@type": "HowToStep",
"position": 4,
"name": "ONLINE METHODS",
"text": "There are T traits, which may be binary or quantitative. We standardize each trait and the genotype for each single-nucleotide polymorphism (SNP) j so that they all have mean zero and variance one. The length- T vector of marginal (i.e., not controlling for other SNPs), true effects of SNP j on each of the traits is denoted β j. We assume that these are random effects with mean 0 and variance-covariance matrix Ω that is the same across j. The mean is zero because we treat the choice of reference allele as arbitrary. We make the common assumption,, that the β j 's are identically distributed across j. The assumption implies that the expected amount of phenotypic variance explained is equal for each SNP, regardless of SNP characteristics such as allele frequency."
},
{
"@type": "HowToStep",
"position": 5,
"name": "Perfect genetic correlation and equal heritabilities",
"text": "This special case corresponds to the \"traits\" being (the same measure of) a single trait; in other words, applying MTAG instead of inverse-variance-weighted meta-analysis to T GWAS results. Doing so can be useful if there is sample overlap in the GWAS results. In this case, as noted in the main text, MTAG specializes to β ^ MTAG, j, t = 1 ′ ∑ j - 1 1 ′ ∑ j - 1 1 β ^ j for all t, and it is no longer necessary to estimate Ω."
}
],
"tool": [],
"supply": [],
"isBasedOn": {
"@type": "ScholarlyArticle",
"headline": "Multi-trait analysis of genome-wide association summary statistics using MTAG",
"datePublished": "2018",
"author": [
{
"@type": "Person",
"name": "Patrick Turley"
},
{
"@type": "Person",
"name": "Raymond K. Walters"
},
{
"@type": "Person",
"name": "Omeed Maghzian"
},
{
"@type": "Person",
"name": "Aysu Okbay"
},
{
"@type": "Person",
"name": "James J. Lee"
},
{
"@type": "Person",
"name": "Mark Alan Fontana"
},
{
"@type": "Person",
"name": "Tuan Anh Nguyen-Viet"
},
{
"@type": "Person",
"name": "Robbee Wedow"
},
{
"@type": "Person",
"name": "Meghan Zacher"
},
{
"@type": "Person",
"name": "Nicholas A. Furlotte"
},
{
"@type": "Person",
"name": "Patrik Magnusson"
},
{
"@type": "Person",
"name": "Sven Oskarsson"
},
{
"@type": "Person",
"name": "Magnus Johannesson"
},
{
"@type": "Person",
"name": "Peter M. Visscher"
},
{
"@type": "Person",
"name": "David Laibson"
},
{
"@type": "Person",
"name": "David Cesarini"
},
{
"@type": "Person",
"name": "Benjamin M. Neale"
},
{
"@type": "Person",
"name": "Daniel J. Benjamin"
}
],
"identifier": "10.1038/s41588-017-0009-4"
}
},
{
"@context": "https://schema.org",
"@type": "BreadcrumbList",
"itemListElement": [
{
"@type": "ListItem",
"position": 1,
"name": "Experiments",
"item": "https://replicatescience.com/experiments"
},
{
"@type": "ListItem",
"position": 2,
"name": "Multi-trait analysis of genome-wide association summary statistics using MTAG methods",
"item": "https://replicatescience.com/experiments/multi-trait-analysis-of-genome-wide-association-summary-statistics-using-mtag-methods-patrick-turley-pmc5805593/multi-trait-analysis-of-genome-wide-association-summary-statistics-using-mtag-mlpgy8ee"
}
]
}
]