SPAGxE+

SPAGxE+ is a scalable and accurate G×E analytical framework that controls for sample relatedness and unbalanced phenotypic distribution.

Introduction of SPAGxE+

SPAGxE+ is applicable to a wide range of complex traits with intricate structures, including binary, quantitative, time-to-event, ordinal categorical, longitudinal, and other complex traits. The framework involves two main steps:

Step 1: SPAGxE+ fits a covariates-only model to calculate model residuals. These covariates include, but are not limited to, confounding factors such as age, sex, SNP-derived principal components (PCs), and environmental factors. The specifics of the model and residuals vary depending on the trait type. Since the covariates-only model is genotype-independent, it only needs to be fitted once across a genome-wide analysis. Incorporating random effects to account for sample relatedness in null model fitting is optional, rather than required.
Step 2: SPAGxE+ identifies genetic variants with marginal G×E effects on the trait of interest. First, marginal genetic effects are tested using score statistics. If the marginal genetic effect is not significant, S_G×E is used as the test statistic to characterize the marginal G×E effect. If significant, S_G×E is updated to genotype-adjusted test statistics. To balance computational efficiency and accuracy, SPAGxE+ employs a hybrid strategy combining normal distribution approximation and SPA to calculate p-values, as used in SPAGxE_CCT and previous studies such as SAIGE and SPAGE.

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Main features of SPAGxE+

Currently, there is still a lack of scalable and accurate gene-environmental interaction analytical frameworks that can control for sample relatedness and be applicable to binary, time-to-event, ordinal categorical, or longitudinal trait analysis. It is usually challenging to detect gene-environmental interaction effects efficiently and accurately while adjusting for sample relateness in a large-scale genome-wide analysis. In GWAS for thousands of phenotypes in large biobanks, most binary traits have substantially fewer cases than controls. Existing methods based on logistic mixed model produce inflated type I errors in the presence of unbalanced case-control ratios.

SPAGxE+ is a scalable and accurate G×E analytical framework that uses saddlepoint approximation to calibrate the null distribution of test statistics while controlling for sample relatedness and case-control imbalance.

Compared to SPAGxE, a sparse genetic relationship matrix (GRM) is used for characterizing familial structure.
SPAGxE+ provides accurate p-values even when case-control ratios are extremely unbalanced (e.g. case:control = 1:99).
SPAGxE+ is applicable to other complex traits including time-to-event, ordinal categorical, and longitudinal traits, and it maintains highly accuracy even when phenotypic distribution is unbalanced.

Quick start-up examples (genotype input using R matrix format)

The following example illustrates how to use SPAGxE+ to analyze a binary trait, with genotype data input provided in the R matrix format.

Step 1. Read in data and fit a genotype-independent model

library(SPAGxECCT)
# load in binary phenotype, genotype, and sparseGRM
data("Phen.mtx.SPAGxEPlus.binary")
data("sparseGRM.SPAGxEPlus")
data("GenoMat.SPAGxEPlus")

Phen.mtx = Phen.mtx.SPAGxEPlus.binary    # phenotype data
E = Phen.mtx$E                           # environmental factor
Cova.mtx = Phen.mtx[,c("Cov1","Cov2")]   # Covariate matrix excluding environmental factor

### fit a genotype-independent model for the SPAGxE+ analysis
obj.SPAGxE_Plus_Nullmodel = SPAGxE_Plus_Nullmodel(traits = "binary",
                                                  Y ~ Cov1+Cov2+E,family=binomial(link="logit"),
                                                  data = Phen.mtx,
                                                  pIDs = Phen.mtx$IID,
                                                  gIDs = rownames(GenoMat.SPAGxEPlus),
                                                  sparseGRM = sparseGRM.SPAGxEPlus,
                                                  E = E)

Step 2. Conduct a marker-level association study

# calculate p values
binary.res = SPAGxE_Plus(Geno.mtx = GenoMat.SPAGxEPlus,
                         E = E,
                         Phen.mtx = Phen.mtx,
                         Cova.mtx = Cova.mtx,
                         obj.SPAGxE_Plus_Nullmodel = obj.SPAGxE_Plus_Nullmodel)

binary.res = as.data.frame(binary.res)

# we recommand using column of 'p.value.spaGxE.plus' as p-values testing for marginal GxE effect
head(binary.res)

Quick start-up examples (genotype input using PLINK file format)

The following example illustrates how to use SPAGxE+ to analyze a binary trait, with genotype data input provided in PLINK file format.

Step 1. Read in data and fit a genotype-independent model

library(SPAGxECCT)
# load in binary phenotype, genotype, and sparseGRM
data("Phen.mtx.SPAGxEPlus.binary")
data("sparseGRM.SPAGxEPlus")

Phen.mtx = Phen.mtx.SPAGxEPlus.binary                                         # phenotype data
E = Phen.mtx$E                                                                # environmental factor
Cova.mtx = Phen.mtx[,c("Cov1","Cov2")]                                        # Covariate matrix excluding environmental factor
GenoFile = system.file("", "GenoMat_SPAGxE_Plus.bed", package = "SPAGxECCT")  # PLINK format for genotype data

### fit a genotype-independent model for the SPAGxE+ analysis
obj.SPAGxE_Plus_Nullmodel = SPAGxE_Plus_Nullmodel(traits = "binary",
                                                  Y ~ Cov1+Cov2+E,family=binomial(link="logit"),
                                                  data = Phen.mtx,
                                                  pIDs = Phen.mtx$IID,
                                                  gIDs = rownames(GenoMat.SPAGxEPlus),
                                                  sparseGRM = sparseGRM.SPAGxEPlus,
                                                  E = E)

Step 2. Conduct a marker-level association study

# calculate p values
binary.res = SPAGxE_Plus(GenoFile = GenoFile,
                         E = E,
                         Phen.mtx = Phen.mtx,
                         Cova.mtx = Cova.mtx,
                         obj.SPAGxE_Plus_Nullmodel = obj.SPAGxE_Plus_Nullmodel)

binary.res = as.data.frame(binary.res)

# we recommand using column of 'p.value.spaGxE.plus' as p-values testing for marginal GxE effect
head(binary.res)

Quick start-up examples (genotype input using BGEN file format)

The following example illustrates how to use SPAGxE+ to analyze a binary trait, with genotype data input provided in BGEN file format.

Step 1. Read in data and fit a genotype-independent model

library(SPAGxECCT)
# load in binary phenotype, genotype, and sparseGRM
data("Phen.mtx.SPAGxEPlus.binary")
data("sparseGRM.SPAGxEPlus")

Phen.mtx = Phen.mtx.SPAGxEPlus.binary         # phenotype data
E = Phen.mtx$E                                # environmental factor
Cova.mtx = Phen.mtx[,c("Cov1","Cov2")]        # Covariate matrix excluding environmental factor

# BGEN format for genotype data
GenoFile = system.file("", "GenoMat_SPAGxE_Plus.bgen", package = "SPAGxECCT")
GenoFileIndex = c(system.file("", "GenoMat_SPAGxE_Plus.bgen.bgi", package = "SPAGxECCT"),
                  system.file("", "GenoMat_SPAGxE_Plus.sample", package = "SPAGxECCT"))

### fit a genotype-independent model for the SPAGxE+ analysis
obj.SPAGxE_Plus_Nullmodel = SPAGxE_Plus_Nullmodel(traits = "binary",
                                                  Y ~ Cov1+Cov2+E,family=binomial(link="logit"),
                                                  data = Phen.mtx,
                                                  pIDs = Phen.mtx$IID,
                                                  gIDs = rownames(GenoMat.SPAGxEPlus),
                                                  sparseGRM = sparseGRM.SPAGxEPlus,
                                                  E = E)

Step 2. Conduct a marker-level association study

# calculate p values
binary.res = SPAGxE_Plus(GenoFile = GenoFile,
                         GenoFileIndex = GenoFileIndex,
                         E = E,
                         Phen.mtx = Phen.mtx,
                         Cova.mtx = Cova.mtx,
                         obj.SPAGxE_Plus_Nullmodel = obj.SPAGxE_Plus_Nullmodel)

binary.res = as.data.frame(binary.res)

# we recommand using column of 'p.value.spaGxE.plus' as p-values testing for marginal GxE effect
head(binary.res)

Citation

A scalable and accurate framework for large-scale genome-wide gene-environment interaction analysis and its application to time-to-event and ordinal categorical traits (to be updated).