GRSxE is a software package for detecting GxE (gene-environment) interactions using GRS (genetic risk scores). A GRS is constructed on the data and evaluated for testing an interaction with an environmentalm exposure while adjusting for potential confounders. The GRS is constructed using bagging and evaluated performing OOB (out-of-bag) predictions such that the full data set can be used for both GRS construction and GxE interaction testing.

You can install the released version of GRSxE from CRAN with:

`install.packages("GRSxE")`

Here is an example of an epidemiological toy data set consisting of some SNPs, an environmental covariable and a quantitative outcome/phenotype.

`library(GRSxE)`

```
set.seed(101299)
<- 0.25
maf <- 50
n.snps <- 2000
N <- matrix(sample(0:2, n.snps * N, replace = TRUE,
X prob = c((1-maf)^2, 1-(1-maf)^2-maf^2, maf^2)), ncol = n.snps)
colnames(X) <- paste("SNP", 1:n.snps, sep="")
<- rnorm(N, 20, 10)
E < 0] <- 0 E[E
```

For illustration purposes, an outcome involving a GxE interaction and an outcome not containing a GxE interaction are constructed and analyzed.

```
<- -0.75 + log(2) * (X[,"SNP1"] != 0) +
y.GxE log(4) * E/20 * (X[,"SNP2"] != 0 & X[,"SNP3"] == 0) +
rnorm(N, 0, 2)
```

```
<- -0.75 + log(2) * (X[,"SNP1"] != 0) +
y.no.GxE log(4) * E/20 + log(4) * (X[,"SNP2"] != 0 & X[,"SNP3"] == 0) +
rnorm(N, 0, 2)
```

The GxE test can now be performed by applying the `GRSxE`

function. Since a GLM (generalized linear model) is returned, detailed
results can be retrieved through `summary(...)`

.

First, the outcome involving a GxE interaction is tested.

```
summary(GRSxE(X, y.GxE, E))
#>
#> Call:
#> glm(formula = as.formula(form), family = glm.family, data = dat)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -7.3934 -1.2871 -0.0123 1.3691 6.8683
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.513301 0.103061 -4.981 6.88e-07 ***
#> G 0.521352 0.280726 1.857 0.0634 .
#> E 0.028518 0.004626 6.165 8.52e-10 ***
#> G:E 0.055216 0.012654 4.363 1.35e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 3.871335)
#>
#> Null deviance: 8574.0 on 1999 degrees of freedom
#> Residual deviance: 7727.2 on 1996 degrees of freedom
#> AIC: 8388.9
#>
#> Number of Fisher Scoring iterations: 2
```

The corresponding p-value (`G:E`

) is very low, indicating
there is a GxE interaction.

Next, the outcome not containing a GxE interaction is tested.

```
summary(GRSxE(X, y.no.GxE, E))
#>
#> Call:
#> glm(formula = as.formula(form), family = glm.family, data = dat)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -7.609 -1.439 -0.022 1.446 6.906
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -1.9775535 0.3784215 -5.226 1.92e-07 ***
#> G 1.5660013 0.2953620 5.302 1.27e-07 ***
#> E 0.0634424 0.0172752 3.672 0.000247 ***
#> G:E 0.0002192 0.0135055 0.016 0.987054
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 4.453263)
#>
#> Null deviance: 10339.6 on 1999 degrees of freedom
#> Residual deviance: 8888.7 on 1996 degrees of freedom
#> AIC: 8669
#>
#> Number of Fisher Scoring iterations: 2
```

The corresponding p-value (`G:E`

) is rather high, leaving
no evidence that there might be a GxE interaction.