lit Package Vignette

Andrew J. Bass and Michael P. Epstein



The lit package implements a flexible kernel-based multivariate testing procedure, called Latent Interaction Testing (LIT), to detect latent genetic interactions in a genome-wide association study. In a standard GWAS analysis, one typically attempts to determine which SNPs are associated with one (or many) traits. Another important question is

This question has been very difficult to answer because effect sizes of interactions are likely small, interactive variables are unknown, and there’s often a large multiple testing burden from testing many candidate interactive variables.

One way to help address some of these issues is to use a variance-based testing procedure which does not require the interactive variable(s) to be specified or observed. These procedures can detect any unequal residual trait variation among genotype categories at a specific SNP (i.e., heteroskedasticity), which could suggest an unobserved (or latent) genetic interaction. However, researchers apply such procedures on a trait-by-trait basis and ignore any biological pleiotropy among traits. In fact, it is simple to show that a latent genetic interaction not only induces a variance effect but also a covariance effect between traits, and these covariance patterns can be harnessed to improve the statistical power.

The lit package addresses this gap by leveraging both the differential variance and differential covariance patterns to substantially increase power to detect latent genetic interactions in a GWAS. In particular, LIT assesses whether the trait variances/covariances vary as a function of genotype using a kernel-based distance covariance (KDC) framework. LIT often provides substantial increases in power compared to trait-by-trait univariate approaches, in part because LIT uses shared information (i.e., pleiotropy) across tests and does not require a multiple testing correction which negatively impacts power.

Note that this package contains the core functionality for the methods described in

Bass AJ, Bian S, Wingo AP, Wingo TS, Culter DJ, Epstein MP. Identifying latent genetic interactions in genome-wide association studies using multiple traits. Submitted; 2023.

Additional software features will be added in the future.


# install development version of package

Quick start

We provide two ways to use the lit package. For small GWAS datasets where the genotypes can be loaded in R, the lit() function can be used:

# set seed

# generate SNPs and traits
X <- matrix(rbinom(10 * 10, size = 2, prob = 0.25), ncol = 10)
Y <- matrix(rnorm(10 * 4), ncol = 4)

# test for latent genetic interactions
out <- lit(Y, X)
#>        wlit      ulit      alit
#> 1 0.2681410 0.3504852 0.3056363
#> 2 0.7773637 0.3504852 0.6044655
#> 3 0.4034423 0.3504852 0.3760632
#> 4 0.7874949 0.3504852 0.6157108
#> 5 0.8701189 0.3504852 0.7337565
#> 6 0.2352616 0.3504852 0.2847600

The output is a data frame of \(p\)-values where the rows are SNPs and the columns are different implementations of LIT to test for latent genetic interactions: the first column (wlit) uses a linear kernel, the second column (ulit) uses a projection kernel, and the third column (alit) maximizes the number of discoveries by combining the \(p\)-values of the linear and projection kernels.

For large GWAS datasets (e.g., biobank-sized), the lit() function is not computationally feasible. Instead, the lit_plink() function can be applied directly to plink files. To demonstrate how to use the function, we use the example plink files from the genio package:

# load genio package

# path to plink files
file <- system.file("extdata", 'sample.bed', package = "genio", mustWork = TRUE)

# generate trait expression
Y <- matrix(rnorm(10 * 4), ncol = 4)

# apply lit to plink file
out <- lit_plink(Y, file = file, verbose = FALSE)
#>   chr         id     pos alt ref       maf      wlit      ulit      alit
#> 1   1  rs3094315  752566   G   A 0.3888889 0.7908763 0.3422960 0.6150572
#> 2   1  rs7419119  842013   T   G 0.3888889 0.1552580 0.3422960 0.2194972
#> 3   1 rs13302957  891021   G   A 0.2500000 0.4088937 0.3325939 0.3687589
#> 4   1  rs6696609  903426   C   T 0.3125000 0.5857829 0.3325939 0.4519475
#> 5   1     rs8997  949654   A   G 0.4375000 0.6628300 0.3325939 0.4969663
#> 6   1  rs9442372 1018704   A   G 0.2500000 0.3192430 0.3325939 0.3258332

See ?lit and ?lit_plink for additional details and input arguments.

Note that a marginal testing procedure for latent genetic interactions based on the squared residuals and cross products (Marginal (SQ/CP)) can also be implemented using the marginal and marginal_plink functions:

# apply Marginal (SQ/CP) to loaded genotypes
out <- marginal(Y, X)

# apply Marginal (SQ/CP) to plink file
out <- marginal_plink(Y, file = file, verbose = FALSE)