# lit Package Vignette

#### Andrew J. Bass and Michael P. Epstein

#### 2023-08-12

## Overview

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

- Do any SNPs demonstrate any interactive effects, e.g., gene-by-gene or gene-by-environment interactions?

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.

## Installation

    # install development version of package
    install.packages("devtools")
    library("devtools")
    devtools::install_github("ajbass/lit")

## 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:

    library(lit)
    # set seed
    set.seed(123)

    # 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)
    head(out)
    #>        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
    library(genio)

    # 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)
    head(out)
    #>   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)