Find the full package documentation including examples and articles here: Multivariate MAPIT Documentation.

This R package is a generalization of the MAPIT implementation by Crawford et al. (2017)^{1} for any number of traits as described by Stamp et al. (2022)^{2}.

mvMAPIT is implemented as a set of R and C++ routines, which can be carried out within an R environment.

Epistasis, commonly defined as the interaction between genetic loci, is known to play an important role in the phenotypic variation of complex traits. As a result, many statistical methods have been developed to identify genetic variants that are involved in epistasis, and nearly all of these approaches carry out this task by focusing on analyzing one trait at a time. However, because of the large combinatorial search space of interactions, most epistasis mapping methods face enormous computational challenges and often suffer from low statistical power.

Previous studies have shown that jointly modeling multiple phenotypes can often dramatically increase statistical power for association mapping. Therefore, here we present the **multivariate MArginal ePIstasis Test (mvMAPIT)** – a multi-outcome generalization of a recently proposed epistatic detection method which seeks to detect *marginal epistasis* or the combined pairwise interaction effects between a given variant and all other variants. By searching for marginal epistatic effects, one can identify genetic variants that are involved in epistasis without the need to identify the exact partners with which the variants interact – thus, potentially alleviating much of the statistical and computational burden associated with conventional explicit search based methods. Our proposed mvMAPIT builds upon this strategy by leveraging correlation structures between traits to improve the identification of variants involved in epistasis. We formulate mvMAPIT as a multivariate linear mixed model and develop a multi-trait variance component estimation algorithm for efficient parameter inference and *P*-value computation. Together with reasonable model approximations, our proposed approach is scalable to moderately sized GWA studies.

The **multivariate MArginal ePIstasis Test** is a multi-outcome extension of the statistical framework MAPIT which aims to identify variants that are involved in epistatic interactions by leveraging the correlation structure of non-additive genetic variation that is shared between multiple traits. The key idea behind the concept of marginal epistasis is to identify variants that are involved in epistasis while avoiding the need to explicitly conduct an exhaustive search over all possible pairwise interactions. As an overview of mvMAPIT and its corresponding software implementation, we will assume that we have access to a GWA study on `N`

individuals denoted as `D = {X,Y}`

where `X`

is an `N x J`

matrix of genotypes with `J`

denoting the number of SNPs (each of which is encoded as `{0,1,2}`

copies of a reference allele at each locus `j`

) and `Y`

denoting a `N x D`

matrix holding `D`

different traits that are measured for each of the `N`

individuals.

The goal of mvMAPIT is to identify variants that have non-zero interaction effects with any other variant in the data. To accomplish this, we examine each SNP in turn and assess the null hypothesis that its corresponding variance component is zero. In practice, we use a computationally efficient method of moments algorithm called MQS from Zhou (2017)^{3} to estimate model parameters and to carry out calibrated statistical tests within mvMAPIT.

The package needs compilation but the released version can be installed from CRAN.

`install.packages("mvMAPIT")`

R is a widely used, free, and open source software environment for statistical computing and graphics. The most recent version of R can be downloaded from the Comprehensive R Archive Network (CRAN). CRAN provides precompiled binary versions of R for Windows, macOS, and select Linux distributions that are likely sufficient for many users’ needs. Users can also install R from source code; however, this may require a significant amount of effort. For specific details on how to compile, install, and manage R and R-packages, refer to the manual R Installation and Administration.

mvMAPIT requires the installation of the following R libraries:

- checkmate
- CompQuadForm
- dplyr
- foreach
- harmonicmeanp
- logging
- mvtnorm
- Rcpp
- RcppAlgos
- RcppArmadillo
- RcppParallel
- RcppSpdlog
- tidyr

The easiest method to install these packages is with the following example command entered in an R shell:

```
install.packages(c( 'checkmate',
'CompQuadForm',
'dplyr',
'foreach',
'harmonicmeanp',
'logging',
'mvtnorm',
'Rcpp',
'RcppAlgos',
'RcppArmadillo',
'RcppParallel',
'RcppSpdlog',
'testthat',
'tidyr'),
dependencies = TRUE);
```

Alternatively, one can also install R packages from the command-line.

The easiest way to install the package from sources is to change into the directory of mvMAPIT and run `R CMD INSTALL . --preclean`

. The `--preclean`

flag makes sure that the latest state is run.

The code in this repository assumes that basic Fortran and C++ libraries and compilers are already set up on the running personal computer or cluster. If not, the mvMAPIT functions and necessary Rcpp packages will not work properly. A simple option is to use gcc. macOS users may use this collection by installing the Homebrew package manager and then typing the following into the terminal:

`brew install gcc`

Note that mvMAPIT takes advantage of OpenMP, an API for multi-platform shared-memory parallel programming in C/C++. This is to speed up the computational time of the modeling algorithm. Unfortunately, macOS does not currently support OpenMP under the default compiler. A work around to use OpenMP in R on macOS can be found here. mvMAPIT can be compiled without OpenMP, but we recommend using it if applicable for scalability.

When your compiler changes, some R package dependencies might need to be recompiled. This is likely the case if the compilation error explicitly names an R package in the local library.

On macOS, you might need to run

`brew reinstall z3`

to fix`'libz3.4.11.dylib' (no such file)`

related errors (clang issues).For extra tips on how to run C++ on macOS, please visit https://seananderson.ca/2013/11/18/rcpp-mavericks.html.

For tips on how to avoid errors dealing with

`-lgfortran`

or`-lquadmath`

, please visit https://thecoatlessprofessor.com/programming/rcpp-rcpparmadillo-and-os-x-mavericks-lgfortran-and-lquadmath-error/.

For questions or concerns with the MAPIT functions, please contact Lorin Crawford or Julian Stamp.

We appreciate any feedback you may have with our repository and instructions.

L. Crawford, P. Zeng, S. Mukherjee, X. Zhou (2017). Detecting epistasis with the marginal epistasis test in genetic mapping studies of quantitative traits.

*PLoS Genet*.**13**(7): e1006869. https://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1006869↩︎J. Stamp, A. DenAdel, D. Weinreich, L. Crawford (2022). Leveraging the Genetic Correlation between Traits Improves the Detection of Epistasis in Genome-wide Association Studies. bioRxiv 2022.11.30.518547; doi: https://doi.org/10.1101/2022.11.30.518547↩︎

X. Zhou (2017). A unified framework for variance component estimation with summary statistics in genome-wide association studies.

*Ann Appl Stat*.**11**(4): 2027-2051. https://projecteuclid.org/journals/annals-of-applied-statistics/volume-11/issue-4/A-unified-framework-for-variance-component-estimation-with-summary-statistics/10.1214/17-AOAS1052.full↩︎