Interpretable eQTL Effect Sizes Using a Log of Linear Model"

In ACMEeqtl: Estimation of Interpretable eQTL Effect Sizes Using a Log of Linear Model

# knitr::opts_chunk$set(echo = TRUE)

Introduction

We present a package for estimation of cis-eQTL effect sizes, using a new model called ACME which respects biological understanding of cis-eQTL action. The model, fully presented and validated in [@palowitch2017estimation], involves an additive effect of allele count and multiplicative component random noise (hence "ACME": Additive-Contribution, Multiplicative-Error), and is defined as

$$y_i = \log(\beta_0 + \beta_1 s_i) + Z_i^T \gamma + \epsilon_i$$

where

• $y_i$ -- log-transformed normalized gene read count from sample $i$
• $s_i$ -- minor allele count for the SNP of sample $i$
• $Z_i$ -- the $p \times 1$ vector of covarites for the sample $i$
• $\beta_0$ -- unknown "baseline" mean of raw expression
• $\beta_1$ -- unknown linear contribution of $s_i$ on the raw expression
• $\gamma$ -- unknown $p \times 1$ covariate coefficient
• $\epsilon_i$ -- noise

We estimate the model using a fast iterative algorithm.\ The algorithm estimates the model which is nonlinear only with respect to $\eta = \beta_1 / \beta_0$

$$y_i = \log(1 + s_i \eta) + \log(\beta_0) + Z_i^T \gamma + \epsilon_i$$

Installation

ACMEeqtl can be installed with the following command.

install.packages("ACMEeqtl")

Using the Package

ACMEeqtl package provides functions for analysis of a single gene-SNP pair as well as fast parallel testing of all local gene-SNP pairs.

library(pander)
panderOptions("digits", 3)
library(ACMEeqtl)

library(ACMEeqtl)

Testing a Single Gene-SNP Pair

First we generate sample gene expression, SNP allele counts, and a set of covariates.

# Model parameters
beta0 = 10000
beta1 = 50000

# Data dimensions
nsample = 1000
ncvrt = 19

### Data generation
### Zero average covariates
cvrt = matrix(rnorm(nsample * ncvrt), nsample, ncvrt)
cvrt = t(t(cvrt) - colMeans(cvrt))

# Generate SNPs
s = rbinom(n = nsample, size = 2, prob = 0.2)

# Generate log-normalized expression
y = log(beta0 + beta1 * s) + 
    cvrt %*% rnorm(ncvrt) + 
    rnorm(nsample)

We provide two equivalent functions for model estimation.

• effectSizeEstimationR -- fully coded in R
• effectSizeEstimationC -- faster version with core coded in C.

z1 = effectSizeEstimationR(s, y, cvrt)
z2 = effectSizeEstimationC(s, y, cvrt)

pander(rbind(z1,z2))

Variables z1, z2 show that the estimation was done in r z1[3] iterations, with estimated parameters

• $\hat\beta_0$ = r as.character(round(z1[1],1)) (true parameter is r as.character(beta0))
• $\hat\beta_1$ = r as.character(round(z1[2],1)) (true parameter is r as.character(beta1))

Testing All Local Gene-SNP Pairs

First we generate a eQTL dataset in filematrix format (see filematrix package).

tempdirectory = tempdir()
z = create_artificial_data(
    nsample = 100,
    ngene = 100,
    nsnp = 501,
    ncvrt = 1,
    minMAF = 0.2,
    saveDir = tempdirectory,
    returnData = FALSE,
    savefmat = TRUE,
    savetxt = FALSE,
    verbose = FALSE)

In this example, we use 2 CPU cores (threads) for testing of all gene-SNP pairs within 100,000 bp.

multithreadACME(
    genefm = "gene",
    snpsfm = "snps",
    glocfm = "gene_loc",
    slocfm = "snps_loc",
    cvrtfm = "cvrt",
    acmefm = "ACME",
    cisdist = 1.5e+06,
    threads = 2,
    workdir = file.path(tempdirectory, "filematrices"),
    verbose = FALSE)

Now the filematrix ACME holds estimations for all local gene-SNP pairs.

fm = fm.open(file.path(tempdirectory, "filematrices", "ACME"))
TenResults = fm[,1:10]
rownames(TenResults) = rownames(fm)
close(fm)

pander(t(TenResults))

Testing Multi-SNP Model for All Local Gene-SNP Pairs

Now we can estimate multi-SNP ACME models for each gene:

multisnpACME(
    genefm = "gene",
    snpsfm = "snps",
    glocfm = "gene_loc",
    slocfm = "snps_loc",
    cvrtfm = "cvrt",
    acmefm = "ACME",
    workdir = file.path(tempdirectory, "filematrices"),
    genecap = Inf,
    verbose = FALSE)

Now the filematrix ACME_multiSNP holds estimations for all multi-SNP models.

fm = fm.open(file.path(tempdirectory, "filematrices", "ACME_multiSNP"))
TenResults = fm[,1:10]
rownames(TenResults) = rownames(fm)
close(fm)

pander(t(TenResults))

Note that each multi-SNP model will contain at least one SNP, even if that initial SNP was not significant under the single-SNP models. This initial SNP will be the one with the highest adjusted-R$^2$ value among the single-SNP models. However, after the initial SNP, further SNPs are added only if the combined model's adjusted-R$^2$ is greater than that from the previous combined model.

References

ACMEeqtl documentation built on May 2, 2019, 4:03 p.m.