Package 'corrcoverage'

Internal function: Simulate nrep ABFs from joint Z-score vector

Description

Does not include posterior probabilities for null model

Usage

.zj_abf(Zj, int.Sigma, int.nrep, int.ERR, int.r)

Arguments

Zj	joint z vector
int.Sigma	internal sigma
int.nrep	internal nrep
int.ERR	internal error matrix
int.r	internal r

Value

Matrix of simulated ABFs, one simulation per row

---

Simulate posterior probabilities of causality from joint Z-score vector

Description

Internal function: Simulate nrep posterior probabilities of causality from joint Z-score vector

Usage

.zj_pp(Zj, int.Sigma, int.nrep, int.ERR, int.r)

Arguments

Zj	joint z vector
int.Sigma	internal sigma
int.nrep	internal nrep
int.ERR	internal error matrix
int.r	internal r

Details

Does not include posterior probabilities for null model

Value

Matrix of simulated posterior probabilties of causality, one simulation per row

---

Find approx. Bayes factors (ABFs)

Description

Wakefield's log asymptotic Bayes factor (lABF) with prior standard deviation of effect size as a parameter

Usage

approx.bf.p(pvals, f, type, N, s, W = 0.2)

Arguments

pvals	P-values
f	Minor allele frequencies
type	Type of experiment ('quant' or 'cc')
N	Total sample size
s	Proportion of cases (N1/N0+N1), ignored if type=='quant'
W	Prior for the standard deviation of the effect size parameter beta (W=0.2 default)

Details

([Wakefield et al. 2009](https://onlinelibrary.wiley.com/doi/abs/10.1002/gepi.20359) This function converts p-values to log ABFs, also reporting intermediate calculations

Value

data.frame containing lABF and intermediate calculations

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3)
p_values <- 2 * pnorm( - abs ( z_scores ) )

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
maf <- colMeans(X)

approx.bf.p(pvals = p_values, f = maf, type = "cc", N = N0+N1, s = N1/(N0+N1))

---

Calculate ABFs from Z scores

Description

Calculate ABFs from Z scores

Usage

bf_func(z, V, W = 0.2)

Arguments

z	Vector of Z-scores
V	Variance of the estimated effect size
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)

Details

Note, z and V should both be vectors or both be matrices

Value

ABFs

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3)

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
maf <- colMeans(X)

varbeta = Var.data.cc(f = maf, N = N0 + N1, s = 0.5)

bf_func(z_scores, V = varbeta)

---

Correlation matrix of SNPS

Description

Correlation matrix of SNPs

Usage

cor2(x)

Arguments

x	Phased haplotype matrix, rows as samples and columns as SNPs

Details

Quick function to find a correlation matrix

Value

Correlation matrix

Author(s)

Chris Wallace

---

Corrected coverage estimate using Z-scores and MAFs

Description

Corrected coverage estimate using Z-scores and mafs

Usage

corrcov(z, f, N0, N1, Sigma, thr, W = 0.2, nrep = 1000,
  pp0min = 0.001)

Arguments

z	Marginal Z-scores
f	Minor allele frequencies
N0	Number of controls
N1	Number of cases
Sigma	SNP correlation matrix
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
nrep	The number of simulated posterior probability systems to consider for the corrected coverage estimate (default 1000)
pp0min	Only average over SNPs with pp0 > pp0min

Details

This function only requires the marginal summary statistics from GWAS

Value

Corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3) # simulate a vector of Z-scores

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

corrcov(z = z_scores, f = maf, N0, N1, Sigma = LD, thr = 0.95)

---

Corrected coverage estimate using estimated effect sizes and their standard errors

Description

Corrected coverage estimate using estimated effect sizes and their standard errors

Usage

corrcov_bhat(bhat, V, N0, N1, Sigma, thr, W = 0.2, nrep = 1000,
  pp0min = 0.001)

Arguments

bhat	Estimated effect sizes from single-SNP logistic regressions
V	Variance of estimated effect sizes
N0	Number of controls
N1	Number of cases
Sigma	SNP correlation matrix
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
nrep	The number of simulated posterior probability systems to consider for the corrected coverage estimate (default 1000)
pp0min	Only average over SNPs with pp0 > pp0min

Details

This function only requires the marginal summary statistics from GWAS

Value

Corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps <- 100
N0 <- 1000 # number of controls
N1 <- 1000 # number of cases

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

varbeta <- Var.data.cc(f = maf, N = N0 + N1, s = N1/(N0+N1))

bhats = rnorm(nsnps, 0, 0.2) # log OR

corrcov_bhat(bhat = bhats, V = varbeta, N0, N1, Sigma = LD, thr = 0.95)

---

Confidence interval for corrected coverage estimate using Z-scores and MAFs

Description

Obtain confidence interval for corrected coverage estimate using Z-scores and mafs

Usage

corrcov_CI(z, f, N0, N1, Sigma, thr, W = 0.2, nrep = 1000, CI = 0.95,
  pp0min = 0.001)

Arguments

z	Marginal Z-scores
f	Minor allele frequencies
N0	Number of controls
N1	Number of cases
Sigma	SNP correlation matrix
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
nrep	The number of simulated posterior probability systems to consider for the corrected coverage estimate (nrep = 1000 default)
CI	The size of the confidence interval (as a decimal)
pp0min	Only average over SNPs with pp0 > pp0min

Value

CI for corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

# this is a long running example
set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3) # simulate a vector of Z-scores

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

corrcov_CI(z = z_scores, f = maf, N0, N1, Sigma = LD, thr = 0.95)

---

Confidence interval for corrected coverage estimate using estimated effect sizes and their standard errors

Description

Obtain confidence interval for corrected coverage estimate using estimated effect sizes and their standard errors

Usage

corrcov_CI_bhat(bhat, V, N0, N1, Sigma, thr, W = 0.2, nrep = 1000,
  CI = 0.95, pp0min = 0.001)

Arguments

bhat	Estimated effect sizes from single-SNP logistic regressions
V	Variance of estimated effect sizes
N0	Number of controls
N1	Number of cases
Sigma	SNP correlation matrix
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter beta
nrep	The number of simulated posterior probability systems to consider for the corrected coverage estimate (nrep = 1000 default)
CI	The size of the confidence interval (as a decimal)
pp0min	Only average over SNPs with pp0 > pp0min

Value

CI for corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

# this is a long running example
set.seed(1)
nsnps <- 100
N0 <- 5000 # number of controls
N1 <- 5000 # number of cases

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

varbeta <- Var.data.cc(f = maf, N = N0 + N1, s = N1/(N0+N1))

bhats = rnorm(nsnps,0,0.2) # log OR

corrcov_CI_bhat(bhat = bhats, V = varbeta, N0, N1, Sigma = LD)

---

Corrected coverage estimate using Z-scores and MAFs (fixing nvar)

Description

Obtain corrected coverage estimate using Z-scores and mafs (limiting simulations used for estimation to those with correct nvar)

Usage

corrcov_nvar(z, f, N0, N1, Sigma, nvar, thr, W = 0.2, nrep = 10000,
  pp0min = 0.001)

Arguments

z	Marginal Z-scores
f	Minor allele frequencies
N0	Number of controls
N1	Number of cases
Sigma	SNP correlation matrix
nvar	The number of variants that simulated credible sets used for estimation should contain
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
nrep	The number of simulated posterior probability systems to consider for the corrected coverage estimate (nrep = 10000 default due to trimming)
pp0min	Only average over SNPs with pp0 > pp0min

Details

This function requires the marginal summary statistics from GWAS and an nvar value. It should only be used when nvar is very low (<3) and there is some evidence to suggest that only simulated credible sets with this nvar value should be used to derive the corrected coverage estimate.

Value

Corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3) # simulate a vector of Z-scores

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

corrcov_nvar(z = z_scores, f = maf, N0, N1, Sigma = LD, thr = 0.95, nvar = 1, nrep = 100)

# note that nrep should be at least the default value (nrep = 10000) but is
# lower here for speed of computation

---

Corrected coverage estimate using estimated effect sizes and their standard errors (fixing nvar)

Description

Obtain corrected coverage estimate using estimated effect sizes and their standard errors (limiting simulations used for estimation to those with correct nvar)

Usage

corrcov_nvar_bhat(bhat, V, N0, N1, Sigma, nvar, thr, W = 0.2,
  nrep = 10000, pp0min = 0.001)

Arguments

bhat	Estimated effect sizes from single-SNP logistic regressions
V	Variance of estimated effect sizes
N0	Number of controls
N1	Number of cases
Sigma	SNP correlation matrix
nvar	The number of variants that simulated credible sets used for estimation should contain
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
nrep	The number of simulated posterior probability systems to consider for the corrected coverage estimate (nrep = 10000 default due to trimming)
pp0min	Only average over SNPs with pp0 > pp0min

Details

This function requires the marginal summary statistics from GWAS and an nvar value. It should only be used when nvar is very low ($<3$) and there is some evidence to suggest that only simulated credible sets with this nvar value should be used to derive the corrected coverage estimate.

Value

Corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps <- 100
N0 <- 5000 # number of controls
N1 <- 5000 # number of cases

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

varbeta <- Var.data.cc(f = maf, N = N0 + N1, s = N1/(N0+N1))

bhats = rnorm(nsnps,0,0.2) # log OR

corrcov_nvar_bhat(bhat = bhats, V = varbeta, N0, N1, Sigma = LD, thr = 0.95, nvar = 1, nrep = 1000)

# note that nrep should be at least the default value (nrep = 10000) but is
# lower here for speed of computation

---

Corrected coverage estimate of the causal variant in the credible set

Description

Corrected coverage estimate of the causal variant in the credible set

Usage

corrected_cov(pp0, mu, V, Sigma, thr, W = 0.2, nrep = 1000,
  pp0min = 0.001)

Arguments

pp0	Posterior probabilities of SNPs
mu	The true effect at the CV (estimate using corrcoverage::est_mu function)
V	Variance of the estimated effect size (can be obtained using coloc::Var.beta.cc function)
Sigma	SNP correlation matrix
thr	Minimum threshold for fine-mapping experiment
W	Prior for the standard deviation of the effect size parameter, beta (W=0.2 default)
nrep	Number of posterior probability systems to simulate for each variant considered causal (nrep = 1000 default)
pp0min	Only average over SNPs with pp0 > pp0min

Details

Requires an estimate of the true effect at the CV (e.g. use maximum absolute z-score or output from corrcoverage::est_mu function)

Value

Corrected coverage estimate

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps <- 100
N0 <- 5000
N1 <- 5000

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

## generate V (variance of estimated effect sizes)
varbeta <- Var.data.cc(f = maf, N = 5000, s = 0.5)

pp <- rnorm(nsnps, 0.2, 0.05)
pp <- pp/sum(pp)

corrected_cov(pp0 = pp, mu = 4, V = varbeta, Sigma = LD, thr = 0.95, nrep = 100)

---

Corrected credible set using Z-scores and MAFs

Description

Corrected credible set using Z-scores and MAFs

Usage

corrected_cs(z, f, N0, N1, Sigma, W = 0.2, lower = 0, upper = 1,
  desired.cov, acc = 0.005, max.iter = 20, pp0min = 0.001)

Arguments

z	Z-scores
f	Minor allele frequencies
N0	Number of controls
N1	Number of cases
Sigma	Correlation matrix of SNPs
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
lower	Lower threshold (default = 0)
upper	Upper threshold (default = 1)
desired.cov	The desired coverage of the causal variant in the credible set
acc	Accuracy of corrected coverage to desired coverage (default = 0.005)
max.iter	Maximum iterations (default = 20)
pp0min	Only average over SNPs with pp0 > pp0min

Value

List of variants in credible set, required threshold, the corrected coverage and the size of the credible set

Author(s)

Anna Hutchinson

Examples

# this is a long running example

# In this example, the function is used to find a corrected 95% credible set
# using Z-scores and MAFs, that is the smallest set of variants
# required such that the resultant credible set has coverage close to (/within
# some accuracy of) the "desired coverage" (here set to 0.95). Max.iter parameter
# defines the maximum number of iterations to try in the root bisection algorithm,
# this should be increased to ensure convergence to the desired coverage, but is set
# to 1 here for speed (and thus the resultant credible set will not be accurate).

set.seed(2)
nsnps = 200
N0 = 1000
N1 = 1000
z_scores <- rnorm(nsnps, 0, 1) # simulate a vector of Z-scores

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

names(z_scores) <- seq(1,length(z_scores))

corrected_cs(z = z_scores, f = maf, N0, N1, Sigma = LD, desired.cov = 0.9, max.iter = 1)
# max.iter set low for speed, should be set to at least
# the default to ensure convergence to desired coverage

---

Corrected credible set using estimated effect sizes and their standard errors

Description

Corrected credible set using estimated effect sizes and their standard errors

Usage

corrected_cs_bhat(bhat, V, N0, N1, Sigma, W = 0.2, lower = 0,
  upper = 1, desired.cov, acc = 0.005, max.iter = 20,
  pp0min = 0.001)

Arguments

bhat	Estimated effect sizes
V	Prior variance of estimated effect sizes
N0	Number of controls
N1	Number of cases
Sigma	Correlation matrix of SNPs
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
lower	Lower threshold (default = 0)
upper	Upper threshold (default = 1)
desired.cov	The desired coverage of the causal variant in the credible set
acc	Accuracy of corrected coverage to desired coverage (default = 0.005)
max.iter	Maximum iterations (default = 20)
pp0min	Only average over SNPs with pp0 > pp0min

Value

List of variants in credible set, required threshold, the corrected coverage and the size of the credible set

Author(s)

Anna Hutchinson

Examples

# this is a long running example

# In this example, the function is used to find a corrected 95% credible set
# using bhats and their standard errors, that is the smallest set of variants
# required such that the resultant credible set has coverage close to (/within
# some accuracy of) the "desired coverage" (here set to 0.95). Max.iter parameter
# defines the maximum number of iterations to try in the root bisection algorithm,
# this should be increased to ensure convergence to the desired coverage, but is set
# to 1 here for speed (and thus the resultant credible set will not be accurate).

set.seed(18)
nsnps <- 100
N0 <- 500 # number of controls
N1 <- 500 # number of cases

# simulate fake haplotypes to obtain MAFs and LD matrix
## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

varbeta <- Var.data.cc(f = maf, N = N0 + N1, s = N1/(N0+N1))

bhats = rnorm(nsnps,0,0.2) # log OR

names(bhats) <- seq(1,length(bhats))

corrected_cs_bhat(bhat = bhats, V = varbeta, N0, N1, Sigma = LD, desired.cov = 0.9, max.iter = 1)
# max.iter set low for speed, should be set to at
# least the default to ensure convergence to desired coverage

---

Credible set of genetic variants

Description

Credible set of putative causal variants

Usage

credset(pp, CV, thr)

Arguments

pp	Vector of posterior probabilities of causality
CV	Optional parameter: Index of CV
thr	Minimum threshold for credible set size

Details

If the CV parameter is supplied (index of causal variant) then the output includes a binary indicator of whether the CV is contained in the set

Value

list of the variants in the credible set, the claimed.cov (cumulative sum of the posterior probabilities of the variants forming the credible set), binary covered indicator (1 if CV is contained in the credible set) and nvar (number of variants in the set)

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps <- 100
pp <- rnorm(nsnps, 0.3, 0.05)
pp <- pp/sum(pp)

credset(pp, thr = 0.9)

iCV <- 71

credset(pp, CV = iCV, thr = 0.9)

---

Credible set of variants from matrix of PPs

Description

Quick credset function for matrix of posterior probabilities (using RCpp)

Usage

credsetC(pp, CV, thr)

Arguments

pp	Matrix of posterior probabilities of causality (one row per system)
CV	Vector of CV indices (one per system/row)
thr	Minimum threshold for credible set size

Value

Data.frame of claimed coverage (sum of posterior probabilities of variants in the set), binary covered indicator and number of variants (nvar).

Examples

set.seed(1)
nsnps <- 100

# simulate matrix of posterior probabilities
# 1 simulation per row

pp <- matrix(rnorm(nsnps*100, 0.3, 0.05), ncol = nsnps)
pp <- pp/rowSums(pp)

iCV <- rep(71, times = dim(pp)[1])

credsetC(pp, CV = iCV, thr = 0.9)

---

Obtain credible sets from a matrix of posterior probabilities

Description

Obtain credible sets from a matrix of posterior probabilities

Usage

credsetmat(pp, iCV, threshold)

Arguments

pp	Matrix of posterior probabilities (one row for each simulation)
iCV	A vector of the indices of the CV
threshold	The threshold to use to generate the credible set

---

Estimate the true effect at the causal variant using Z-scores and MAFs

Description

Estimate the true effect at the causal variant using Z-scores and MAFs

Usage

est_mu(z, f, N0, N1, W = 0.2)

Arguments

z	Vector of marginal Z-scores
f	Minor allele frequencies
N0	Number of controls
N1	Number of cases
W	Prior for the standard deviation of the effect size parameter, beta, default 0.2

Value

Estimate of the true effect at the causal variant

Author(s)

Anna Hutchinson

Examples

nsnps <- 100
z_scores <- rnorm(nsnps, 0, 3) # simulate a vector of Z-scores
N0 <- 5000 # number of controls
N1 <- 5000 # number of cases

maf <- runif(nsnps, 0.05, 0.5)

est_mu(z = z_scores, f = maf, N0 = N0, N1 = N1)

---

Estimate the true effect at the causal variant using estimated effect sizes and their standard errors

Description

Estimate the true effect at the causal variant using estimated effect sizes and their standard errors

Usage

est_mu_bhat(bhat, V, N0, N1, p1 = 1e-04, W = 0.2)

Arguments

bhat	Vector of estimated effect sizes
V	Prior variance for estimated effect sizes
N0	Number of controls
N1	Number of cases
p1	Prior probability a SNP is associated with the trait, default 1e-4
W	Prior for the standard deviation of the effect size parameter, beta

Value

Estimate of the true effect at the causal variant

Author(s)

Anna Hutchinson

Examples

nsnps <- 100
N0 <- 5000 # number of controls
N1 <- 5000 # number of cases

maf <- runif(nsnps, 0.05, 0.3)

varbeta <- Var.data.cc(f = maf, N = N0 + N1, s = N1/(N0+N1))

bhats = rnorm(nsnps,0,0.2) # log(OR)

est_mu_bhat(bhat = bhats, V = varbeta, N0 = N0, N1 = N1)

---

logsum

Description

Internal function, logsum

Usage

logsum(x)

Arguments

x	numeric vector

Details

This function calculates the log of the sum of the exponentiated logs taking out the max, i.e. insuring that the sum is not Inf

Value

max(x) + log(sum(exp(x - max(x))))

Author(s)

Chris Wallace

---

logsum rows of a matrix

Description

matrix-ified version of logsum to avoid needing apply()

Usage

logsum_matrix(x)

Arguments

x	numeric matrix

Value

rowwise sums

Author(s)

Chris Wallace

---

Find PPs of SNPs from Z-scores

Description

Posterior probabilities of causality from marginal Z-scores

Usage

ppfunc(z, V, W = 0.2)

Arguments

z	Vector of marginal Z-scores
V	Variance of the estimated effect size (can be obtained using Var.beta.cc function)
W	Prior for the standard deviation of the effect size parameter, beta (W = 0.2 default)

Details

This function converts Z-scores to posterior probabilities of causality i.e. not including the null model of no genetic effects, so that the sum of the posterior probabilities for all variants is 1

Value

Vector of posterior probabilities

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3)

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
maf <- colMeans(X)

varbeta <- Var.data.cc(f = maf, N = N0+N1, s = N1/(N0+N1))

res <- ppfunc(z = z_scores, V = varbeta)
sum(res)
res

---

Find PPs of SNPs from matrix of Z-scores

Description

Posterior probabilities of causality from matrix of marginal Z-scores (1 simulation per row)

Usage

ppfunc.mat(zstar, V, W = 0.2)

Arguments

zstar	Matrix of marginal z-scores, one replicate per row
V	Variance of the estimated effect size, one element per column of zstar
W	Prior for the standard deviation of the effect size parameter, beta

Details

This function converts a matrix of Z-scores (one row per simulation) to posterior probabilities of causality, not including the null model of no genetic effects, so that the sum of the posterior probabilities for each simulation (each row) is 1.

Value

Matrix of posterior probabilities of causality

Author(s)

Chris Wallace

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
maf <- colMeans(X)

varbeta <- Var.data.cc(f = maf, N = N0+N1, s = N1/(N0+N1))

# simulate matrix of Z scores
# 1 simulation per row
z_scores <- matrix(rnorm(nsnps*100, 0, 3), ncol = nsnps)

# each row is a vector of simulated PPs
res <- ppfunc.mat(zstar = z_scores, V = varbeta)

rowSums(res)

---

Proportion of credible sets containing the causal variant

Description

Proportion of simulated credible sets containing the causal variant

Usage

prop_cov(x)

Arguments

x	data.frame with a binary 'covered' column

Value

Proportion of x with x = 1

Author(s)

Anna Hutchinson

---

Find PPs for SNPs and null model from P-values and MAFs

Description

Posterior probabilities of causality from P-values

Usage

pvals_pp(pvals, f, type, N, s, W = 0.2, p1 = 1e-04)

Arguments

pvals	P-values of SNPs
f	Minor allele frequencies
type	Type of experiment ('quant' or 'cc')
N	Total sample size
s	Proportion of cases (N1/N0+N1), ignored if type=='quant'
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
p1	Prior probability a SNP is associated with the trait (default 1e-4)

Details

This function converts p-values to posterior probabilities of causality, including the null model of no genetic effect

Value

Posterior probabilities of null model (no genetic effect) and causality for each SNP

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3)
p_values <- 2 * pnorm( - abs ( z_scores ) )

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
maf <- colMeans(X)

res <- pvals_pp(pvals = p_values, f = maf, type = "cc", N = N0+N1, s = N1/(N0+N1))
sum(res)
res

---

Variance of the estimated effect size for case-control data

Description

Variance of the estimated effect size for case-control data

Usage

Var.data.cc(f, N, s)

Arguments

f	Minor allele frequencies
N	Total sample size (N0+N1)
s	Proportion of cases (N1/N0+N1)

Value

Variance of estimated effect size $\hat{\beta}$, V.

Author(s)

Chris Wallace

Examples

maf =  runif(100, 0.05, 0.5)
N0 = 5000 # number of controls
N1 = 5000 # number of cases

Var.data.cc(f = maf, N = N0 + N1, s = N1/(N0+N1))

---

Simulate marginal Z-scores from joint Z-score vector

Description

Simulate marginal z-scores ($Z_m$) from the joint z-scores ($Z_j$) using $E(Z_m) = Z_j \times \Sigma$ and $Z* \sim MVN(E(Z_m), \Sigma)$

Usage

z_sim(Zj, Sigma, nrep)

Arguments

Zj	Vector of joint Z-scores (a vector of 0s except at the CV)
Sigma	SNP correlation matrix
nrep	Number of Z-score systems to simulate

Value

Matrix of simulated posterior probabilties, one simulation per row

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps <- 100

# derive joint Z score vector
Zj <- rep(0, nsnps)
iCV <- 4 # index of CV
mu <- 5 # true effect at CV
Zj[iCV] <- mu

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)

res <- z_sim(Zj, Sigma = LD, nrep = 100)
res[c(1:5), c(1:5)]

---

Find PPs for SNPs and null model from Z-scores and MAFs

Description

Posterior probabilities of causality from marginal Z-scores with prior SD as a parameter

Usage

z0_pp(z, f, type, N, s, W = 0.2, p1 = 1e-04)

Arguments

z	Marginal Z-scores of SNPs
f	Minor allele frequencies
type	Type of experiment ('quant' or 'cc')
N	Total sample size
s	Proportion of cases (N1/N0+N1), ignored if type=='quant'
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
p1	Prior probability a SNP is associated with the trait (default 1e-4)

Details

Converts Z-scores to posterior probabilities of causality, including the null model of no genetic effects

Value

Posterior probabilities of null model (no genetic effect) and causality for each SNP

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps = 100
N0 = 5000
N1 = 5000
z_scores <- rnorm(nsnps, 0, 3)

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
maf <- colMeans(X)

res <- z0_pp(z = z_scores, f = maf, type = "cc", N = N0+N1, s = N1/(N0+N1))
sum(res)
res

---

Simulate posterior probabilities of causality from joint Z-score vector

Description

Simulate nrep marginal Z-scores from joint Z-scores and convert these to posterior probabilities of causality

Usage

zj_pp(Zj, V, nrep = 1000, W = 0.2, Sigma)

Arguments

Zj	Vector of joint Z-scores (0s except at CV)
V	Variance of the estimated effect size (can be obtained using Var.beta.cc function)
nrep	Number of posterior probability systems to simulate (default 1000)
W	Prior for the standard deviation of the effect size parameter, beta (default 0.2)
Sigma	SNP correlation matrix

Details

Does not include posterior probabilities for null model

Value

Matrix of simulated posterior probabilties, one simulation per row

Author(s)

Anna Hutchinson

Examples

set.seed(1)
nsnps <- 100
Zj <- rep(0, nsnps)
iCV <- 4 # index of CV
mu <- 5 # true effect at CV
Zj[iCV] <- mu

## generate example LD matrix and MAFs
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)
maf <- colMeans(X)

## generate V (variance of estimated effect sizes)
varbeta <- Var.data.cc(f = maf, N = 5000, s = 0.5)

res <- zj_pp(Zj, V = varbeta, nrep = 5, W = 0.2, Sigma = LD)

res[c(1:5), c(1:5)]

---

Obtain pp from a matrix of Zj and ERR

Description

Obtain pp from a matrix of Zj and ERR

Usage

zj_pp_arma(Zj, sigma, nrep, ERR, r)

Arguments

Zj	vector of joint Z scores
sigma	SNP correlation matrix
nrep	Number of simulations
ERR	Error matrix
r	Shrinkage values

Value

pp Matrix of posterior probabilities (one row for each simulation)

---