kappa_calc {gnonadd}

Genetic correlation effects

Description

This function estimates the correlation effect of a genetic variant on a pair of quantitative traits. The effect (kappa) is measured on Fisher transformed correlation values. The genotype is coded as 0 (non-carrier), 1 (single copy of effect allele) and 2 (two copies of effect allele). We use a likelihood ratio test with 1 degree of freedom: * H0: z_0 = z_1 = z_2, * H1: z_j = z_null +kappa*j, where z_j is the Fisher-transformed correlation between the traits amongst subjects of genotype j.

If the traits follow a joint normal distribution, then (thoretically) the Fisher-transformed sample correlation (z) is approximately normally distributed with mean 0 and standard error 1/sqrt(n-3). Otherwise, we have to correct for possible bias in the estimators and scale the weights we assign to them appropriately

Note, that even though each trait follows a normal distribution individually, that does not necessarily imply that the pair of them follow a joint normal distirbution.

Usage

kappa_calc(qt1, qt2, g, weight_scale = 1, bias_scale = 0)

Arguments

qt1

A numeric vector.

qt2

A numeric vector.

g

An integer vector.

weight_scale

Used to appropriately scale the weight assigned to the correlation estimators

bias_scale

Used to appropriately scale the bias of the correlation estimators

Value

A list with the values:

* kappa, the estimated correlation effect * pval, the p-value of the likelihood ratio test

Examples

Sigma0 <- matrix(c(1,0,0,1),nrow=2,ncol=2)
Sigma1 <- matrix(c(1,0.3,0.3,1),nrow=2,ncol=2)
Sigma2 <- matrix(c(1,0.6,0.6,1),nrow=2,ncol=2)
geno_vec <- c(rep(0,10000),rep(1,1000),rep(2,100))
Q0 <- MASS::mvrnorm(n = 10000, mu = c(0,0), Sigma = Sigma0)
Q1 <- MASS::mvrnorm(n = 1000, mu = c(0,0), Sigma = Sigma1)
Q2 <- MASS::mvrnorm(n = 100, mu = c(0,0), Sigma = Sigma2)
Q <- rbind(Q0,Q1)
Q <- rbind(Q,Q2)
qt1_val <- Q[,1]
qt2_val <- Q[,2]
res <- kappa_calc(qt1_val, qt2_val, geno_vec)