calculate effect size and se from z scores

eff_from_z.R

get_beta_se_from_p_z_n_vary <- function(z, n, vy, maf)
{
	qval <- qchisq(pnorm(abs(z), low=FALSE)*2, 1, low=F) / (qchisq(pnorm(abs(z), low=FALSE)*2, n-2, low=F)/(n-2))
	r <- sqrt(sum(qval / (n - qval)))
	b <- sign(z) * sqrt(r^2 * vy / (2*maf*(1-maf)))
	se <- b / z
	return(list(b=b, se=se))
}


n <- 100000
x <- rbinom(n, 2, 0.2)
y <- rnorm(n) * 50 + x

mod <- summary(lm(y ~ x))

z <- mod$coefficients[2,1] / mod$coefficients[2,2]
p <- mean(x)/2
vy <- var(y)

get_beta_se_from_p_z_n_vary(z, n, var(y), p)
mod$coefficients