Estimate causal effect using two-sample MR

waldratio.R

# SNP-disease association - need effect size and standard error, can use log(OR) instead of effect size
y_or <- 1.244
y_upperconf <- 1.375
y_lowerconf <- 1.126

y_eff <- log(y_or)
y_se <- (log(y_upperconf) - log(y_lowerconf)) / (2*1.96)

# Alternative method from Shinn 2000, but uncertain what scale this transforms to
# y_eff <- log(y_or) / 1.81
# y_se <- (log(y_upperconf) - log(y_lowerconf)) / (2*1.96) / 1.81
 
# SNP-exposure association - effect size and standard error
x_eff <- -1.00
x_se <- 0.06

# Are the effects estimated from the same sample?
sample_overlap <- 0

# Estimate the approx causal log(OR) of disease per unit change of exposure
wald.ratio <- y_eff / x_eff

# Standard error using delta method
ratio.se <- sqrt(y_se^2/x_eff^2 + (y_eff^2/x_eff^4) * x_se^2 - 2 * (y_eff/x_eff^3) * sample_overlap)

wald.ratio
ratio.se

# p-value (assuming sample size 1000?)
pt(wald.ratio / ratio.se, 1000)