Convert 95% confidence interval (estimate, odds ratio, risk ratio or hazard ratio) to a p-value

convert-confidence-interval-to-p-value.r

# Convert a 95% confidence interval to a p-value (two-sided).
# Based on:
# How to obtain the P value from a confidence interval
# BMJ 2011; 343 doi: https://doi.org/10.1136/bmj.d2304 

# From estimate to p-value.
estimate.to.pvalue <- function(estimate, lower, upper) {
  stderror = (upper - lower) / (2 * 1.96)      # Get standard error.
  z = estimate / stderror                      # Get test statistic.
  p.value = exp(-0.717 * z - 0.416 * (z ^ 2))  # Get p-value.
  return(p.value)
}

# From odds ratio, risk ratio, and hazard ratio to p-value.
ratio.to.pvalue <- function(estimate, lower, upper) {
  stderror <- (log(upper) - log(lower)) / (2 * 1.96)
  z <- abs(log(estimate) / stderror)
  p.value <- exp(-0.717 * z - 0.416 * z ^ 2)
  return(p.value)
}

# 1.9, 95% CI [−0.6, 4.3] to p-value = 0.123.
estimate.to.pvalue(estimate=1.9, lower=-0.6, upper=4.3)

# 0.81, 95% CI [0.70, 0.94] to p-value = 0.005.
ratio.to.pvalue(estimate=0.81, lower=0.70, upper=0.94)