#' Quick rates and confidence intervals
#'
#' This function creates rates and 1-alpha confidence intervals using the Rothman/Greenland method.
#' @param numerator The numerator of the rate.
#' @param denominator The denominator of the rate.
#' @param alpha The significance level for the confidence interval
#' @param multiplier The multiplier for the rate. Defaults to 100,000.
#' @keywords Rates
#' @export
#' @examples
#' rate_ci()
rate_ci<-function(numerator, denominator, alpha, multiplier=100000){
list(
(numerator/denominator)*multiplier,
exp(log((numerator/denominator)*multiplier)-(qnorm(alpha/2, lower.tail=FALSE)*(1/sqrt(numerator)))),
exp(log((numerator/denominator)*multiplier)+(qnorm(alpha/2, lower.tail=FALSE)*(1/sqrt(numerator))))
)
}
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