R/ratio.prop.is.R

In cwendorf/dgb: DGB

# DGB
## Ratio of Proportions from Two (Independent) Samples

ci.ratio.prop.is <- function(alpha, f1, f2, n1, n2) {
 # Computes adjusted Wald confidence interval for ratio of
 # population proportions in 2-group design
 # Arguments:
 #   alpha:  alpha level for 1-alpha confidence
 #   f1:     number of participants in group 1 with attribute
 #   f2:     number of participants in group 2 with attribute
 #   n1:     sample size of group 1
 #   n2:     sample size of group 2
 # Values:
 #   proportions, lower limit, upper limit
 z <- qnorm(1 - alpha/2)
 mle1 <- f1/n1
 mle2 <- f2/n2
 p1 <- (f1 + 1/4)/(n1 + 7/4)
 p2 <- (f2 + 1/4)/(n2 + 7/4)
 v1 <- 1/(f1 + 1/4 + (f1 + 1/4)^2/(n1 - f1 + 3/2))
 v2 <- 1/(f2 + 1/4 + (f2 + 1/4)^2/(n2 - f2 + 3/2))
 se <- sqrt(v1 + v2)
 LL <- exp(log(p1/p2) - z*se)
 UL <- exp(log(p1/p2) + z*se)
 out <- t(c(mle1, mle2, LL, UL))
 colnames(out) <- c("prop1", "prop2", "LL", "UL")
 return(out)
}

size.ci.ratio.prop.is <- function(alpha, p1, p2, r) {
 # Computes sample size per group required to estimate a ratio
 # of proportions in 2-group design with desired precision
 # Arguments: 
 #   alpha:  alpha level for 1-alpha confidence 
 #   p1:     planning value of proportion for group 1
 #   p2:     planning value of proportion for group 2
 #   r:      desired upper to lower interval endpoint ratio
 # Values:
 #   required sample size
 z <- qnorm(1 - alpha/2)
 n <- ceiling(4*((1 - p1)/p1 + (1 - p2)/p2)*(z/log(r))^2)
 return(n)
}