Sample Size for Two Correlated Proportions Based on McNemar Test

sample.size.for.two.correlated.proportions.test <- function(p.diff = 0.1, p.discordant = 0.2, alpha = 0.025, beta = 0.2)
{
    ## Purpose: Sample Size for Two Correlated Proportions Test based on McNemar Test
    ##   H0: p2 <= p1
    ##   H1: p2 >  p1
    ##   (Application: tests of sensitivity, specificity with three-way, matched-pairs study)
    ## Arguments:
    ##   p.diff: Effect size for the difference between two correlated proportions. Default to 10%. 
    ##   p.discordant: Proportion of pairs for which the responses differed. Default to 20%. 
    ##   alpha: type I error. Default to 0.025 (for one-sided test).
    ##   beta: type II error (1 - power). Default to 0.2 (so power is 80%). 
    ## Return:
    ##   Sample Size
    ## Author: Feiming Chen
    ## Reference: Machin, Campbell, Fayers, and Pinol (1997).
    ## ________________________________________________

    p10 <- (p.discordant + p.diff) / 2  # with default, p10 = 0.15
    p01 <- (p.discordant - p.diff) / 2  # default: p01 = 0.05
    OR <- p10 / p01                     # default: OR = 3
    OR.plus.one <- OR + 1               # default: 4
    OR.minus.one <- OR - 1              # default: 2
    
    N = (qnorm(1 - alpha) * OR.plus.one + qnorm(1 - beta) * sqrt(OR.plus.one^2 - OR.minus.one^2 * p.discordant))^2 / (OR.minus.one^2 * p.discordant)
    ceiling(N)
}
if (F) {                                # Unit Test
    sample.size.for.two.correlated.proportions.test() # 155 (PASS output: 155 under normal approx.)
}