Confidence Interval of the Difference between Two Correlated Proportions (McNemar Test)

CI.diff.two.correlated.proportions <- function(A, B, C, D, alpha = 0.05)
{
    ## Purpose: CI of the difference between two correlated proportions (McNemar Test)
    ## Arguments:
    ##   A, B, C, D: the 2x2 incidence count table for the matched pairs. 
    ##               A = both positive;
    ##               B = treatment positive, control negative;
    ##               C = treatment negative; control positive;
    ##               D = both negative;
    ##   alpha: type I error. Default to 0.05 (for two-sided CI).
    ## Return: 95% Confidence Interval of the Difference
    ## Author: Feiming Chen
    ## Method: Wald Z Method with Continuity Correction
    ## Reference: Newcombe (1998c), page 2638.
    ## ________________________________________________

    N <- A + B + C + D                  # total number of matched pairs
    Delta <- (B - C) / N
    sw <- sqrt(((A + D) * (B + C) + 4 * B * C) / N^3)
    z <- qnorm(1 - alpha / 2)           # default: 1.96
    corr.term <- 1 / N                  # continuity correction 
    L <- Delta - z * sw - corr.term
    U <- Delta + z * sw + corr.term
    x <- matrix(c(A, B, C, D), 2, 2, byrow = TRUE, 
                dimnames = list(c("Test.POS", "Test.NEG"), c("Control.POS", "Control.NEG")))
    cat("Raw Data (x):\n")
    print(x)
    cat("\nData Converted to Proportions:\n")
    print(round(x/N, 2))
    cat("\nDifference of Two Paired Proportions =", round(Delta, 3), "\n")
    p.discordant <- (B+C) / N
    cat("Proportion of Discordant Pairs =", round(p.discordant, 3), "\n")
    N.future <- sample.size.for.two.correlated.proportions.test(Delta, p.discordant)
    cat("\nCurrent Sample Size =", N, "\n")
    cat("Future  Sample Size =", N.future, "\n")

    print(mcnemar.test(x))
    cat("\nConfidence Interval = (", round(L, 4), ",", round(U, 4), ")\n\n")
}
if (F) {                                # Unit Test
    CI.diff.two.correlated.proportions(12, 9, 2, 21) 
    ## Confidence Interval = ( -0.0037 , 0.3219 )
    CI.diff.two.correlated.proportions(25, 20, 5, 25) 
    ## Raw Data (x):
    ##          Control.POS Control.NEG
    ## Test.POS          25          20
    ## Test.NEG           5          25

    ## Data Converted to Proportions:
    ##          Control.POS Control.NEG
    ## Test.POS        0.33        0.27
    ## Test.NEG        0.07        0.33

    ## Difference of Two Paired Proportions = 0.2 
    ## Proportion of Discordant Pairs = 0.333 

    ## Current Sample Size = 75 
    ## Future  Sample Size = 63 

    ##  McNemar's Chi-squared test with continuity correction

    ## data:  x
    ## McNemar's chi-squared = 7.84, df = 1, p-value = 0.00511


    ## Confidence Interval = ( 0.0641 , 0.3359 )
}