Search for the sample size that produces a specific (lower) confidence limit

search.n.binary.proportion <- function(p, cl, alpha = 0.05)
{
    ## Purpose: Search for the sample size that produces a specific (lower) confidence limit.
    ## Arguments:
    ##   p: reported point estimate
    ##   cl: reported lowered confidence limit
    ##   alpha: type I error rate for two-sided confidence interval. Default to 5%. 
    ## Return: a conservative estimate for the 95% confidence interval
    ## Author: Feiming Chen
    ## ________________________________________________

    N <- 50                             # start at sample size of 50
    while (N < 2000) {                  # end at sample size of 1000
        x <- round(N * p)
        r <- prop.test(x, N, conf.level = 1 - alpha, correct = FALSE)
        cl2 <- r$conf.int[1]
        if (cl2 > cl) break
        N <- N + 1 
    }
    N <- N - 1
    x <- floor(N * p)
    cat("Sample Size =", N, ", X =", x, "\n")
    prop.test(x, N, conf.level = 0.95)
}
if (F) {                                # Unit Test
    search.n.binary.proportion(0.849, 0.804, alpha = 0.1)

    ## Sample Size = 194 , X = 164 

    ##  1-sample proportions test with continuity correction

    ## data:  x out of N, null probability 0.5
    ## X-squared = 91.2, df = 1, p-value <2e-16
    ## alternative hypothesis: true p is not equal to 0.5
    ## 95 percent confidence interval:
    ##  0.78497 0.89167
    ## sample estimates:
    ##       p 
    ## 0.84536 

}