Expected Specificity Given Sensitivity, PPV, and Prevalence Assumption

specificity.given.PPV <- function(Sensitivity = 0.5, 
                                  PPV = 0.3, 
                                  Prevalence = 0.1)
{
    ## Purpose: calculate specificity based on sensitivity, PPV, and prevalence. 
    ## 
    ## Arguments:
    ##   Sensitivity: performance target for sensitivity
    ##   PPV: performance target for PPV (positive predictive value)
    ##   Prevalence: assumed disease prevalence in the target population
    ## 
    ## Return:
    ##   Specificity: expected performance target for specificity 
    ##
    ## Author: Feiming Chen (Copyright 2024; GPLv3; No Warranty; gnu.org/licenses)
    ## ________________________________________________

    ## Assume 1000 patients
    N <- 1000
    n.pos <- N * Prevalence
    n.neg <- N - n.pos
    n.true.pos <- n.pos * Sensitivity
    n.false.neg <- n.pos - n.true.pos
    Specificity <- 1 - n.true.pos / (n.neg * (PPV / (1 - PPV)))

    cat("What should the Specificity be if we want", paste0(round(100*Sensitivity), "%"), "Sensitivity and", paste0(round(100*PPV), "%"),
        "PPV under", paste0(round(100*Prevalence), "%"), "Prevalence assumption?\n")
    cat("Specificity =", round(Specificity, 3), "\n\n")

    make.Sankey.diagram.for.Dx.performance(Sensitivity = Sensitivity, Specificity = Specificity, Prevalence = Prevalence)

}
if (F) {                                # Unit Test
    specificity.given.PPV(Sensitivity = 0.7, PPV = 0.3, Prevalence = 0.05)
}