##' Calculate false discovery rate of identifying transmission pairs in a sample
##'
##' This function calculates the false discovery rate (proportion of linked pairs that are false positives) in a sample given the sensitivity
##' and specificity of the linkage criteria, and sample size \eqn{M}. Assumptions about transmission and linkage (single or multiple)
##' can be specified.
##'
##' @param sensitivity scalar or vector giving the sensitivity of the linkage criteria
##' @param specificity scalar or vector giving the specificity of the linkage criteria
##' @param rho scalar or vector giving the proportion of the final outbreak size that is sampled
##' @param M scalar or vector giving the number of cases sampled
##' @param R scalar or vector giving the effective reproductive number of the pathogen (default=NULL)
##' @param assumption a character vector indicating which assumptions about transmission and linkage criteria. Default = `'mtml'`. Accepted arguments are:
##' \enumerate{
##' \item `'stsl'` for the single-transmission single-linkage assumption.
##' \item `'mtsl'` for the multiple-transmission single-linkage assumption.
##' \item `'mtml'` for the multiple-transmission multiple-linkage assumption.
##' }
##'
##' @return scalar or vector giving the true discovery rate
##'
##' @author John Giles, Shirlee Wohl, and Justin Lessler
##'
##' @examples
##' # The simplest case: single-transmission, single-linkage, and perfect sensitivity
##' translink_fdr(sensitivity=1, specificity=0.9, rho=0.5, M=100, assumption='stsl')
##'
##' # Multiple-transmission and imperfect sensitivity
##' translink_fdr(sensitivity=0.99, specificity=0.9, rho=1, M=50, R=1, assumption='mtsl')
##'
##' # Small outbreak, larger sampling proportion
##' translink_fdr(sensitivity=0.99, specificity=0.95, rho=1, M=50, R=1, assumption='mtml')
##'
##' # Large outbreak, small sampling proportion
##' translink_fdr(sensitivity=0.99, specificity=0.95, rho=0.5, M=1000, R=1, assumption='mtml')
##'
##' @family transmission linkage functions
##'
##' @export
##'
translink_fdr <- function(sensitivity, specificity, rho, M, R = NULL, assumption = "mtml") {
suppressMessages(1 - translink_tdr(sensitivity = sensitivity, specificity = specificity,
rho = rho, M = M, R = R, assumption = assumption))
}
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