#' Binomial Log-Likelihood Ratio Test
#'
#' Performs the log-likelihood ratio test for
#' a collection of 2 x 2 tables of the form
#' \tabular{lcc}{
#' \tab event \tab not event\cr
#' drug \tab \code{a} \tab \code{c}\cr
#' not drug \tab \code{b} \tab \code{d}
#' }
#'
#' @template standardParams
#' @return The log-likelihood ratio
#'
#' @references Lian Duan, Khoshneshin, M., Street, W. N.,
#' & Mei Liu. (2013). Adverse drug effect detection.
#' IEEE Journal of Biomedical and Health Informatics,
#' 17(2), 305–11. https://doi.org/10.1109/TITB.2012.2227272
#' @export
logLikelihoodRatioBinomial <- function(a, b, c, d) {
N <- a + b + c + d
r <- a / N # actual observed ratio
r0 <- ((a + c) * (a + b)) / N^2 # expected ratio under H0
# log-likelihood
a * (log(r) - log(r0)) + (N - a) * (log(1 - r) - log(1 - r0))
}
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