#' Power calculation for the win odds test (no ties)
#'
#' @param N a numeric vector of sample size values.
#' @param WO the given win odds for the alternative hypothesis. A numeric vector of length 1.
#' @param SD assumed standard deviation of the win proportion. By default uses the conservative SD. A numeric vector of length 1.
#' @param k proportion of active group in the overall sample size. Default is 0.5 (balanced randomization). A numeric vector of length 1.
#' @param alpha the significance level for the 2-sided test. Default is 0.05. A numeric vector of length 1.
#' @param WOnull the win odds value of the null hypothesis (default is 1). A numeric vector of length 1.
#'
#' @return a data frame containing the calculated power with input values.
#' @export
#' @md
#' @seealso [hce::sizeWO()], [hce::minWO()] for WO sample size or minimum detectable WO calculation.
#' @references Gasparyan SB et al. (2021) "Power and sample size calculation for the win odds test: application to an ordinal endpoint in COVID-19 trials." Journal of Biopharmaceutical Statistics 31.6 : 765-787. <doi:10.1080/10543406.2021.1968893>
#' @examples
#' # Example 1- Use the default standard deviation
#' powerWO(N = 1000, WO = 1.2)
#' powerWO(N = seq(500, 1500, 100), WO = 1.2)
#' # Example 2 - Use data-driven win odds and standard deviation from the COVID19 dataset
#' res <- calcWO(x = COVID19, AVAL = "GROUP", TRTP = "TRTP", ref = "Placebo")
#' print(res)
#' powerWO(N = 500, WO = res$WO, SD = res$SD_WP)
#' powerWO(N = 500, WO = res$WO) # power with the default standard deviation for the win proportion.
#' # Example 3 - Non-balanced 3:1 randomization
#' powerWO(N = 1000, WO = 1.2, k = 0.75)

powerWO <- function(N, WO, SD = NULL, k = 0.5, alpha = 0.05, WOnull = 1){
  WO <- WO[1]
  SD <- SD[1]
  alpha <- alpha[1]
  WOnull <- WOnull[1]
  k <- k[1]
  if(k < 0 | k > 1) stop("k should be between 0 and 1.")
  VAR <- 1/(12*k*(1 - k))
  if(is.null(SD)) SD <- sqrt(VAR)
  WP <- WO/(WO + 1)
  WPnull <- WOnull/(WOnull + 1)
  SE <- SD/base::sqrt(N)
  C <- stats::qnorm(1 - alpha/2)

  power <- stats::pnorm(-C + (WP - WPnull)/SE) + stats::pnorm( -C - (WP - WPnull)/SE)
  d <- base::data.frame(power = power, SampleSize = N, WO = WO, WP = WP, WPnull = WPnull, WOnull = WOnull, alpha = alpha, SD = SD, k = k)

  l <- base::list( result = d, value = power, input = N, input_name = "Sample Size", value_name = "Power")
  attr(d, "res") <- l
  base::class(d) <- c("hce_results")
  d
}