R/LogOR.R

In SMARTbayesR: Bayesian Set of Best Dynamic Treatment Regimes and Sample Size in SMARTs for Binary Outcomes

#' @title Log-Odds Ratios for Embedded Dynamic Treatment Regimes
#'
#' @description Computes the embedded dynamic treatment regime specific log-odds ratios.
#'
#' @param response_prob the probability of response for each of embedded treatment sequences. In the case of the design 1 SMART, there are 6,
#'  for the general design there are 8, and for Design-3 there are 9 embedded treatment sequences.
#' @param stage_one_trt_one_response_prob the probability of response to stage-1 treatment given stage-1 treatment one.
#' @param stage_one_trt_two_response_prob the probability of response to stage-1 treatment given stage-1 treatment two.
#' @param stage_one_trt_three_response_prob the probability of response to stage-1 treatment given stage-1 treatment three (for design-3 only)
#' @param design which SMART design: design-1 (ENGAGE-type), general, or design-3.

#' @return The embedded dynamic treatment regime specific log-OR.
#'
#' @export


LogOR <- function(response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8),
                  stage_one_trt_one_response_prob = 0.6,
                  stage_one_trt_two_response_prob = 0.3,
                  stage_one_trt_three_response_prob = 0.4,
                  design = "general") {
  
  
  
  if (any(response_prob < 0 | response_prob > 1)) {
    stop("Treatment sequence response probabilities must be between 0 and 1")
  }
  
  if (stage_one_trt_one_response_prob < 0 | stage_one_trt_one_response_prob > 1 | stage_one_trt_two_response_prob < 0 | stage_one_trt_two_response_prob > 1 | stage_one_trt_three_response_prob < 0 | stage_one_trt_three_response_prob > 1) {
    stop("Stage-1 treatment response probabilities must be between 0 and 1")
  }
  
  if (!(design %in% c("design-1","general","design-3"))) {
    stop("'design' must be 'design-1', 'general', or 'design-3'")
  }
  
  if (design == "design-1" & length(response_prob) != 6) {
    stop("Design-1 must have 6 treatment sequences.")
  }
  
  if (design == "general" & length(response_prob) != 8) {
    stop("The general SMART must have 8 treatment sequences.")
  }
  
  if (design == "design-3" & length(response_prob) != 9) {
    stop("The design-3 SMART must have 9 treatment sequences.")
  }
  
  if (design == "design-1") {
    EDTRs <- c(
      response_prob[1] * stage_one_trt_one_response_prob + response_prob[2] * (1 - stage_one_trt_one_response_prob),
      response_prob[1] * stage_one_trt_one_response_prob + response_prob[3] * (1 - stage_one_trt_one_response_prob),
      response_prob[4] * stage_one_trt_two_response_prob + response_prob[5] * (1 - stage_one_trt_two_response_prob),
      response_prob[4] * stage_one_trt_two_response_prob + response_prob[6] * (1 - stage_one_trt_two_response_prob)
    )
  }

  if (design == "general") {
    EDTRs <- c(
      response_prob[1] * stage_one_trt_one_response_prob + response_prob[3] * (1 - stage_one_trt_one_response_prob),
      response_prob[1] * stage_one_trt_one_response_prob + response_prob[4] * (1 - stage_one_trt_one_response_prob),
      response_prob[2] * stage_one_trt_one_response_prob + response_prob[3] * (1 - stage_one_trt_one_response_prob),
      response_prob[2] * stage_one_trt_one_response_prob + response_prob[4] * (1 - stage_one_trt_one_response_prob),
      response_prob[5] * stage_one_trt_two_response_prob + response_prob[7] * (1 - stage_one_trt_two_response_prob),
      response_prob[5] * stage_one_trt_two_response_prob + response_prob[8] * (1 - stage_one_trt_two_response_prob),
      response_prob[6] * stage_one_trt_two_response_prob + response_prob[7] * (1 - stage_one_trt_two_response_prob),
      response_prob[6] * stage_one_trt_two_response_prob + response_prob[8] * (1 - stage_one_trt_two_response_prob)
    )
  }

  if (design == "design-3") {
    EDTRs <- c(
      response_prob[1] * stage_one_trt_one_response_prob + response_prob[2] * (1 - stage_one_trt_one_response_prob),
      response_prob[1] * stage_one_trt_one_response_prob + response_prob[3] * (1 - stage_one_trt_one_response_prob),
      response_prob[4] * stage_one_trt_two_response_prob + response_prob[5] * (1 - stage_one_trt_two_response_prob),
      response_prob[4] * stage_one_trt_two_response_prob + response_prob[6] * (1 - stage_one_trt_two_response_prob),
      response_prob[7] * stage_one_trt_three_response_prob + response_prob[8] * (1 - stage_one_trt_three_response_prob),
      response_prob[7] * stage_one_trt_three_response_prob + response_prob[9] * (1 - stage_one_trt_three_response_prob)
    )
  }

  # Compute log-OR
  thetadraws_log_odds <- log(EDTRs / (1 - EDTRs))

  # Compute index of best EDTR
  max_odds_ind <- (which.max((thetadraws_log_odds)))

  Log_OR_output1 <- matrix((thetadraws_log_odds - thetadraws_log_odds[max_odds_ind]), nrow = 1, ncol = length(thetadraws_log_odds))

  if (design == "general") {
    colnames(Log_OR_output1) <- c(
      "EDTR 1",
      "EDTR 2",
      "EDTR 3",
      "EDTR 4",
      "EDTR 5",
      "EDTR 6",
      "EDTR 7",
      "EDTR 8"
    )
  }

  if (design == "design-1") {
    colnames(Log_OR_output1) <- c(
      "EDTR 1",
      "EDTR 2",
      "EDTR 3",
      "EDTR 4"
    )
  }
  
  if (design == "design-3") {
    colnames(Log_OR_output1) <- c(
      "EDTR 1",
      "EDTR 2",
      "EDTR 3",
      "EDTR 4",
      "EDTR 5",
      "EDTR 6"
    )
  }
  
  return(Log_OR_output1)
}