R/extended_EWOC.R

In dnzmarcio/ewoc: Escalation with Overdose Control

#'Escalation With Overdose Control
#'
#'Finding the next dose for a phase I clinical trial based on the
#'Escalation with Overdose Control (EWOC) design considering the
#'extended parametrization for binary response and single agent.
#'
#'@param formula an object of class \code{\link[Formula]{Formula}}: a symbolic
#'description of the model to be fitted with only one regressor term
#'corresponding to the dose for the right side and a numeric vector as a response
#'containing number of DLT for the left side.
#'@param theta a numerical value defining the proportion of expected patients
#'to experience a medically unacceptable, dose-limiting toxicity (DLT) if
#'administered the MTD.
#'@param alpha a numerical value defining the probability that the dose selected
#'by EWOC is higher than the MTD.
#'@param rho_prior a matrix 3 x 2 of hyperparameters for the Beta prior
#'distribution associated with each parameter rho. Each row corresponds to a parameter.
#'@param type a character describing the type of the Maximum Tolerable Dose
#'(MTD) variable.
#'@param min_dose a numerical value defining the lower bound of the support of
#'the MTD.
#'@param max_dose a numerical value defining the upper bound of the support of
#'the MTD.
#'@param first_dose a numerical value for the first allowable dose in the trial.
#'@param last_dose a numerical value for the last allowable dose in the trial.
#'@param dose_set a numerical vector of allowable doses in the trial. It is only
#'necessary if type = "discrete".
#'@param max_increment a numerical value indicating the maximum increment from the current dose to the next dose.
#'It is only applied if type = 'continuous'.
#'@param no_skip_dose a logical value indicating if it is allowed to skip doses.
#'It is only necessary if type = 'discrete'. The default is TRUE.
#'@param rounding a character indicating how to round a continuous dose to the
#'one of elements of the dose set.
#'It is only necessary if type = "discrete".
#'@param n_adapt the number of iterations for adaptation.
#'See \code{\link[rjags]{adapt}} for details.
#'@param burn_in the number of iterations before to start monitoring.
#'@param n_mcmc the number of iterations to monitor.
#'@param n_thin thinning interval for monitors.
#'@param n_chains the number of parallel chains for the model.
#'
#'@return \code{next_dose} the next recommend dose.
#'@return \code{mtd} a numerical vector for the posterior MTD distribution considering the next patient covariable.
#'@return \code{rho} a matrix for the posterior rho_0 and rho_1 distributions.
#'@return \code{sample} a list of the MCMC chains distribution.
#'@return \code{trial} a list of the trial conditions.
#'
#'@references Tighiouart, M., Cook-Wiens, G., & Rogatko, A. (2018). A Bayesian adaptive design for cancer phase I trials using a flexible range of doses. Journal of biopharmaceutical statistics, 28(3), 562-574.
#'
#'@examples
#'DLT <- 0
#'dose <- 20
#'
#'test <- ewoc_d1extended(DLT ~ dose, type = 'discrete',
#'                        theta = 0.33, alpha = 0.25,
#'                        dose_set = seq(20, 100, 20),
#'                        min_dose = 20, max_dose = 100,
#'                        rho_prior = matrix(1, ncol = 2, nrow = 2),
#'                        rounding = "nearest")
#'summary(test)
#'plot(test)
#'
#'@import stats
#'
#'@export
ewoc_d1extended <- function(formula, theta, alpha,
                            rho_prior,
                            min_dose, max_dose,
                            type = c('continuous', 'discrete'),
                            first_dose = NULL, last_dose = NULL,
                            dose_set = NULL,
                            max_increment = NULL, no_skip_dose = TRUE,
                            rounding = c("down", "nearest"),
                            n_adapt = 5000, burn_in = 1000,
                            n_mcmc = 1000, n_thin = 1, n_chains = 1) {

  formula <- Formula::Formula(formula)
  if (class(formula)[2] != "formula")
    stop("Invalid formula! \n")

  data_base <- model.frame(formula, na.action = na.exclude,
                                  drop.unused.levels = FALSE)

  dose_matrix <- model.matrix(formula, data_base, rhs = 1)

  if (length(formula)[2] == 1){
    design_matrix <- dose_matrix
    colnames(design_matrix) <- c("intercept", "dose")
  } else {
    stop("This design cannot accommodate a covariable.")
  }
  colnames(design_matrix) <- c("intercept", "dose")

  response <- model.response(data_base)

  if (length(type) > 1 | !(type == "continuous" | type == "discrete"))
    stop("'type' should be either 'continuous' or 'discrete'.")

  if (type == "discrete") {
    if (is.null(dose_set))
      stop("'dose_set' should be informed for type = 'discrete'.")

    if (length(rounding) > 1 | !(rounding == "down" | rounding == "nearest"))
      stop("'rounding' should be either 'down' or 'nearest'.")
  }

  if (!(alpha > 0 & alpha < 1))
    stop("'alpha' should be in the interval (0, 1).")

  if (!(theta > 0 & theta < 1))
    stop("'theta' should be in the interval (0, 1).")

  if (nrow(rho_prior) != 2 | ncol(rho_prior) != 2)
    stop(paste0("'rho_prior' should be a matrix with 2 columns and 2 rows."))

  limits <- limits_d1nocov(first_dose = first_dose, last_dose = last_dose,
                           min_dose = min_dose, max_dose = max_dose,
                           type = type, rounding = rounding,
                           dose_set = dose_set)

  if (is.null(max_increment))
    max_increment <- limits$last_dose - limits$first_dose

  current_dose <- design_matrix[nrow(design_matrix), 2]

  if (type == "continuous"){
    if (current_dose < min_dose | current_dose > max_dose)
      stop("The first patient is receiving a dose outside of the dose boundaries given by
           'min_dose' and 'max_dose'.")
  } else {
    if (!(current_dose %in% dose_set))
      stop("The first patient is receiving a dose outside of the dose set")
  }

  design_matrix[, 2] <-
    standard_dose(dose = design_matrix[, 2],
                  min_dose = limits$min_dose,
                  max_dose = limits$max_dose)

  my_data <- list(response = response, design_matrix = design_matrix,
                  theta = theta, alpha = alpha,
                  limits = limits,
                  dose_set = dose_set,
                  max_increment = max_increment,
                  no_skip_dose = no_skip_dose,
                  current_dose = current_dose,
                  rho_prior = rho_prior,
                  type = type, rounding = rounding)
  class(my_data) <- c("ewoc_d1extended", "d1extended")

  my_data$mcmc <- jags(my_data, n_adapt, burn_in, n_mcmc, n_thin, n_chains)
  out <- next_dose(my_data)

  design_matrix[, 2] <-
    inv_standard_dose(dose = design_matrix[, 2],
                      min_dose = limits$min_dose,
                      max_dose = limits$max_dose)

  trial <- list(response = response, design_matrix = design_matrix,
                theta = theta, alpha = alpha,
                first_dose = limits$first_dose, last_dose = limits$last_dose,
                min_dose = limits$min_dose, max_dose = limits$max_dose,
                dose_set = dose_set,
                max_increment = max_increment,
                no_skip_dose = no_skip_dose,
                rho_prior = rho_prior,
                type = type, rounding = rounding,
                n_adapt = n_adapt, burn_in = burn_in, n_mcmc = n_mcmc,
                n_thin = n_thin, n_chains = n_chains)
  out$trial <- trial

  class(out) <- c("ewoc_d1extended", "d1extended")

  return(out)
}

#'@importFrom rjags jags.model coda.samples
jags.d1extended <- function(data, n_adapt, burn_in,
                                 n_mcmc, n_thin, n_chains) {

  min_dose <- data$limits$min_dose
  max_dose <- data$limits$max_dose
  lb <- - min_dose/(max_dose - min_dose)

  # JAGS model function
  jfun <- "model {

    for(i in 1:nobs) {
      dlt[i] ~ dbin(p[i], 1)
      p[i] <- ifelse(1/(1 + exp(-lp[i])) == 1, 0.99, 1/(1 + exp(-lp[i])))
      lp[i] <- inprod(design_matrix[i, ], beta)
    }

    beta[1] <- logit(rho[1])
    beta[2] <- logit(rho[2]) - logit(rho[1])

    rho[1] <- min*v[1]
    min <- min(rho[2], limit)
    v[1] ~ dbeta(rho_prior[1, 1], rho_prior[1, 2])

    limit <- plogis(numerator/denominator, 0, 1)
    numerator <- logit(theta) - lb*logit(rho[2])
    denominator <- 1 - lb

    rho[2] <- v[2]
    v[2] ~ dbeta(rho_prior[2, 1], rho_prior[2, 2])
  }"

  data_base <- list('dlt' = data$response,
                    'design_matrix' = data$design_matrix,
                    'nobs' = length(data$response),
                    'rho_prior' = data$rho_prior,
                    'theta' = data$theta,
                    'lb' = lb)

  inits <- function() {
    v <- rep(NA, 2)
    v <- rbeta(2, data$rho_prior[, 1], data$rho_prior[, 2])
    out <- list(v = v)
    return(v)
  }

  # Calling JAGS
  j <- jags.model(textConnection(jfun),
                  data = data_base,
                  inits = list(v = inits()),
                  n.chains = n_chains,
                  n.adapt = n_adapt)
  update(j, burn_in)
  sample <- coda.samples(j, variable.names = c("beta", "rho"),
                         n.iter = n_mcmc, thin = n_thin,
                         n.chains = n_chains)

  beta <- sample[[1]][, 1:2]
  rho <- sample[[1]][, 3:4]

  out <- list(beta = beta, rho = rho, sample = sample)

  return(out)
}


#'Convert mtd to rho_1 and vice-versa
#'
#'Converting mtd to rho_1 given rho_0 for EWOC design using extended parametrization
#'and vice-versa.
#'
#'@param mtd a numerical value defining the mtd value to be converted into rho_1 value.
#'@param rho_1 a numerical value defining the  probability of DLT at the max_dose.
#'@param rho_0 a numerical value defining the  probability of DLT at the min_dose.
#'@param theta a numerical value defining the proportion of expected patients
#'to experience a medically unacceptable, dose-limiting toxicity (DLT) if
#'administered the MTD.
#'@param min_dose a numerical value defining the lower bound of the support of
#'the MTD.
#'@param max_dose a numerical value defining the upper bound of the support of
#'the MTD.
#'
#'@return \code{mtd} a numerical value for the maximum tolerable dose.
#'@return \code{rho_1} a numerical value for the probability of DLT at the max_dose.
#'
#'@export
mtd_rho_d1extended <- function(mtd = NULL, rho_1 = NULL, rho_0,
                               theta, min_dose, max_dose){

  if (is.null(mtd) & is.null(rho_1)) {
    stop("At least one between 'mtd' or 'rho_1' should be defined.")

  } else {

    if (is.null(mtd)){
      gamma <- (logit(theta) - logit(rho_0))/(logit(rho_1) - logit(rho_0))
      mtd <- inv_standard_dose(gamma, min_dose = min_dose, max_dose = max_dose)

      out <- list(mtd = mtd, rho_1 = rho_1)
    }

    if (is.null(rho_1)){
      gamma <- standard_dose(mtd, min_dose = min_dose, max_dose = max_dose)

      rho_1 <- plogis((logit(theta) + (gamma - 1)*logit(rho_0))/gamma)

      out <- list(mtd = mtd, rho_1 = rho_1)
    }
  }

  return(out)
}