#'Escalation With Overdose Control
#'
#'Finding the next dose for a phase I clinical trial based on Escalation
#'with Overdose Control (EWOC) design considering parametrization for time
#'to event 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 matrix as a response
#'containing time and status 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 tau a numerical value defining the period of time for a possible
#'toxicity be observed.
#'@param mtd_prior a matrix 1x2 of hyperparameters for the Beta prior
#'distribution associated with the parameter MTD.
#'@param rho_prior a matrix 1x2 of hyperparameters for the Beta prior
#'distribution associated with the parameter rho.
#'@param shape_prior a matrix 1x2 of hyperparameters for the Gamma prior
#'distribution associated with the shape parameter r for the Weibull
#'distribution.
#'It is only necessary if distribution = 'weibull'.
#'@param type a character describing the type of the Maximum Tolerable Dose
#'(MTD) variable. It can be 'discrete' or 'continuous'.
#'@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.
#'It is only necessary if type = 'continuous'.
#'@param last_dose a numerical value for the last allowable dose in the trial.
#'It is only necessary if type = 'continuous'.
#'@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 distribution a character establishing the distribution for the time of
#'events. It can be defined as 'exponential' or 'weibull'.
#'@param rounding a character indicating how to round a continuous dose to the
#'one of elements of the dose set. It can be 'nearest' or 'down'.
#'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} the posterior MTD distribution.
#'@return \code{rho} the posterior rho_0 distribution.
#'@return \code{sample} a list of the MCMC chains distribution.
#'@return \code{trial} a list of the trial conditions.
#'
#'@references Tighiouart M, Liu Y, Rogatko A. Escalation with overdose control using time to toxicity for cancer phase I clinical trials. PloS one. 2014 Mar 24;9(3):e93070.
#'
#'@examples
#'time <- 9
#'status <- 0
#'dose <- 20
#'
#'test <- ewoc_d1ph(cbind(time, status) ~ dose, type = 'discrete',
#' theta = 0.33, alpha = 0.25, tau = 10,
#' min_dose = 20, max_dose = 100,
#' dose_set = seq(20, 100, 20),
#' rho_prior = matrix(1, ncol = 2, nrow = 1),
#' mtd_prior = matrix(1, ncol = 2, nrow = 1),
#' distribution = 'exponential',
#' rounding = 'nearest')
#'summary(test)
#'plot(test)
#'
#'@import stats
#'
#'@export
ewoc_d1ph <- function(formula, theta, alpha, tau,
type = c('continuous', 'discrete'),
rho_prior, mtd_prior, shape_prior = NULL,
min_dose, max_dose,
first_dose = NULL, last_dose = NULL,
dose_set = NULL,
max_increment = NULL, no_skip_dose = TRUE,
distribution = c('exponential', 'weibull'),
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){
covariable_matrix <- NULL
design_matrix <- dose_matrix
colnames(design_matrix) <- c("intercept", "dose")
} else {
stop("This design cannot accommodate a covariable.")
}
response <- model.response(data_base)
if (!is.matrix(response))
stop("The left side of the formula should be a matrix: time and status!\n")
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) != 1 | ncol(rho_prior) != 2)
stop("'rho_prior' should be a matrix with 1 column and 2 rows.")
if (nrow(mtd_prior) != 1 | ncol(mtd_prior) != 2)
stop("'mtd_prior' should be a matrix with 1 column and 2 rows.")
if (distribution == 'weibull')
if (is.null(shape_prior)) {
stop("'shape_prior' should be informed if 'distribution' = 'weibull'")
} else {
if (!(nrow(shape_prior) == 1 & ncol(shape_prior) == 2))
stop("'shape_prior' should be a matrix with 2 columns and 1 row.")
}
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, mtd_prior= mtd_prior,
shape_prior = shape_prior,
distribution = distribution, tau = tau,
type = type, rounding = rounding)
class(my_data) <- c("ewoc_d1ph", "d1ph")
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$max_dose,
dose_set = dose_set,
max_increment = max_increment,
no_skip_dose = no_skip_dose,
rho_prior = rho_prior, mtd_prior = mtd_prior,
shape_prior = shape_prior,
distribution = distribution, tau = tau,
type = type, rounding = rounding,
n_adapt = n_adapt, burn_in = burn_in, n_mcmc = n_mcmc,
n_thin = n_thin, n_chains = n_chains)
out$trial <- trial
class(out) <- c("ewoc_d1ph", "d1ph")
return(out)
}
#'@importFrom rjags jags.model coda.samples
jags.d1ph <- function(data, n_adapt, burn_in,
n_mcmc, n_thin, n_chains) {
time_cens <- data$response[, 1]
status <- data$response[, 2]
time_mod <- time_cens
time_mod[status == 0] <- NA
censored <- as.numeric(!status)
# JAGS model function
if (data$distribution == "weibull") {
jfun <- "model {
for(i in 1:nobs) {
censored[i] ~ dinterval(time_mod[i], time_cens[i])
time_mod[i] ~ dweib(shape, rate[i])
rate[i] <- exp(inprod(design_matrix[i, ], beta))
}
beta[1] <- log(-log(1 - rho)) - shape*log(tau)
beta[2] <- (log(-log(1 - theta)) -
log(-log(1 - rho)))*
exp(-log(gamma))
rho <- theta*r
gamma <- g + 10^(-2)
shape <- s + 10^(-2)
r ~ dbeta(rho_prior[1, 1], rho_prior[1, 2])
g ~ dbeta(mtd_prior[1, 1], mtd_prior[1, 2])
s ~ dgamma(shape_prior[1, 1], shape_prior[1, 2])
}"
inits <- function() {
time_init <- rep(NA, length(time_mod))
time_init[which(!status)] <- time_cens[which(!status)] + 1
out <- list(r = rbeta(nrow(data$rho_prior),
data$rho_prior[, 1], data$rho_prior[, 2]),
g = rbeta(nrow(data$mtd_prior),
data$mtd_prior[, 1], data$mtd_prior[, 2]),
s = rgamma(nrow(data$shape_prior),
data$shape_prior[, 1], data$shape_prior[, 2]),
time_mod = time_init)
return(out)
}
data_base <- list('time_mod' = time_mod, 'time_cens' = time_cens,
'censored' = censored, 'tau' = data$tau,
'design_matrix' = data$design_matrix,
'theta' = data$theta,
'nobs' = length(time_cens[!is.na(time_cens)]),
'rho_prior' = data$rho_prior,
'mtd_prior' = data$mtd_prior,
'shape_prior' = data$shape_prior)
} else {
jfun <- "model {
for(i in 1:nobs) {
censored[i] ~ dinterval(time_mod[i], time_cens[i])
time_mod[i] ~ dexp(rate[i])
rate[i] <- exp(inprod(design_matrix[i, ], beta) + 10^(-3))
}
beta[1] <- log(-log(1 - rho[1])) - log(tau)
beta[2] <- (log(-log(1 - theta)) -
log(-log(1 - rho[1])))*
exp(-log(gamma + 10^(-2)))
rho[1] <- theta*r
r ~ dbeta(rho_prior[1, 1], rho_prior[1, 2])
gamma ~ dbeta(mtd_prior[1, 1], mtd_prior[1, 2])
}"
inits <- function() {
time_init <- rep(NA, length(time_mod))
time_init[which(!status)] <- time_cens[which(!status)] + 1
out <- list(r = rbeta(nrow(data$rho_prior),
data$rho_prior[, 1], data$rho_prior[, 2]),
gamma = rbeta(nrow(data$mtd_prior),
data$mtd_prior[, 1], data$mtd_prior[, 2]),
time_mod = time_init)
return(out)
}
data_base <- list('time_mod' = time_mod, 'time_cens' = time_cens,
'censored' = censored, 'tau' = data$tau,
'design_matrix' = data$design_matrix,
'theta' = data$theta,
'nobs' = length(time_cens[!is.na(time_cens)]),
'rho_prior' = data$rho_prior,
'mtd_prior' = data$mtd_prior)
}
initial <- inits()
# Calling JAGS
j <- jags.model(textConnection(jfun),
data = data_base,
inits = initial,
n.chains = n_chains,
n.adapt = n_adapt)
update(j, burn_in)
if (data$distribution == "weibull"){
sample <- coda.samples(j,
variable.names =
c("beta", "gamma", "rho", "shape"),
n.iter = n_mcmc, thin = n_thin,
n.chains = n_chains)
beta <- sample[[1]][, 1:2]
gamma <- sample[[1]][, 3]
rho <- sample[[1]][, 4]
shape <- sample[[1]][, 5]
out <- list(beta = beta, gamma = gamma, rho = rho, shape = shape,
sample = sample)
} else {
sample <- coda.samples(j, variable.names = c("beta", "gamma", "rho"),
n.iter = n_mcmc, thin = n_thin,
n.chains = n_chains)
beta <- sample[[1]][, 1:2]
gamma <- sample[[1]][, 3]
rho <- sample[[1]][, 4]
out <- list(beta = beta, gamma = gamma, rho = rho, sample = sample)
}
return(out)
}
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