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#' @title Stage 2 Adaptive Randomization with nTTP to monitor toxicity
#'
#' @description Function \code{rand.stg2.nTTP()} fits a linear regression for the continuous
#' efficacy outcomes, computes the randomization probabilities/dose and allocates the next patient
#' to a dose that is considered acceptably safe and has the highest efficacy. Dose safety
#' (with nTTP) is still monitored using LR and doses that become unacceptable are discarded
#' (never re-visited).
#'
#' @return List of the following objects:
#' \itemize{
#' \item Y.final - vector of all efficacy outcomes (Ys) corresponding to dose assignments
#' (Stages 1&2)
#' \item d.final - vector of all dose assignments(Stage 1&2)
#' \item n1 - Stage 1 sample size
#' }
#' If dose allocation stops early, put NAs in d.final and y.final until it reaches the total
#' sample size.
#'
#' @param dose number of doses to be tested (scalar)
#' @param p1 toxicity under null (unsafe nTTP). Values range from 0 - 1.
#' @param p2 toxicity under alternative (safe nTTP). Values range from 0 - 1; p1 > p2
#' @param K threshold for LR. Takes integer values: 1,2,...(recommended K=2)
#' @param coh.size cohort size (number of patients) per dose (Stage 1)
#' @param m vector of mean efficacies per dose. Values range from 0 - 100.
#' (e.g, T cell persistence - values b/w 5 and 80 per cent)
#' @param v vector of efficacy variances per dose. Values range from 0 - 1. (e.g., 0.01)
#' @param nbb binomial parameter (default = 100 cells per patient)
#' @param N total sample size for stages 1&2
#' @param stop.rule if only dose 1 safe, allocate up to 9 (default) patients at dose 1 to
#' collect more info
#' @param cohort cohort size (number of patients) per dose (Stage 2). Default is 1.
#' @param samedose designates whether the next patient is allocated to the same dose as the
#' previous patient. Default is TRUE. Function adjusts accordingly.
#' @param ntox number (integer) of different toxicity types
#' @param W matrix defining burden weight of each grade level for all toxicity types.
#' The dimensions are ntox rows by 4 columns (for grades 0-4).
#' See Ezzalfani et al. (2013) for details.
#' @param TOX matrix array of toxicity probabilities. There should be ntox matrices.
#' Each matrix represents one toxicity type, where probabilities of each toxicity grade are
#' specified across each dose. Each matrix has the same dimensions:
#' n rows, representing number of doses, and 5 columns (for grades 0-4).
#' Probabilities across each dose (rows) must sum to 1.
#' See Ezzalfani et al. (2013) for details.
#' @param std.nTTP the standard deviation of nTTP scores at each dose level (constant across doses)
#'
#' @examples
#' # Number of pre-specified dose levels
#' dose <- 6
#'
#' # Acceptable (p2) and unacceptable nTTP values
#' p1 <- 0.35
#' p2 <- 0.10
#'
#' # Likelihood-ratio (LR) threshold
#' K <- 2
#'
#' # Cohort size used in stage 1
#' coh.size <- 3
#'
#' # Total sample size (stages 1&2)
#' N <- 25
#'
#' # Efficacy (equal) variance per dose
#' v <- rep(0.01, 6)
#'
#' # Dose-efficacy curve
#' m = c(10, 20, 30, 40, 70, 90)
#'
#' # Number of toxicity types
#' ntox <- 3
#'
#' # Toxicity burden weight matrix
#' W = matrix(c(0, 0.5, 0.75, 1.0, 1.5, # Burden weight for grades 0-4 for toxicity 1
#' 0, 0.5, 0.75, 1.0, 1.5, # Burden weight for grades 0-4 for toxicity 2
#' 0, 0.00, 0.00, 0.5, 1), # Burden weight for grades 0-4 for toxicity 3
#' nrow = ntox, byrow = TRUE)
#'
#' # Standard deviation of nTTP value
#' std.nTTP = 0.15
#'
#' # Array of toxicity event probabilities
#' TOX <- array(NA, c(dose, 5, ntox))
#'
#' TOX[, , 1] = matrix(c(0.823, 0.152, 0.022, 0.002, 0.001,
#' 0.791, 0.172, 0.032, 0.004, 0.001,
#' 0.758, 0.180, 0.043, 0.010, 0.009,
#' 0.685, 0.190, 0.068, 0.044, 0.013,
#' 0.662, 0.200, 0.078, 0.046, 0.014,
#' 0.605, 0.223, 0.082, 0.070, 0.020),
#' nrow = 6, byrow = TRUE)
#' TOX[, , 2] = matrix(c(0.970, 0.027, 0.002, 0.001, 0.000,
#' 0.968, 0.029, 0.002, 0.001, 0.000,
#' 0.813, 0.172, 0.006, 0.009, 0.000,
#' 0.762, 0.183, 0.041, 0.010, 0.004,
#' 0.671, 0.205, 0.108, 0.011, 0.005,
#' 0.397, 0.258, 0.277, 0.060, 0.008),
#' nrow = 6, byrow = TRUE)
#' TOX[, , 3] = matrix(c(0.930, 0.060, 0.005, 0.001, 0.004,
#' 0.917, 0.070, 0.007, 0.001, 0.005,
#' 0.652, 0.280, 0.010, 0.021, 0.037,
#' 0.536, 0.209, 0.031, 0.090, 0.134,
#' 0.015, 0.134, 0.240, 0.335, 0.276,
#' 0.005, 0.052, 0.224, 0.372, 0.347),
#' nrow = 6, byrow = TRUE)
#'
#' rand.stg2.nTTP(dose = dose, p1 = p1, p2 = p2, K = K, coh.size = coh.size,
#' m = m, v = v, N = N, stop.rule = 9,
#' cohort = 1, samedose = TRUE, nbb = 100, W = W, TOX = TOX, ntox = ntox, std.nTTP = std.nTTP)
#'
#' @export
rand.stg2.nTTP <- function(dose, p1, p2, K, coh.size, m, v, N, stop.rule = 9,
cohort = 1, samedose = TRUE, nbb = 100, W, TOX, ntox, std.nTTP = 0.15) {
res <- eff.stg1.nTTP(dose, p1, p2, K, coh.size, m, v, nbb = 100,
W = W, TOX = TOX, ntox = ntox, std.nTTP = std.nTTP) # stage 1
dose <- c(1:dose)
yk.safe <- res$Y.safe # efficacy of all safe doses
yk.final <- res$Y.alloc # efficacy of all patients enrolled in stage 1
dk.safe <- res$d.safe # dose allocation for all safe doses
dk.final <- dk1 <- dk2 <- res$d.alloc # dose allocation of all patients enrolled in stage 1
toxk <- res$tox.safe # mnTTP at each dose level in stage 1
n1 <- res$n1 # number of patients enrolled in stage 1
nmore <- N - n1 # number of subjects left to randomize
all_nttp <- res$all_nttp
nd <- length(unique(dk.safe)) # number of safe doses
rp <- NULL
stop <- 0
if (nd == 0) { # if no doses found safe
yk.final <- yk.final
dk.final <- dk.final
stop <- 1
}
if (nd == 1) { # if exactly one dose found safe
extra <- stop.rule - length(dk.safe)
ab <- beta.ab(m[1]/100, v[1])
y.extra <- 100 * stats::rbinom(extra, nbb, stats::rbeta(1, ab$a, ab$b))/nbb
yk.final <- c(yk.final, y.extra)
dk.final <- c(dk.final, rep(1, extra))
stop <- 1
}
if (nd > 1) { # if more than one dose found safe
coh.toxk <- cbind(matrix(dk.safe, ncol = coh.size, byrow = TRUE)[, 1], toxk)
for (k in 1:nmore) {
if (stop == 0) {
reg <- stats::lm(log(yk.safe + 1) ~ factor(dk.safe))
fit <- as.vector(reg$fitted.values)
dose.unique <- duplicated(dk.safe)
fitp <- exp(fit)
fitp <- fitp[dose.unique == FALSE]
rp <- fitp/sum(fitp)
rp <- ifelse(rp < 0.02, 0.02, rp)
dj <- stats::rmultinom(1, 1, prob = rp)
if (samedose == TRUE) {
dj <- rep((1:length(dj))[dj == 1], cohort)
} else {
dosemat <- as.vector(dj * matrix(1:nd, ncol = cohort,
nrow = nd))
dj <- dosemat[dosemat > 0]
}
ab <- beta.ab(m[dj]/100, v[dj])
p <- stats::rbeta(1, ab$a, ab$b)
yj <- 100 * stats::rbinom(1, nbb, p)/nbb
# simulate nTTP for next individual
toxj <- nTTP.indiv.sim(W = W,
TOX = TOX,
ntox = ntox,
dose = dose[dj])
coh.toxj <- c(dj, toxj)
yk.safe <- c(yk.safe, yj)
yk.final <- c(yk.final, yj)
dk.safe <- c(dk.safe, dj)
dk.final <- c(dk.final, dj)
all_nttp <- append(all_nttp, toxj)
coh.toxk <- data.frame(dose = dk.final,
nttp = all_nttp)
# calculate new LR for all patients on the given dose
l.p2 <- NULL
l.p1 <- NULL
LR <- NULL
accept.dose <- NULL
a = 0
b = 1
for (j in 1:max(coh.toxk[, 1])) {
rows = which(coh.toxk[,1] == j)
nttp = coh.toxk[rows, 2]
nj = length(rows)
# likelihood of acceptable/alternative hypothesis
l.p2[j] <- prod(sapply(nttp, FUN = function(i){ dnorm((i - p2)/std.nTTP) })) /
(std.nTTP*(pnorm((b - p2)/std.nTTP) - pnorm((a - p2)/std.nTTP)))^nj
# likelihood of unacceptable/null hypothesis
l.p1[j] <- prod(sapply(nttp, FUN = function(i){ dnorm((i - p1)/std.nTTP) })) /
(std.nTTP*(pnorm((b - p1)/std.nTTP) - pnorm((a - p1)/std.nTTP)))^nj
# likelihood ratio
LR[j] <- round(l.p2[j]/l.p1[j], 2)
accept.dose[j] <- ifelse(LR[j] > (1/K), 1, 0)
}
unsafe_dose = which(accept.dose == 0)
if (length(unsafe_dose) > 0) {
smallest_unsafe_dose = unsafe_dose[1]
dk.safe[dk.safe >= smallest_unsafe_dose] <- NA
coh.toxk <- coh.toxk[!apply(coh.toxk, 1, function(x) {
any(x >= smallest_unsafe_dose)
}), ]
}
new.model <- cbind(dk.safe, yk.safe)
new.model <- stats::na.omit(new.model)
dk.safe <- new.model[, 1]
yk.safe <- new.model[, 2]
yk.final <- yk.final
dk.final <- dk.final
if (length(unique(dk.safe)) > 1) {
dk.safe <- dk.safe
yk.safe <- yk.safe
dk.final <- dk.final
yk.final <- yk.final
} else if (length(unique(dk.safe)) == 1) {
new.size <- nmore + length(dk2)
length.dk1 <- length(dk.final)
if ((length(dk.safe) < stop.rule) && (length.dk1 <
new.size)) {
extra.one <- min(new.size - length.dk1,
stop.rule - length(dk.safe))
ab <- beta.ab(m[1]/100, v[1])
yj.one <- 100 * stats::rbinom(extra.one,
nbb, stats::rbeta(1, ab$a, ab$b))/nbb
yk.final <- c(yk.final, yj.one)
dk.final <- c(dk.final, rep(1, extra.one))
stop <- 1
} else {
dk.final <- dk.final
yk.final <- yk.final
stop <- 1
}
} else if (length(unique(dk.safe)) < 1) {
dk.final <- dk.final
yk.final <- yk.final
stop <- 1
}
} else {
dk.final <- dk.final
yk.final <- yk.final
}
}
}
return(list(Y.final = yk.final,
d.final = dk.final,
n1 = n1))
}
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