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find2armDesigns.R
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find2armDesigns.R
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find2armDesigns <- function(nmin,
nmax,
block.size,
pc,
pt,
alpha,
power,
maxtheta0=NULL,
mintheta1=0.7,
bounds="ahern",
fixed.r=NULL,
max.combns=1e6,
rm.dominated.designs=TRUE,
exact.theta0=NULL,
exact.theta1=NULL,
fast.method=FALSE)
{
require(tcltk)
require(data.table)
Bsize <- block.size
if(Bsize%%2!=0) stop("Block size must be an even number")
if((2*nmin)%%Bsize!=0) stop("2*nmin must be a multiple of block size")
if((2*nmax)%%Bsize!=0) stop("2*nmax must be a multiple of block size")
nposs <- seq(from=nmin, to=nmax, by=Bsize/2)
qc <- 1-pc
qt <- 1-pt
################ Function for finding the Prob(reponses on treatment + non-responses on control)=0, 1, 2,... Bsize:
findProbVec <- function(Bsize, pt=pt, qt=qt, pc=pc, qc=qc){
prob.vec <- rep(NA, Bsize+1)
for(i in 1:(Bsize+1)){
positives <- i-1
full.vec <- expand.grid(rep(list(0:1), Bsize))
positive.mat <- full.vec[rowSums(full.vec) == positives,]
negative.mat <- -1*(positive.mat-1)
positive.vec <- rep(c(pt,qc), each=Bsize/2)
negative.vec <- rep(c(qt,pc), each=Bsize/2)
posneg.mat <- t(t(positive.mat)*positive.vec) + t(t(negative.mat)*negative.vec)
prob.vec[i] <- sum(apply(posneg.mat, 1, prod))
}
if(sum(prob.vec)-1 > 1e-8) stop("Probabilities do not sum to 1.")
prob.vec
}
################ Function for finding the uncurtailed CP matrix:
findBlock2armUncurtailedMatrix <- function(n, r, Bsize, pat.cols, prob.vec){
cpmat <- matrix(3, ncol=2*n, nrow=min(n+r+Bsize+2, 2*n+1))
rownames(cpmat) <- 0:(nrow(cpmat)-1)
cpmat[(n+r+2):nrow(cpmat),] <- 1
cpmat[1:(n+r+1),2*n] <- 0 # Fail at end
for(i in (n+r+1):1){
for(j in pat.cols){ # Only look every C patients (no need to look at final col)
if(i-1<=j){ # Condition: Sm<=m
cpmat[i,j] <- ifelse(test=j-(i-1) >= n-r+1, yes=0, no=sum(prob.vec*cpmat[i:(i+Bsize), j+Bsize]))
# IF success is not possible (i.e. [total no. of pats-Xa+Ya-Xb] >= n-r+1), THEN set CP to zero. Otherwise, calculate it based on "future" CPs.
}
}
}
for(i in 3:nrow(cpmat)){
cpmat[i, 1:(i-2)] <- NA
}
cpmat
}
prob.vec <- findProbVec(Bsize=Bsize, pt=pt, qt=qt, pc=pc, qc=qc)
prob.vec.p0 <- findProbVec(Bsize=Bsize, pt=pc, qt=qc, pc=pc, qc=qc)
pat.cols.list <- lapply(nposs, function(x) seq(from=2*x, to=Bsize, by=-Bsize)[-1])
names(pat.cols.list) <- nposs
if(is.null(maxtheta0)){
maxtheta0 <- pt
}
r.list <- list()
for(i in 1:length(nposs))
{
r.list[[i]] <- 0:(nposs[i]-2) # r values: 0 to nposs[i]-2
}
ns <- NULL
for(i in 1:length(nposs)){
ns <- c(ns, rep(nposs[i], length(r.list[[i]])))
}
sc.subset <- data.frame(n=ns, r=unlist(r.list))
if(!is.null(bounds)){
# Incorporate A'Hern's bounds:
if(bounds=="ahern") {
#sc.subset <- sc.subset[sc.subset$r >= pc*sc.subset$n & sc.subset$r <= pt*sc.subset$n, ] # One-arm case
sc.subset <- sc.subset[sc.subset$r >= 1 & sc.subset$r <= pt*sc.subset$n, ] # Try this for two-arm case -- interval [1, pt*Narm]
}
if(bounds=="wald"){
# Even better to incorporate Wald's bounds:
denom <- log(pt/pc) - log((1-pt)/(1-pc))
accept.null <- log((1-power)/(1-alpha)) / denom + nposs * log((1-pc)/(1-pt))/denom
accept.null <- floor(accept.null)
reject.null <- log((power)/alpha) / denom + nposs * log((1-pc)/(1-pt))/denom
reject.null <- ceiling(reject.null)
r.wald <- NULL
ns.wald <- NULL
for(i in 1:length(nposs)){
r.wald <- c(r.wald, accept.null[i]:reject.null[i])
ns.wald <- c(ns.wald, rep(nposs[i], length(accept.null[i]:reject.null[i])))
}
sc.subset <- data.frame(n=ns.wald, r=r.wald)
sc.subset <- sc.subset[sc.subset$n - sc.subset$r >=2, ]
}
}
# In case you want to specify values for r:
if(!is.null(fixed.r)) {
sc.subset <- sc.subset[sc.subset$r %in% fixed.r,]
}
###### Find thetas for each possible {r, N} combn:
mat.list <- vector("list", nrow(sc.subset))
for(i in 1:nrow(sc.subset)){
mat.list[[i]] <- findBlock2armUncurtailedMatrix(n=sc.subset[i,"n"], r=sc.subset[i,"r"], Bsize=Bsize, pat.cols=pat.cols.list[[paste(sc.subset$n[i])]], prob.vec=prob.vec)
}
store.all.thetas <- lapply(mat.list, function(x) {sort(unique(c(x))[unique(c(x)) <= 1])})
##### To cut down on computation, try cutting down the number of thetas used:
##### max.combns:=max. number of (theta0, theta1) combinations.
##### n.thetas*(n.thetas-1)/2 = n.combns, so if n.thetas > sqrt(2*max.combns), take out every other value, excluding 0 and 1.
##### Note: further below, more combns are removed if constraints on maxtheta0 and mintheta1 are specified.
# check ####
if(max.combns!=Inf){
maxthetas <- sqrt(2*max.combns)
for(i in 1:nrow(sc.subset))
{
while(length(store.all.thetas[[i]]) > maxthetas)
{
every.other.element <- rep(c(FALSE, TRUE), 0.5*(length(store.all.thetas[[i]])-2))
store.all.thetas[[i]] <- store.all.thetas[[i]][c(TRUE, every.other.element, TRUE)]
}
}
}
if(!is.null(exact.theta0) & !is.null(exact.theta1)){ # if exact thetas are given (to speed up a result check):
for(i in 1:length(store.all.thetas)){
keep <- abs(store.all.thetas[[i]]-exact.theta0)<1e-3 | abs(store.all.thetas[[i]]-exact.theta1)<1e-3
store.all.thetas[[i]] <- store.all.thetas[[i]][keep]
}
}
h.results.list <- vector("list", nrow(sc.subset)) #
pb <- txtProgressBar(min = 0, max = nrow(sc.subset), style = 3)
# Now, find the designs, looping over each possible {r, N} combination, and within each {r, N} combination, loop over all combns of {theta0, theta1}:
for(h in 1:nrow(sc.subset)){
#k <- 1
blank.mat <- matrix(NA, nrow=nrow(mat.list[[h]]), ncol=ncol(mat.list[[h]]))
rownames(blank.mat) <- 0:(nrow(blank.mat)-1)
zero.mat <- matrix(0, nrow=nrow(mat.list[[h]]), ncol=ncol(mat.list[[h]]))
rownames(zero.mat) <- rownames(blank.mat)
pat.cols.single <- pat.cols.list[[paste(sc.subset$n[h])]]
if(fast.method==TRUE){
h.results <- fastSearch(thetas=store.all.thetas[[h]],
maxtheta0=maxtheta0,
mintheta1=mintheta1,
sc.h=sc.subset[h,],
Bsize=Bsize,
mat.h=mat.list[[h]],
blank.mat=blank.mat,
zero.mat=zero.mat,
power=power,
alpha=alpha,
pat.cols.single=pat.cols.single,
prob.vec=prob.vec,
prob.vec.p0=prob.vec.p0)
}else{
h.results <- slowSearch(thetas=store.all.thetas[[h]],
maxtheta0=maxtheta0,
mintheta1=mintheta1,
sc.h=sc.subset[h,],
Bsize=Bsize,
mat.h=mat.list[[h]],
blank.mat=blank.mat,
zero.mat=zero.mat,
power=power,
alpha=alpha,
pat.cols.single=pat.cols.single,
prob.vec=prob.vec,
prob.vec.p0=prob.vec.p0)
}
setTxtProgressBar(pb, h)
h.results.df <- do.call(rbind, h.results)
if(!is.null(h.results.df)){
# Remove all "skipped" results:
colnames(h.results.df) <- c("n", "r", "block", "alpha", "power", "EssH0", "Ess", "theta0", "theta1", "eff.n")
h.results.df <- h.results.df[!is.na(h.results.df[, "Ess"]),]
if(nrow(h.results.df)>0){
# Remove dominated and duplicated designs:
discard <- rep(NA, nrow(h.results.df))
for(i in 1:nrow(h.results.df)){
discard[i] <- sum(h.results.df[i, "EssH0"] > h.results.df[, "EssH0"] & h.results.df[i, "Ess"] > h.results.df[, "Ess"] & h.results.df[i, "n"] >= h.results.df[, "n"])
}
h.results.df <- h.results.df[discard==0,, drop=FALSE]
#if(is.matrix(h.results.df)){ # i.e. if there is more than one design (if not, h.results.df is a vector)
# duplicates <- duplicated(h.results.df[, c("n", "Ess", "EssH0"), drop=FALSE])
# h.results.df <- h.results.df[!duplicates,, drop=FALSE]
# }
h.results.list[[h]] <- h.results.df
}
}
} # End of "h" loop
full.results <- do.call(rbind, h.results.list)
#if(length(full.results)==0) stop("There are no feasible designs for this combination of design parameters" , call. = FALSE)
if(length(full.results)>0){
# Discard all "inferior" designs:
discard <- rep(NA, nrow(full.results))
for(i in 1:nrow(full.results)){
discard[i] <- sum(full.results[i, "EssH0"] > full.results[, "EssH0"] & full.results[i, "Ess"] > full.results[, "Ess"] & full.results[i, "n"] >= full.results[, "n"])
#print(i)
}
subset.results <- full.results[discard==0,,drop=FALSE]
# Remove duplicates:
duplicates <- duplicated(subset.results[, c("n", "EssH0", "Ess"), drop=FALSE])
admissible.ds <- subset.results[!duplicates,,drop=FALSE]
admissible.ds$looks <- admissible.ds[,"eff.n"]/admissible.ds[,"block"]
admissible.ds$pc <- rep(pc, nrow(admissible.ds))
admissible.ds$pt <- rep(pt, nrow(admissible.ds))
return(admissible.ds)
}
}