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1-reproduce-results-functions-find-designs.R
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1-reproduce-results-functions-find-designs.R
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####
#### These functions are used to run the code that finds the designs used.
#### The main function, used to find designs, is findSCdes.
####
rmDominatedDesigns <- function(df, essh0="EssH0", essh1="Ess", n="n"){
discard <- rep(NA, nrow(df))
if("tbl_df" %in% class(df)){
essh0.vec <- df[[essh0]]
essh1.vec <- df[[essh1]]
n.vec <- df[[n]]
for(i in 1:nrow(df)){
discard[i] <- any(essh0.vec[i] > essh0.vec & essh1.vec[i] > essh1.vec & n.vec[i] >= n.vec)
}
} else {
essh0.vec <- df[, essh0]
essh1.vec <- df[, essh1]
n.vec <- df[, n]
for(i in 1:nrow(df)){
discard[i] <- any(essh0.vec[i] > essh0.vec & essh1.vec[i] > essh1.vec & n.vec[i] >= n.vec)
}
}
newdf <- df[discard==FALSE,,drop=FALSE]
newdf
}
find2armBlockOCs <- function(n,r, Bsize, mat, theta0, theta1, power, alpha, pat.cols, prob.vec, prob.vec.p0, blank.mat, zero.mat){
######################## UPDATE CP MATRIX USING THETA0/1 VALUES:
for(i in (n+r+1):1){
for(j in pat.cols){ # Only look every Bsize patients (no need to look at final col)
if(i-1<=j){ # Condition: Sm<=m
newcp <- sum(prob.vec*mat[i:(i+Bsize), j+Bsize])
if(newcp > theta1) mat[i,j] <- 1
if(newcp < theta0) mat[i,j] <- 0
if(newcp <= theta1 & newcp >= theta0) mat[i,j] <- newcp
}
}
}
###### STOP if design is pointless, i.e either failure or success is not possible:
# IF DESIGN GUARANTEES FAILURE (==0) or SUCCESS (==2) at n=C:
first.cohort <- sum(mat[,Bsize], na.rm = T)
if(first.cohort==Bsize+1){
return(c(n, r, Bsize, 1, 1, NA, NA, theta0, theta1, NA))
}
if(first.cohort==0){
return(c(n, r, Bsize, 0, 0, NA, NA, theta0, theta1, NA))
}
########################### FIND PROB. OF REACHING EACH POINT:
################# START WITH AN INDICATOR MATRIX OF NON-TERMINAL POINTS:
tp.mat <- blank.mat
tp.mat[which(mat==0 | mat==1)] <- 0
tp.mat[which(mat>0 & mat<1)] <- 1
############ CREATE MATRIX OF "POSSIBLE POINTS" -- IE, LIKE MATRIX OF NON-TERMINAL POINTS ***PLUS*** THE TERMINAL POINTS:
##### THIS WILL BE USED AS AN INDICATOR MATRIX FOR WHICH POINTS TO CALCULATE THE PROB'Y OF REACHING.
# Start with non-terminal points and add the terminal points
poss.mat <- tp.mat
poss.mat[1:(Bsize+1), Bsize] <- 1 # It is of course possible to reach 0,1,...Bsize after Bsize patients. This line is included in case CP=0 or CP=1 at first check (i.e. m=Bsize)
# Failures first:
fail.mat <- zero.mat
rows.with.cp0 <- which(apply(mat, 1, function(x) {any(x==0, na.rm = T)}))
fail.n <- apply(mat[rows.with.cp0,], 1, which.min)
for(i in 1:length(fail.n)){
poss.mat[names(fail.n)[i],fail.n[i]] <- 1
fail.mat[names(fail.n)[i],fail.n[i]] <- 1
}
# Now successes: what are the successful terminal points?
# Points with mat[i,j]==1 AND (0>mat[i,j-2]>1 OR 0>mat[i-1,j-2]>1 OR 0>mat[i-2,j-2]>1)
success.mat <- zero.mat
rows.with.cp1 <- which(apply(mat, 1, function(x) {any(x==1, na.rm = T)}))
# browser()
for(i in rows.with.cp1){
for(j in seq(Bsize, 2*n, by=Bsize)){
if(i-1<=j & mat[i,j]==1 & (j==Bsize | any(tp.mat[i:max(1,(i-Bsize)), j-Bsize]==1, na.rm=TRUE))){ # max() condition to take care of cases where
# Conditions ensure CP=1 and that it is possible to actually reach the point (tp.mat==1 indicates non terminal point)
poss.mat[i, j] <- 1
success.mat[i,j] <- 1
}
}
}
######################## PROBABILITY OF REACHING EACH POINT
############################## FIRSTLY, UNDER PT=PT
final.probs.mat <- poss.mat
# First n=Bsize rows (0,1,... Bsize-1) are special cases:
# fill in first column:
final.probs.mat[1:(Bsize+1), Bsize] <- prob.vec
for(i in 1:Bsize){
row.index <- which(poss.mat[i,]==1)[-1] # First entry (ie first column) has been inputted already, directly above, hence [-1]
for(j in row.index){
final.probs.mat[i, j] <- sum(prob.vec[1:i]*final.probs.mat[i:1, j-Bsize]*tp.mat[i:1, j-Bsize])
}
}
#if(n==16 & r==8) browser()
# For the remaining rows:
for(i in (Bsize+1):nrow(final.probs.mat)){ # Skip first Bsize rows; they have been taken care of above.
for(j in seq(2*Bsize, 2*n, by=Bsize)){ # skip first column of patients (n=2) -- again, they have been taken care of above.
if(i-1<=j & poss.mat[i,j]==1){
final.probs.mat[i,j] <- sum(prob.vec*final.probs.mat[i:(i-Bsize), j-Bsize]*tp.mat[i:(i-Bsize), j-Bsize], na.rm = TRUE)
}
}
}
# IMPORTANT: end early if pwr < power.
# Note 2: Could comment this out to ensure that the final test in undertaken for all runs, not just feasible ones.
prob.success <- final.probs.mat[success.mat==1]
pwr <- sum(prob.success)
if(pwr < power) # | pwr < power+tol )
{
return(c(n, r, Bsize, NA, pwr, NA, NA, theta0, theta1, NA))
}
############################## SECONDLY, UNDER PT=PC
final.probs.mat.p0 <- poss.mat
# First n=Bsize rows (0,1,... Bsize-1) are special cases:
# fill in first column:
final.probs.mat.p0[1:(Bsize+1), Bsize] <- prob.vec.p0
for(i in 1:Bsize){
row.index <- which(poss.mat[i,]==1)[-1] # First entry (ie first column) has been inputted already, directly above, hence [-1]
for(j in row.index){
final.probs.mat.p0[i, j] <- sum(prob.vec.p0[1:i]*final.probs.mat.p0[i:1, j-Bsize]*tp.mat[i:1, j-Bsize])
}
}
# For the remaining rows:
for(i in (Bsize+1):nrow(final.probs.mat.p0)){ # Skip first Bsize rows; they have been taken care of above.
for(j in seq(2*Bsize, 2*n, by=Bsize)){ # skip first column of patients (n=2) -- again, they have beene taken care of above.
if(i-1<=j & poss.mat[i,j]==1){
final.probs.mat.p0[i,j] <- sum(prob.vec.p0*final.probs.mat.p0[i:(i-Bsize), j-Bsize]*tp.mat[i:(i-Bsize), j-Bsize], na.rm = TRUE)
}
}
}
prob.success.p0 <- final.probs.mat.p0[success.mat==1]
typeIerr <- sum(prob.success.p0)
# IMPORTANT: end early if type I error > alpha
# Note 2: Could comment this out to ensure that the final test in undertaken for all runs, not just feasible ones.
if( typeIerr > alpha) # | alpha < alpha-tol)
{
return(c(n, r, Bsize, typeIerr, pwr, NA, NA, theta0, theta1, NA))
}
########################## ESS FOR SUCCESS POINTS
success.n <- which(success.mat==1, arr.ind = T)[,"col"] # Note: this is potentially dangerous if this and final.probs.mat[success.mat==1] are found in a different order, though this shouldn't be the case.
success.df <- data.frame(prob=prob.success, prob.p0=prob.success.p0, ess=prob.success*success.n, essH0=prob.success.p0*success.n)
################## ESS FOR FAILURE POINTS
fail.n <- which(fail.mat==1, arr.ind = T)[,"col"] # Note: this is potentially dangerous if this and final.probs.mat[success.mat==1] are found in a different order, though this shouldn't be the case.
prob.fail <- final.probs.mat[fail.mat==1]
prob.fail.p0 <- final.probs.mat.p0[fail.mat==1]
fail.df <- data.frame(prob=prob.fail, prob.p0=prob.fail.p0, ess=prob.fail*fail.n, essH0=prob.fail.p0*fail.n)
all.df <- rbind(fail.df, success.df)
###### CHECK PROBS ALL SUM TO 1
# sum(all.df$prob)
if(sum(all.df$prob)+sum(all.df$prob.p0)-2 > 1e-8) stop("Total probability of failure + success =/= 1. Something has gone wrong." , call. = FALSE)
ess <- sum(all.df$ess)
essH0 <- sum(all.df$essH0)
############ EFFECTIVE N. THE "EFFECTIVE N" OF A STUDY IS THE "REAL" MAXIMUM SAMPLE SIZE
######## The point is where every Sm for a given m equals zero or one is necessarily where a trial stops
cp.colsums <- apply(mat, 2, function(x) { sum(x==0, na.rm=TRUE)+sum(x==1, na.rm=TRUE)} ) # Sum the CP values that equal zero or one in each column
possible.cps <- apply(mat, 2, function(x) {sum(!is.na(x))})
effective.n <- min(which(cp.colsums==possible.cps))
return(data.frame(n=n, r=r, Bsize=Bsize, typeIerr=typeIerr, pwr=pwr, EssH0=essH0, Ess=ess, theta0=theta0, theta1=theta1, eff.n=effective.n))
}
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 designs:
if(rm.dominated.designs==TRUE){
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]
}
# Remove duplicated designs:
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)
}
}
findN1N2R1R2twoarm <- function(nmin, nmax, e1=FALSE){
nposs <- nmin:nmax
n1.list <- list()
n2.list <- list()
for(i in 1:length(nposs)){
n1.list[[i]] <- 1:(nposs[i]-1)
n2.list[[i]] <- nposs[i]-n1.list[[i]]
}
# All possibilities together:
n1 <- rev(unlist(n1.list))
n2 <- rev(unlist(n2.list))
n <- n1 + n2
ns <- cbind(n1, n2, n)
################################ FIND COMBNS OF R1 AND R ###############################
r1.list <- vector("list")
ns.list <- vector("list")
for(i in 1:nrow(ns)){
r1.list[[i]] <- -n1[i]:n1[i] # r1 values: -n1 to n1, for each possible n1
#ns.list[[i]] <-
}
rownames(ns) <- 1:nrow(ns)
ns <- ns[rep(row.names(ns), sapply(r1.list, length)), ] # duplicate each row so that there are sufficient rows for each r1 value
ns <- cbind(ns, unlist(r1.list))
colnames(ns)[4] <- "r1"
######### Add possible r values:
r.list1 <- apply(ns, 1, function(x) {(x["r1"]-x["n2"]):x["n"]}) # r must satisfy r > r1 and r < n. Also, number of responses required in stage 2 (r2-r1) must be at most n2
how.many.rs <- sapply(r.list1, length)
row.names(ns) <- 1:nrow(ns)
ns <- ns[rep(row.names(ns), how.many.rs), ] # duplicate each row a certain number of times
ns <- cbind(ns, unlist(r.list1))
colnames(ns)[5] <- "r2"
### Finally, add e1 for stopping for benefit:
if(e1==TRUE)
{
} else {
rownames(ns) <- 1:nrow(ns)
ns <- data.frame(ns)
}
return(ns)
}
findCarstenChenTypeITypeIIRmRows <- function(nr.list, pc, pt, runs, alpha, power, seed, method){
set.seed(seed)
########### Function for single row: Carsten #############
carstenSim <- function(h0, n1, n, a1, r2, pc, pt, runs){
if(h0==TRUE){
pt <- pc
}
n2 <- n-n1
nogo <- 0
go <- 0
ss <- rep(NA, runs)
all.pairs <- rbinom(runs*n, 1, prob=pt) - rbinom(runs*n, 1, prob=pc)
pairs.mat <- matrix(all.pairs, nrow=runs, ncol=n, byrow=TRUE)
for(i in 1:runs){
pair <- pairs.mat[i, ]
successes <- 0
fails <- 0
y <- 0
j <- 1
### Stage 1
while(y<n1 & successes<a1 & fails<n1-a1+1){
if(pair[j]==1){
successes <- successes+1
} else {
fails <- fails+1
}
y <- y+1
j <- j+1
}
### Trial fails at stage 1:
if(fails==n1-a1+1){
nogo <- nogo+1
ss[i] <- 2*y
} else {
### Trial does not fail at stage 1 -- recruit the remaining participants until curtailment or end:
while(y<n & successes<r2 & fails<n1+n2-r2+1){
if(pair[j]==1){
successes <- successes+1
} else {
fails <- fails+1
}
y <- y+1
j <- j+1
}
### Trial fails at stage 2:
if(fails==n1+n2-r2+1){
#print("fail at stage 2", q=F)
nogo <- nogo+1
} else {
go <- go+1
}
ss[i] <- 2*y
}
}
return(c(n1, n, a1, r2, go/runs, mean(ss)))
}
########### End of function for single row #############
########### Function for single row: Chen #############
chenSim <- function(h0, n1, n, a1, r2, pc, pt, runs){
n2 <- n-n1
# Stopping rules for S1 and S2:
s1.nogo <- n1-a1+1
s2.go <- n+r2
s2.nogo <- n-r2+1
# h0: Set TRUE to estimate type I error and ESS|pt=pc, set to FALSE for power and ESS|pt=pt
if(h0==TRUE){
pt <- pc
}
# Simulate all successes together, on trt and on control. "Success" means reponse if on trt, non-response if on control:
trt <- rbinom(n*runs, 1, prob=pt)
con <- rbinom(n*runs, 1, prob=1-pc)
##### Build matrix of successes, both stage 1 and stage 2 #####
# Allocate pats to trt or control. Note: Balance only required by end of trial.
alloc <- vector("list", runs)
n.times.i.minus.1 <- n*((1:runs)-1)
success.s12 <- matrix(rep(0, 2*n*runs), nrow=runs)
# TRUE for TREATMENT, FALSE for CONTROL:
for(i in 1:runs){
alloc[[i]] <- sample(rep(c(T, F), n), size=2*n, replace=F)
s.index <- (n.times.i.minus.1[i]+1):(n.times.i.minus.1[i]+n)
success.s12[i, alloc[[i]]] <- trt[s.index]
success.s12[i,!alloc[[i]]] <- con[s.index]
}
success <- success.s12
failure <- -1*(success-1)
# Cumulative successes and failures over time:
success.cum <- t(apply(success, 1, cumsum))
failure.cum <- t(apply(failure, 1, cumsum))
# Stage 1 only:
success.s1.cum <- success.cum[,1:(2*n1)]
failure.s1.cum <- failure.cum[,1:(2*n1)]
# Split into "curtailed during S1" and "not curtailed during S1". Note: curtail for no go only.
curtailed.s1.bin <- apply(failure.s1.cum, 1, function(x) any(x==s1.nogo))
curtailed.s1.index <- which(curtailed.s1.bin) # Index of trials/rows that reach the S1 no go stopping boundary
curtailed.s1.subset <- failure.s1.cum[curtailed.s1.index, , drop=FALSE]
# Sample size of trials curtailed at S1:
s1.curtailed.ss <- apply(curtailed.s1.subset, 1, function(x) which.max(x==s1.nogo))
########## All other trials progress to S2. Subset these:
success.cum.nocurtail.at.s1 <- success.cum[-curtailed.s1.index, , drop=FALSE]
failure.cum.nocurtail.at.s1 <- failure.cum[-curtailed.s1.index, , drop=FALSE]
# Trials/rows that reach the S2 go stopping boundary (including trials that continue to the end):
s2.go.bin <- apply(success.cum.nocurtail.at.s1, 1, function(x) any(x==s2.go))
s2.go.index <- which(s2.go.bin)
# Sample size of trials with a go decision:
s2.go.ss <- apply(success.cum.nocurtail.at.s1[s2.go.index, , drop=FALSE], 1, function(x) which.max(x==s2.go))
# Sample size of trials with a no go decision, conditional on not stopping in S1:
s2.nogo.ss <- apply(failure.cum.nocurtail.at.s1[-s2.go.index, , drop=FALSE], 1, function(x) which.max(x==s2.nogo))
ess <- sum(s1.curtailed.ss, s2.go.ss, s2.nogo.ss)/runs
prob.reject.h0 <- length(s2.go.ss)/runs
prob.accept.h0 <- (length(s2.nogo.ss)+length(s1.curtailed.ss))/runs
return(c(n1, n, a1, r2, prob.reject.h0, ess))
}
########### End of function for single row ############
output <- vector("list", nrow(nr.list))
# n1, n, a1/r1 are the same for each row of the data frame:
n1 <- nr.list[,"n1"][1]
n <- nr.list[,"n"][1]
a1 <- nr.list[,"r1"][1]
r2.vec <- nr.list[,"r2"]
# Run simulations and keep only {n1,n,a1,r2} combns that are feasible in terms of power:
if(method=="carsten"){
for(i in 1:nrow(nr.list)){
output[[i]] <- carstenSim(h0=FALSE, n1=n1, n=n, a1=a1, r2=r2.vec[i], pc=pc, pt=pt, runs=runs)
if(output[[i]][5]<power){ # stop as soon as power drops below fixed value (ie becomes unfeasible) and remove that row:
output[[i]] <- NULL
break
}
}
} else {
for(i in 1:nrow(nr.list)){
output[[i]] <- chenSim(h0=FALSE, n1=n1, n=n, a1=a1, r2=r2.vec[i], pc=pc, pt=pt, runs=runs)
if(output[[i]][5]<power){ # stop as soon as power drops below fixed value (ie becomes unfeasible) and remove that row:
output[[i]] <- NULL
break
}
}
}
output <- do.call(rbind, output)
if(!is.null(output)){
colnames(output) <- c("n1", "n", "r1", "r2", "pwr", "Ess")
output <- subset(output, output[,"pwr"]>=power)
# Now type I error:
typeIoutput <- vector("list", nrow(output))
if(method=="carsten"){
for(i in 1:nrow(output)){
typeIerr <- 0
# Reverse order of r2 values to start with greatest value and decrease, so that type I error increases the code proceeds:
reversed.r2 <- rev(output[,"r2"])
for(i in 1:nrow(output)){
typeIoutput[[i]] <- carstenSim(h0=TRUE, n1=n1, n=n, a1=a1, r2=reversed.r2[i], pc=pc, pt=pt, runs=runs)
if(typeIoutput[[i]][5]>alpha){ # stop as soon as type I error increases above fixed value (ie becomes unfeasible)and remove that row:
typeIoutput[[i]] <- NULL
break
}
}
}
} else{
for(i in 1:nrow(output)){
typeIerr <- 0
# Reverse order of r2 values to start with greatest value and decrease, so that type I error increases the code proceeds:
reversed.r2 <- rev(output[,"r2"])
for(i in 1:nrow(output)){
typeIoutput[[i]] <- chenSim(h0=TRUE, n1=n1, n=n, a1=a1, r2=reversed.r2[i], pc=pc, pt=pt, runs=runs)
if(typeIoutput[[i]][5]>alpha){ # stop as soon as type I error increases above fixed value (ie becomes unfeasible)and remove that row:
typeIoutput[[i]] <- NULL
break
}
}
}
}
} else{ # If there are no designs with pwr >= power, stop and return NULL:
return(output)
}
typeIoutput <- do.call(rbind, typeIoutput)
# If there are feasible designs, merge power and type I error results, o/w stop:
if(!is.null(typeIoutput)){
colnames(typeIoutput) <- c("n1", "n", "r1", "r2", "typeIerr", "EssH0")
all.results <- merge(output, typeIoutput, all=FALSE)
} else{
return(typeIoutput)
}
# # Subset to feasible results:
# subset.results <- all.results[all.results[,"typeIerr"]<=alpha & all.results[,"pwr"]>=power, ]
#
# if(nrow(subset.results)>0){
# # Discard all "inferior" designs:
# discard <- rep(NA, nrow(subset.results))
# for(i in 1:nrow(subset.results)){
# discard[i] <- sum(subset.results[i, "EssH0"] > subset.results[, "EssH0"] & subset.results[i, "Ess"] > subset.results[, "Ess"] & subset.results[i, "n"] >= subset.results[, "n"])
# #print(i)
# }
# subset.results <- subset.results[discard==0,,drop=FALSE]
# }
# return(subset.results)
return(all.results)
}
findSingle2arm2stageJungDesignFast <- function(n1, n2, n, a1, r2, p0, p1, alpha, power){
#print(paste(n, n1, n2), q=F)
k1 <- a1:n1
y1.list <- list()
for(i in 1:length(k1)){
y1.list[[i]] <- max(0, -k1[i]):(n1-max(0, k1[i]))
}
k1 <- rep(k1, sapply(y1.list, length))
y1 <- unlist(y1.list)
combns <- cbind(k1, y1)
colnames(combns) <- c("k1", "y1")
rownames(combns) <- 1:nrow(combns)
k2.list <- vector("list", length(k1))
for(i in 1:length(k1)){
k2.list[[i]] <- (r2-k1[i]):n2
}
combns2 <- combns[rep(row.names(combns), sapply(k2.list, length)), , drop=FALSE] # duplicate each row so that there are sufficient rows for each a1 value
k2 <- unlist(k2.list)
combns2 <- cbind(combns2, k2)
rownames(combns2) <- 1:nrow(combns2)
y2.list <- vector("list", length(k2))
for(i in 1:length(k2)){
current.k2 <- -k2[i]
y2.list[[i]] <- max(0, current.k2):(n2-max(0, current.k2))
}
y2 <- unlist(y2.list)
combns3 <- combns2[rep(row.names(combns2), sapply(y2.list, length)), , drop=FALSE] # duplicate each row so that there are sufficient rows for each a1 value
all.combns <- cbind(combns3, y2)
# Convert to vectors for speed:
k1.vec <- all.combns[,"k1"]
y1.vec <- all.combns[,"y1"]
k2.vec <- all.combns[,"k2"]
y2.vec <- all.combns[,"y2"]
# Easier to understand, but slower:
part1 <- choose(n1, y1.vec)*p0^y1.vec*(1-p0)^(n1-y1.vec) * choose(n2, y2.vec)*p0^y2.vec*(1-p0)^(n2-y2.vec)
typeIerr <- sum(part1 * choose(n1, k1.vec+y1.vec)*p0^(k1.vec+y1.vec)*(1-p0)^(n1-(k1.vec+y1.vec)) * choose(n2, k2.vec+y2.vec)*p0^(k2.vec+y2.vec)*(1-p0)^(n2-(k2.vec+y2.vec)))
pwr <- sum(part1 * choose(n1, k1.vec+y1.vec)*p1^(k1.vec+y1.vec)*(1-p1)^(n1-(k1.vec+y1.vec)) * choose(n2, k2.vec+y2.vec)*p1^(k2.vec+y2.vec)*(1-p1)^(n2-(k2.vec+y2.vec)))
# Harder to understand, but faster:
# q0 <- 1-p0
# q1 <- 1-p1
# n1.minus.y1 <- n1-y1.vec
# n2.minus.y2 <- n1-y1.vec
# k1.plus.y1 <- k1.vec+y1.vec
# k2.plus.y2 <- k2.vec+y2.vec
# n1.minus.k1.and.y1 <- n1-k1.plus.y1
# n2.minus.k2.and.y2 <- n2-k2.plus.y2
# choose.n1.k1.plus.y1 <- choose(n1, k1.plus.y1)
# choose.n2.k2.plus.y2 <- choose(n2, k2.plus.y2)
#
# part1 <- choose(n1, y1.vec)*p0^y1.vec*q0^n1.minus.y1 * choose(n2, y2.vec)*p0^y2.vec*q0^n2.minus.y2 * choose.n1.k1.plus.y1 * choose.n2.k2.plus.y2
# typeIerr <- sum(part1 * p0^k1.plus.y1*q0^n1.minus.k1.and.y1 * p0^k2.plus.y2*q0^n2.minus.k2.and.y2)
# pwr <- sum(part1 * p1^k1.plus.y1*q1^n1.minus.k1.and.y1 * p1^k2.plus.y2*q1^n2.minus.k2.and.y2)
# Find ESS under H0 and H1:
if(typeIerr<=alpha & pwr>=power){
k11 <- -n1:(a1-1)
y11.list <- vector("list", length(k11))
for(i in 1:length(k11)){
y11.list[[i]] <- max(0, -k11[i]):(n1-max(0, k11[i]))
}
k11.vec <- rep(k11, sapply(y11.list, length))
y11.vec <- unlist(y11.list)
petH0 <- sum(choose(n1, y11.vec)*p0^y11.vec*(1-p0)^(n1-y11.vec) * choose(n1, k11.vec+y11.vec)*p0^(k11.vec+y11.vec)*(1-p0)^(n1-(k11.vec+y11.vec)))
petH1 <- sum(choose(n1, y11.vec)*p1^y11.vec*(1-p1)^(n1-y11.vec) * choose(n1, k11.vec+y11.vec)*p1^(k11.vec+y11.vec)*(1-p1)^(n1-(k11.vec+y11.vec)))
# choose.n1.y11 <- choose(n1, y11.vec)
# n1.minus.y11 <- n1-y11.vec
# choose.k11.y11 <- choose(n1, k11.vec+y11.vec)
# k11.y11 <- k11.vec+y11.vec
# n1.minus.k11.y11 <- n1-k11.y11
#
# pet.part1 <- choose.n1.y11 * choose.k11.y11
# petH0 <- sum(pet.part1 * p0^y11.vec*q0^n1.minus.y11 * p0^k11.y11*q0^n1.minus.k11.y11)
# petH1 <- sum(pet.part1 * p1^y11.vec*q1^n1.minus.y11 * p1^k11.y11*q1^n1.minus.k11.y11)
essH0 <- n1*petH0 + n*(1-petH0)
essH1 <- n1*petH1 + n*(1-petH1)
return(c(n1, n2, n, a1, r2, typeIerr, pwr, essH0, essH1))
} else {
return(c(n1, n2, n, a1, r2, typeIerr, pwr, NA, NA))
}
}
######## Find stopping boundaries for one design #########
# The function findBounds can be used to find stopping boundaries for an SC design.
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
}
findBlockCP <- function(n, r, Bsize, pc, pt, theta0, theta1){
pat.cols <- seq(from=2*n, to=2, by=-Bsize)[-1]
qc <- 1-pc
qt <- 1-pt
prob.vec <- findProbVec(Bsize=Bsize,
pt=pt,
qt=qt,
pc=pc,
qc=qc)
# CREATE UNCURTAILED MATRIX
mat <- matrix(3, ncol=2*n, nrow=min(n+r+Bsize+2, 2*n+1))
rownames(mat) <- 0:(nrow(mat)-1)
mat[(n+r+2):nrow(mat),] <- 1
mat[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
# browser()
# print(paste("Rows:", i:(i+Bsize), ", Columns: ", j+Bsize, sep=""))
# print(mat[i:(i+Bsize), j+Bsize])
mat[i,j] <- ifelse(test=j-(i-1) > n-r+1, yes=0, no=sum(prob.vec*mat[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(mat)){
mat[i, 1:(i-2)] <- NA
}
uncurt <- mat
### CREATE CURTAILED MATRIX
for(i in (n+r+1):1){
for(j in pat.cols){ # Only look every Bsize patients (no need to look at final col)
if(i-1<=j){ # Condition: Sm<=m
newcp <- sum(prob.vec*mat[i:(i+Bsize), j+Bsize])
if(newcp > theta1) mat[i,j] <- 1
if(newcp < theta0) mat[i,j] <- 0
if(newcp <= theta1 & newcp >= theta0) mat[i,j] <- newcp
}
}
}
return(mat)
}
findBounds <- function(output){
Bsize <- output$block
mat <- findBlockCP(n=output$n,
r=output$r,
Bsize=output$block,
pc=output$pc,
pt=output$pt,
theta0=output$theta0,
theta1=output$theta1)
boundaries <- matrix(NA, nrow=2, ncol=ncol(mat)/Bsize)
rownames(boundaries) <- c("lower", "upper")
interims <- seq(from=Bsize, to=ncol(mat), by=Bsize)
colnames(boundaries) <- paste(interims)
for(i in 1:length(interims)){
j <- interims[i]
lower <- if (any(mat[,j]==0, na.rm=TRUE) ) max(which(mat[,j]==0))-1 else NA
upper <- if (any(mat[,j]==1, na.rm=TRUE) ) which.max(mat[,j])-1 else NA
# -1 terms to account for the fact that row 1 is equivalent to zero successes.
boundaries[, i] <- c(lower, upper)
}
return(boundaries)
}
# Plot rejection regions ####
# Write a program that will find the sample size using our design and Carsten's design, for a given set of data #
# for p0=0.1, p1=0.3, alpha=0.15, power=0.8, h0-optimal designs are:
# Carsten:
# n1=7; n=16; r1=1; r2=3
# This design should have the following OCs:
# Type I error: 0.148, Power: 0.809, EssH0: 21.27400, EssH1: 19.44200
#
# Our design (not strictly H0-optimal, but is within 0.5 of optimal wrt EssH0 and has N=31, vs N=71 for the actual H0-optimal):
# n=31; r2=3; theta0=0.1277766; theta1=0.9300000
findRejectionRegions <- function(n, r, theta0=NULL, theta1=NULL, pc, pt, method=NULL){
########## Function to find CP matrix for our design:
findBlockCP <- function(n, r, pc, pt, theta0, theta1){
Bsize <- 2
pat.cols <- seq(from=2*n, to=2, by=-2)[-1]