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binom_one_alpha=function(result.success,result.n,p0,failure,success,n){
# calculate exact alpha or p-value for a given binomial design for a given result.
# Adjusts for interim analysis which gives a different result if it is not taken into account.
# design provided (failure,success,n) should be based on the actual trial and not the proposed design.
if(length(which(result.n==n))==0){
stop("The final sample size must match design. Use the actual trial to adjust the design appropriately rather than the planned design")
}
prob.lower=0
prob.upper=0
###################################################################
ln=length(n)
old=c(1,rep(0,max(n)))
for(i in 1:ln){
if(i>1){
patients=n[i-1]
} else {
patients=0
}
ne=rep(0,max(n)+1)
# draw patients from distribution to get to stage i.
prob=dbinom(0:(n[i]-patients),n[i]-patients,p0)
# update current trial distribution
for(j in 1:(patients+1)){
ne[j:(j+n[i]-patients)]=ne[j:(j+n[i]-patients)] + old[j]*prob
}
if(result.n==n[i]){
if(result.success<=failure[i]){
if(result.success==0){
return(1-(prob.lower))
} else {
return(1-(prob.lower+sum(ne[1:(result.success)])))
}
} else {
return(prob.upper+sum(ne[(result.success+1):(n[i]+1)]))
}
}
if(!is.null(failure)){
if(!is.na(failure[i])){
prob.lower=prob.lower+sum(ne[1:(failure[i]+1)])
ne[1:(failure[i]+1)]=0
}}
if(!is.na(success[i])){
prob.upper=prob.upper+sum(ne[(success[i]+1):(n[i]+1)])
ne[(success[i]+1):(n[i]+1)]=0
}
old=ne
}
}
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