Compute the POS of a CT for any given true Treatment Effect

# An R script to compute the Probability of Success of a clinical trial
# for any given true Treatment Effect
#
# (c) 2019 Germain Garand <germain.garand@laposte.net>
#
# This is for information purposes only. Any calculation performed herein could be
# wrong and/or misrepresent reality. Use at your own risk.
#
# License: Creative Commons BY-NC 2.0
#
# Version 0.12
#


library(stats)
library(methods)
library(gsDesign, quietly=1)

# Proportions to test
# -------------------
# success rate in Comparator Arm
p1 = 23/100
# success rate in Treatment Arm
p2 = 33/100

# Trial characteristics
alpha = .05
power = .9
accrual = 400

a2 = alpha/2
b = 1 - power
n = nBinomial(p1=p1, p2=p2, alpha=a2, beta=b)

message("Trial design:")
message("-------------")
message(accrual, " patients ; Type-I error: ", alpha*100, "% ; Power: ", power*100, "%")
message("-------------")
message("Testing hypothesized true effect of ", p1*100, "% for Comparator arm vs. ", p2*100, "% for Treatment arm.")
message("Required accrual for ", power*100, "% probability of success: ", floor(n))
test = gsDesign(k=2, n.fix=n, alpha=a2, beta=b)
theta = test$theta[2]
message("We are looking for a theta value of: ", theta)
orig = gsDesign(k=2, n.fix=accrual, alpha=a2, beta=b)
#message("----------------------------------------")
#show(orig)
#message("----------------------------------------")
p = gsProbability(theta=theta, d=orig)
pos = sum(p$upper$prob)
message("The Probability of Success of the trial is: ", floor(pos*100), "%")