```
# based on code from Marc Schwartz [email protected]
# The possible sample size vector n needs to be selected in such a fashion
# that it covers the possible range of values that include the true
# minima. My example here does with a finite range and makes the
# plot easier to visualize.
# NOTE: this is more conservative than using a 2-sided exact test in binom.test
nBinomial1Sample <- function(p0 = 0.90, p1=0.95,
alpha = 0.025, beta=NULL,
n = 200:250, outtype=1, conservative=FALSE){
Pow = 1-beta
# Required number of events, given a vector of sample sizes (n)
# to be considered at the null proportion, for the given alpha
CritVal <- qbinom(p = 1 - alpha, size = n, prob = p0) + 1
Alpha <- pbinom(q = CritVal - 1, size=n, prob=p0, lower.tail=FALSE)
# Get the Power for each n at the alternate hypothesis
# proportion
Power <- pbinom(CritVal - 1, n, p1, lower.tail=FALSE)
bta <- 1 - Power
if (is.null(beta)) beta <- bta
if (outtype==3 || is.null(beta)) return(data.frame(p0=p0, p1=p1, alpha=alpha, beta=beta,
n=n, b=CritVal,
alphaR=Alpha, Power=Power))
if (max(Power)<Pow) return(NULL)
if (is.null(beta)) beta <- 1-Power
# Find the smallest sample size yielding at least the required power
if (!conservative){SampSize <- min(which(Power >= Pow))
}else if (min(Power >= Pow)==1){SampSize=1
}else SampSize <- max(which(Power < Pow)) + 1
if (outtype==2) return(data.frame(p0=p0, p1=p1, alpha=alpha, beta=beta,
n=n[SampSize], b=CritVal[SampSize],
alphaR=Alpha[SampSize], Power=Power[SampSize]))
return(n[SampSize])
}
```

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