R help - Nov 2011 - Sample size calculations for one sided binomial exact test

I'm trying to compute sample size requirements for a binomial exact test.
 we want to show that the proportion is at least 90% assuming that it is
95%, with 80% power so any asymptotic approximations are out of the
questions.  I was planning on using binom.test to perform the simple test
against a prespecified value, but cannot find any functions for computing
sample size.  do any exist?

Thanks,
Andrew

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From: https://stat.ethz.ch/pipermail/r-help/2011-November/294329.html
> I'm trying to compute sample size requirements for a binomial exact
test.
>  we want to show that the proportion is at least 90% assuming that it is
> 95%, with 80% power so any asymptotic approximations are out of the
> questions.  I was planning on using binom.test to perform the simple test
> against a prespecified value, but cannot find any functions for computing
> sample size.  do any exist?
> 
> Thanks,
> Andrew


Hi,

I don't have the original e-mail, so this reply will be out of the thread in
the archive.

I am not aware of anything pre-existing in R for this application, but stand to
be corrected on that point.

There are at least two "non-R" related options:

1. The G*Power program which is available from:

  http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/


2. There is a paper by A'Hern which contains sample size tables here:

  Sample size tables for exact single-stage phase II designs
  R.P. A'Hern
  STATISTICS IN MEDICINE Statist. Med. 2001; 20:859?866
  http://stat.ethz.ch/education/semesters/as2011/bio/ahernSampleSize.pdf


The author used the BINOMDIST function in Excel to derive the tables.
Notwithstanding criticisms of Excel, these tables, based upon a small test
sample, agree with the G*Power program, as well as my own computations using R
code below. He also uses normal approximations for sample sizes >300, given
the limitations found in the BINOMDIST function.


Here is my R code for deriving the critical value and sample size for a one
sided exact binomial test, given an alpha, a null proportion, an alternate
proportion and the desired power:


# 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.
N <- 100:200

Alpha <- 0.05
Pow <- 0.8
p0 <- 0.90
p1 <- 0.95

# 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)

# Get Beta (Type II error) for each N at the alternate hypothesis
# proportion
Beta <- pbinom(CritVal, N, p1)

# Get the Power
Power <- 1 - Beta

# Find the smallest sample size yielding at least the required power
SampSize <- min(which(Power > Pow))

# Get and print the required number of events to reject the null
# given the sample size required
(Res <- paste(CritVal[SampSize] + 1, "out of", N[SampSize]))


# Plot it all 
plot(N, Power, type = "b", las = 1)

title(paste("One Sided Sample Size and Critical Value for H0 =", p0, 
            "versus HA = ", p1, "\n",
            "For Power = ", Pow),
      cex.main = 0.95)

points(N[SampSize], Power[SampSize], col = "red", pch = 19)

text(N[SampSize], Power[SampSize], col = "red",
     label = Res, pos = 3)

abline(h = Pow, lty = "dashed")




One thing to note here (see the plot) is the non-monotonic function describing
the power at each of the values of the sample size. This is due to the discrete
nature of the binomial distribution. It also generally means that you are
powering the sample size calculation for an alpha at something lower than the
value indicated. The G*Power program provides both the actual alpha and power,
given the input values. So there is a need to search the vector of sample sizes
where the power is greater than that desired, to obtain the smallest sample size
required to satisfy the power desired.

The above could of course be encapsulated in a function to make use easier, but
the code yields values that agree with both the G*Power application and
A'Hern's tables.

Hope that this is helpful.

Regards,

Marc Schwartz