Hi,

I don't have access to the article, but must presume that they are doing something "radically different" if you are "only" getting a total sample size of 20,000. Or is that 20,000 per arm?

Using the G*Power app that Mitchell references below (which I have used previously, since they have a Mac app):

Exact - Proportions: Inequality, two independent groups (Fisher's exact test)

Options: Exact distribution

Analysis: A priori: Compute required sample size

Input: Tail(s) = Two

Proportion p1 = 0.00154

Proportion p2 = 0.00234

? err prob = 0.05

Power (1-? err prob) = 0.8

Allocation ratio N2/N1 = 1

Output: Sample size group 1 = 49851

Sample size group 2 = 49851

Total sample size = 99702

Actual power = 0.8168040

Actual ? = 0.0462658

Using the base R power.prop.test() function:

power.prop.test(p1 = 0.00154, p2 = 0.00234, power = 0.8)

Two-sample comparison of proportions power calculation

n = 47490.34

p1 = 0.00154

p2 = 0.00234

sig.level = 0.05

power = 0.8

alternative = two.sided

NOTE: n is number in *each* group

Using Frank's bsamsize() function in Hmisc:

bsamsize(p1 = 0.00154, p2 = 0.00234, fraction = .5, alpha = .05, power = .8)

n1 n2

47490.34 47490.34

Finally, throwing together a quick Monte Carlo simulation using the FET, I get:

TwoSampleFET <- function(n, p1, p2, power = 0.85,

R = 5000, correct = FALSE)

{

MCSim <- function(n, p1, p2)

{

Control <- rbinom(n, 1, p1)

Treat <- rbinom(n, 1, p2)

fisher.test(cbind(table(Control), table(Treat)))$p.value

}

# Run MC Replicates

MC.res <- replicate(R, MCSim(n, p1, p2))

# Get p value at power quantile

quantile(MC.res, power)

}

# 50,000 per arm

TwoSampleFET(50000, p1 = 0.00154, p2 = 0.00234, power = 0.8, R = 500)

80%

0.04628263

So all four of these are coming back with numbers in the 48,000 to 50,000 ***per arm***.

HTH,

Marc Schwartz

On Nov 8, 2010, at 10:16 AM, Mitchell Maltenfort wrote:Not with R, but look for G*Power3, a free tool for power calc,

includes FIsher's test.

http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3On Mon, Nov 8, 2010 at 10:52 AM, Giulio Di Giovanni

wrote:

Hi,

I'm try to compute the minimum sample size needed to have at least an 80% of power, with alpha=0.05. The problem is that empirical proportions are really small: 0.00154 in one case and 0.00234. These are the estimated failure proportion of two medical treatments.

Thomas and Conlon (1992) suggested Fisher's exact test and proposed a computational method, which according to their table gives a sample size of roughly 20000. Unfortunately I cannot find any software applying their method.

-Does anyone know how to estimate sample size on Fisher's exact test by using R?

-Even better, does anybody know other, maybe optimal, methods for such a situation (small p1 and p2) and the corresponding R software?

Thanks in advance,

Giulio