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)
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)
# Run MC Replicates
MC.res <- replicate(R, MCSim(n, p1, p2))
# Get p value at power quantile
# 50,000 per arm
TwoSampleFET(50000, p1 = 0.00154, p2 = 0.00234, power = 0.8, R = 500)
So all four of these are coming back with numbers in the 48,000 to 50,000 ***per arm***.
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/gpower3
On Mon, Nov 8, 2010 at 10:52 AM, Giulio Di Giovanni
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,