






Yep, it is 20.000 per arm, sorry. The reference it's about an application of the method, and I cannot download the paper with the main algorithm, so I don't know exactly how they did. 
Thanks everybody for the rich and interesting suggestions. Through free web software (PS, others)  I found also an N around 47.000 per arm. I guess these are the values (also seen Marc's Monte Carlo).
Maybe the Poisson models approach suggested by David can be an alternative, even if I guess at this point I won't get big differences in numbers. Would I?

Thanks a lot everybody again for your suggestions,  
if anybody has other comments, they are always welcome.

Best,

Giulio


> Subject: Re: [R] Sample size calculation for differences between two very small proportions (Fisher's exact test or others)?
> From: marc_schwartz@me.com
> Date: Mon, 8 Nov 2010 11:13:12 -0600
> CC: perimessaggini@hotmail.com; r-help@stat.math.ethz.ch
> To: mmalten@gmail.com
> 
> 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
> 			á err prob                 	=	0.05
> 			Power (1-â 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 á                   	=	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/gpower3
> > 
> > On Mon, Nov 8, 2010 at 10:52 AM, Giulio Di Giovanni
> > <perimessaggini@hotmail.com> 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
> 
 		 	   		  
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