Thanks for your reply Marc. I'll look into the information you sent.
It ocurred to me that I could have done a better job of describing what I'm
trying to do. It can be difficult to do that sometimes when your unfamiliar
with a topic and are still trying to figure it out yourself.
In investigating this sample size calculation, I started by learning a little
about Simon Minimax designs. I started out with code that looks like the
following:
> library("clinfun")
>
> #### Single Stage Design ####
>
> ph2single(0.2, 0.4, 0.05, 0.10, 1)
n r Type I error Type II error
1 47 14 0.03663689 0.09877433
>
> #pu unacceptable response rate
> #pa response rate that is desirable
> #ep1 threshold for the probability of declaring drug desirable under p0
> #ep2 threshold for the probability of rejecting the drug under p1
> #nsoln number of designs with given alpha and beta
>
> #### Simon 2-Stage Optimal and Minimax Designs ####
>
> (simon <- ph2simon(0.2, 0.4, 0.05, 0.10))
Simon 2-stage Phase II design
Un
Desirable response rate: 0.4
Error rates: alpha = 0.05 ; beta = 0.1
r1 n1 r n EN(p0) PET(p0)
Optimal 4 19 15 54 30.43 0.6733
Minimax 5 24 13 45 31.23 0.6559
>
> #pu unacceptable response rate
> #pa response rate that is desirable
> #ep1 threshold for the probability of declaring drug desirable under p0
> #ep2 threshold for the probability of rejecting the drug under p1
> #nmax maximum total sample size (default 100; can be at most 500)
Then I needed to simultaneously take into account an efficacy and a toxicity
endpoint. The idea is that the new therapy might be more effective than an
older one but also more toxic. The hope is that it will have substantially
higher response rates without an unacceptable increase in toxicity.
I found a online calculator that does this at:
http://www.upci.upmc.edu/bf/resources.cfm
The calculator produces results like this:
INPUT PARAMATERS
Probability of Accepting Poor Respose (alphar) --> 0.1
Probability of Accepting Toxic Drug (alphat) ----> 0.15
Probability of Rejecting Good Drug (beta) -------> 0.15
Unacceptable Response Probability (Pr0) ---------> 0.2
Acceptable Response Probability (Pr1) -----------> 0.4
Unacceptable Non-toxicity Probability (Pt0) ----> 0.6
Acceptable Non-toxicity Probability (Pt1) ----> 0.8
EARLY TERMINATION PROBABILITY
Poor Response and Excessive Toxicity ------------> 0.79
Poor Response and Acceptable Toxicity -----------> 0.55
Good Response and Excessive Toxicity ------------> 0.56
Good Response and Acceptable Toxicity -----------> 0.05
THE OPTIMAL SOLUTION
First Stage Sample Size ---------------------------> 22
Upper Limit For 1st Stage Rejecting Drug Due To Inadequate Response -> 4
Upper Limit For 1st Stage Rejecting Drug Due To Excessive Toxcity -> 13
Maximum Sample Size -------------------------------> 33
Upper Limit for 2nd Stage Rejecting Drug Due To Inadequate Response -> 9
Upper Limit for 2nd Stage Rejecting Drug Due To Excessive Toxcity -> 22
---> Expected Sample Size 26.93
So this is an extension on the design. What I need though is an extension on an
extension. Specifically, I need a sample size estimate for a two-arm instead of
a one-arm design.
Of course, some other approach to sample size estimation that achieves the same
goal would be most welcome.
I'm not sure I'm likely to find anyone with a solution to this problem. I just
thought I should take the time to restate the problem as clearly as I can just
in case I'm wrong.
Thanks,
Paul
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