[R] Multiple endpoint (possibly group sequential) sample size calculation

[Paul Miller]

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