Wednesday, September 19, 2007

My O'Brien-Fleming design is not the same as your O'Brien-Fleming design

I know this discussion is a little technical, and nonstatisticians can probably skip this, but I hope that a statistician struggling with the O'Brien-Fleming design and its implementation in SAS/IML (notably the SEQ, SEQSHIFT, and SEQSCALE functions) can find this from a search engine and save hours of headache.

There are two ways of designing an O'Brien-Fleming design, a popular design for conducting interim analyses of clinical trials. The first method is to use an error (or alpha) spending function, which essentially gives you a "budget" of error you can spend at each interim analysis. The second is to realize that, if you are looking at cumulative sums in the trial, the O'Brien-Fleming design terminates if you cross a constant threshhold. In the popular design programs LD98 and PASS 2007, the spending function approach is used. In the book Analysis of Clinical Trials using SAS, (a book I highly recommend, by the way), the cumulative sum approach is used at the design stage (the spending function is used at the monitoring stage). When interim analyses are equally spaced, the two approaches give the same answer. When interim analyses are not equally spaced, the two approaches seem to give different answers. What's more, the spending function for O'Brien-Fleming as implemented in LD98 and PASS are different from what they show you in the books. They use:

4 - 4*PHI(z(1-alpha/4)/sqrt(tau))

for two-sided designs.

They don't tell you these things in school. Or in the books.

Update: Steve Simon's post on the topic has moved as of 11/21/2008. Please see the third comment below.