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.

Monday, September 17, 2007

He makes the data sing their story

Hans Rosling gave a TED talk in 2006. If you love to work with data, you must watch this.

By the way, I am a statistician, and I love it. Yeah, this is all observational and "hypothesis-generating," as we like to say, but letting the data sing their story tells us where to concentrate our efforts.

Saturday, September 1, 2007

Bias in group sequential designs - site effect and Cochran-Mantel-Hanszel odds ratio

It is well known that estimating treatment effects from a group sequential design results in a bias. When you use the Cochran-Mantel-Haenszel statistic to estimate an odds ratio, the number of patients within each site affects the bias in the estimate of the odds ratio. I've presented the results of a simulation study, where I created a hypothetical trial and then resampled from this trial 1000 times. I calculated the approximate bias in the log odds ratio (i.e. log of the CMH odds ratio estimate) and plotted that versus the estimated log odds ratio. The line is cubic smoothing spline, made by the statement symbol i=sm75ps in SAS. The actual values are underprinted in light gray circles just to get some idea of the variability.