You may have to increase the sample size to adjust for  the necessity of keeping the p balue significant

thank you

As far as I know, the alpha and beta are calculated for the full sample size. After that, if you decide to perform an interim analysis, you will have to deal with the "alpha spending" issue, but the sample size calculation was already done. At least I used to think that way. I'm curious to see more answers to this question. 

The sample size is determined by the overall alpha and beta, although there may be a very small adjustment. Keep in mind that the expected sample size may not be the target sample size, depending on the decision to be made at the IA, when the IA is performed, and other factors. My favorite reference on this and related topics is the book "Group Sequential Methods with Applications to Clinical Trials" by Jennison and Turnbull - there are many others.

Thank you David!

 Allan,

this is what I learnt too. but I am writing a book chapter on sample size calculation and have been reading that in some cases the sample size is adjusted based on interim analysis finding.

Rachel,

Your original question pertained to a sample size calculation for an IA; I assumed that it was for testing superiority, futility, or similar.

There are a plethora of articles on adaptive designs, including sample size re-estimation. I have written a few.I haven't published any recently, but I have some recent presentations. Check my papers; it should be obvious which pertain to this topic. My recent presentations have focused on the issue that much of the literature is in praise of the technique. It is valuable when it works; however, you don't know when it works because the results depend on unknown parameters. One of my examples shows that if you assume the correct mean and variance, so the assumed sample size is correct and does not need adjustment, the new sample size will more than 3 times larger than necessary about 20% of the time, based on simulations. Simply, this is due to the long tail for the non-central chi-squared distribution.

I also disagree with the FDA Guidance on Adaptive Designs which states that sample size should only be adjusted upward.

Increasing sample size until a significant result is achieved is a form of p-hacking. Terminating an experiment early once significance is achieved is a variant. There are problems with this approach when trying to interpret the literature in that you get many more significant outcomes than you should.

Start with this publication, and look at the papers that it cites, the papers that cite this one. This is part of a long standing debate in the statistical literature and those disciplines that use statistics as a tool.

http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124

Thank you Timothy

it seems to me that the more I read about it the more I perceive that there is no strict rule for when to adjust sample size after interim analyses

 David

yes, I was thinking about stopping rules for superiority trials.

thank you for your suggestions

Rachel,

Just to provide a bit more information. Consider the comparison of 2 normal distributions. The sample size assuming a standardized difference of 0.3 is 175 /group for power of 80% and alpha=5% (two-sided). Using O'Brien-Fleming Boundary, the required sample size is 176/group for one IA at 50% and 179/group for 4 equally spaced IAs. Using the Pocock Boundary, the required sample size is 187/group for 1 IA and 212/group for 4 equally spaced IAs. These values were obtained using EAST 6.4. There is other software available, but this is my favorite.

David

this is really helpful David!

will you be wiling to revise a stat chapter of my book and be a co-author?

your knowledge would be an asset. of course, I understand completely if you cannot.

best regards!

Rachel,

I would be happy to work with you, pending a few more details.

Contact me at

[email protected].

David