multicenter designs and power analysis

#1
Hello all,

I am designing a study for examining the efficacy of a new treatment vs. a standard of care. For simplicity, let's say that my outcome is either continuous (mean diff) or binary (proportions). The problem is, that the study is a multicenter study. Subject will be enrolled to the study in different locations (hospitals). Naturally, different centers differ, if it's different doctors, different equipment, or other reasons. From statistical point of view, the centers are a random effect.

My intuition say that the addition of this random effect causes a lack of power and bring a need to increase the sample size. I wanted to hear your opinion on the matter and to ask if you know any way to correct the sample size formula so that the power will remain in the required level ?

Thank you !
 

Lazar

Phineas Packard
#3
With complex models, simulation approaches to power analysis are a better way to go. Details of how to do this can be found in "Data Analysis Using Regression and Multilevel/Hierarchical Models" (Gelman and Hill)
 

Jake

Cookie Scientist
#4
I would agree with the general sentiment that it is often best to resort to simulation-based methods of power analysis for complicated models/designs, but I don't think the situation described by the OP is quite at that level of complexity. Power analysis for simple multilevel designs is pretty well understood and analytical power results are fairly easy to obtain and understand.

My intuition say that the addition of this random effect causes a lack of power and bring a need to increase the sample size.
Not necessarily. If there is no variance in the treatment effects across centers, the multilevel design is actually more powerful than a simple random sample from one center -- assuming that the total variance of the response is equal in both scenarios. (The OP's intuition might reflect the possibility that the response variable could simply have greater variance in the multilevel case, however this is not really a design issue per se.) If there is variance in the random treatment effects across centers, the multilevel design could be more powerful or less powerful than the simple random sample.

The following excellent chapters by Tom Snijders discuss power in multilevel designs:
http://www.stats.ox.ac.uk/~snijders/sampling.pdf
http://www.stats.ox.ac.uk/~snijders/PowerSampleSizeMultilevel.pdf

I wanted to hear your opinion on the matter and to ask if you know any way to correct the sample size formula so that the power will remain in the required level ?
Tom Snijders's free power analysis program "PINT" is a good start for getting power estimates for this kind of design.