## Sample size for a multicenter study

Regular Contributor
Posts: 180

# Sample size for a multicenter study

Dear all,

I am trying to dig up a sample size for a future multicenter study. My outcome variable is a time to event variable, and it's to be analyzed using the log rank test and the cox proportional hazrad regression model (or an equivalent generalized mixed model).

My problem is the multicenter design. My intuition say that the addition of a random effect, i.e., the "center", and the necessity to estimate it's variance, cause a loss of power and thus require an increment of the sample size. However, I read an article [1] claiming that there can actually be a gain of power (how can it be ?), and, I am yet to find a rule of thumb or a formula for the adjustment or calculation of the sample size.

The aim of the study is to examine a new medical device (surgical) and to compare it to the gold standard. I wish to have 2 groups, with equal sample sizes, one for each treatment. Each subject will have the surgery using the randomized device. The success will then be examined, and the relapse will be examined in 6 follow up times. I wish to show that the new device is better (actually I wish to show that it's non inferior, but to simplify things now let's assume it's a standard hypothesis). I can give the expected failure proportion in both groups, let's call them 'x' and 'y' for now. I do not know how to calculate the median time prior having any data and also not sure how to define the hazard ratio. I do not know if there will be any dropouts, I can only guess a dropout of 5%. The significance level is of course 5%, and the desired power is minimum 80%. I wish to use SAS proc power for the calculations.

How would you deal with the multicenter problem ? I do not wish to lack power in later stages. I was thinking of a simulation, but I wouldn't know where to start.

Edit: In another article I found [2], it is shown for continuous outcome that a multicenter design reduces the sample size, my intuition can't accept it, what can be a possible reason for a reduction, I am actually adding another variance component, and need to estimate more unknown parameters.

[1] Design effect in multicenter studies: gain or loss of power \ Vierron, Giraudeau

[2] Sample size calculation for multicenter randomized trial \ Vierron, Giraudeau

Posts: 2,116

## Re: Sample size for a multicenter study

When designing studies for Pharma, we typically do not include the site in the design.  There are several reasons for this

1) the randomization should address the inherent skill levels of the surgical teams

2) most sites are too small for any one site to have a major impact.

3) it is quite rare for the sites to have even close to the same sample sizes and sponsors don't want to cut off the high enrollers.

That said, we often test for regional effects as a post hock test to understand some variability there.  It is more of a data quality check.  We have rarely found differences in relative outcome, but sometimes found differences in the underlying disease burden of those randomized.

Doc Muhlbaier

Duke Clinical Research Institute

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Regular Contributor
Posts: 180

## Re: Sample size for a multicenter study

Is this approach, of not taking the multicenter effect into account in the sample size stage, acceptable by the FDA (assuming that the regulations for pharma and medical devices are identical when it comes to statistics) ?