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How does one account/control for differences between study sites during the analysis? In my study 2/3 of all participants across the two age groups strata came from 1 of my 2 study sites. Moreover, there are some differences in the level of experience of the health providers between the sites. 2/3 of the study participants were enrolled in the site with more experienced participants.

Is there a way of controlling for this e.g. when calculation the time it took to perform a procedure. Thought that come to mind are the mantel-Haenszel but I don't find it quite appropriate as I am not calculating any Odds ratios.

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If I understand the question correctly, you are trying to assess the relationship of some treatment/exposure on an outcome. However, you're worried that the site in which the patient is recorded can be confounding this relationship.

If you believe there is such a confounding issue, then including site fixed effects may be appropriate. If you believe that there's no confounding, you still need to address the site-level heterogeneity in your model because its presence violates the independence assumption of most models (i.e. you don't have independent patient observations since patients are observed within sites). You can handle this using random effects.

For a good review of random effects and fixed effects see the following sources:

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