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I am analyzing data from a cluster randomized cross over trial. There are 9 clusters and 3 periods in the data. The clusters are dental clinics and in each period different patients are sampled. I have three interventions (control, treatment1, treatment2).

Each cluster receives all three interventions but in random order. My question is how to analyze the data. Obviously there is some clustering going on in the dataset. Patients are clustered in clinics and also clustered in periods within clinics (sometimes referred to as "cluster-periods").

The whole point of the design is to estimate treatment effects within clinics as opposed to between clinics in a standard cluster randomized trial. Because of practical limitations i had no data on the clinics when the randomization was done and the clinics are very geographically spread out. This eliminated any stratification or matching strategies and there are too few clusters (clinics) to ensure balance between experimental groups. To eliminate imbalances between experimental groups aswell as eliminate sampling variability due to between cluster variation a cross over design was used.

The literature seem somewhat confused about how to correctly analyze data from such a trial. Here are my thoughts on how to do is so far:

Since i observe each cluster more than once i can effectively estimate treatment effects within clusters. Does this mean i can run a regression with a fixed effect for cluster (cluster dummies) to eliminate all between cluster variation? Will this also take account of the unobserved cluster-specific component in the error term causing individuals within clusters to be correlated?

Can i include dummies for time periods? Will this correct for common period effects?

How do i correctly account for clustering? I cannot used cluster corrected standard errors clustering patient on the cluster level with so few clusters. Clustering by cluster-period I also have very few clusters.

I am sorry if it is a little confusing.

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This is a very good question and is an area of active research without enough statistical guidelines. Four of the papers listed here are very relevant: http://www.citeulike.org/user/harrelfe/tag/crossover

I think that you'll find that mixed effects models are probably preferred.

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    $\begingroup$ Thank you for the answer. I have read most of the articles you link to but i will look at them again. Do you have a suggestion for a model specification (general or specific) i could use to analyze my data? $\endgroup$ – Jonathan Marin May 21 '17 at 19:17
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    $\begingroup$ Not anything that's not in those papers. The best way to say "thanks" is upvoting an answer :-) $\endgroup$ – Frank Harrell May 21 '17 at 19:39
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    $\begingroup$ Would it be sensible to run a regression with fixed effects for clusters, period and period by cluster interaction. More specifically by including dummies for clinics and time periods aswell as interactions between those? it appears that some of the papers you suggest (morgen et. al) suggests fixed effects for both period and cluster wheras others dont. The idea is to control for common time trends aswell as cluster effects. $\endgroup$ – Jonathan Marin May 21 '17 at 20:23
  • $\begingroup$ Besides the question of whether random effects work better than fixed effects here, see if the treatment contrast you envision would be completely confounded with other factors with the model you mentioned. $\endgroup$ – Frank Harrell May 22 '17 at 1:52

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