Appropriate model choice for analyzing a cluster based longitudinal randomized controlled trial I am performing a randomized controlled trial (RCT) of an educational intervention to improve knowledge, belief and practice among healthcare workers in hospitals. One hospital is assigned to the intervention and the other hospital is selected as a control group. I will measure all outcomes at baseline data from both groups. I wish to compare the effects of my intervention at 1 month post-intervention, then 6 months post-intervention. 
I looked at distributions of baseline values. They appear approximately normally distributed and no difference between control and intervention group. Loss to follow up was minimal (110 respondents per group and only 6 respondents loss to follow up in each group). 
I know of three modeling approaches: generalized linear models, generalized linear mixed models, and generalized estimating equations. Which is better for this analysis? How do I see the effects of intervention within-and-between group and also if taking into account covariates (age, gender, position etc etc).
 A: A couple of points:


*

*Repeated measurements over time on the same subjects/patients are expected to be correlated. Hence, a GLM that assumes independent observations will not be appropriate.

*GEEs and GLMMs are typically used when you have non-normal outcome data, e.g., when your outcome is dichotomous or a count. In the case of normal data, you can use a linear mixed model or a marginal model. Since you only have three time points, and assuming that all subjects came at these specific time points and there were not many fluctuations, the more typical model to use is a marginal model (i.e., multivariate regression model) with unstructured covariance matrix for the error terms. If you work in R, this can be done with function gls() from package nlme.

*You should better check the appropriateness of the normal distribution for your data using the residuals of your model.

A: This cluster-based design is severely limited by the intervention being aliased entirely by the hospital in which it's performed. Ideally you would have included at least two more hospitals, possibly matched on some factors, and randomly permuted treatment assignment between pairs. This design demands adjustment for within-level covariates, adjustment for between level covariates risks reducing power and yet valid inference may not be possible without some control of them such as facility type (teaching hospital, etc.), regional SES, etc.
The collection of 1 and 6 months' post-baseline outcome is redundant except as it may contribute to a secondary hypothesis. The hypothesis to be tested is whether intervention increases education. So we don't expect anything but random variability between the 1 and 6 months' assessment. One could secondarily test a hypothesis of growth by adjusting for time and it's interaction with the outcome. 
If we selected only 1 month outcome data, we could test the hypothesis by using a between-within F-test for cluster randomized trials as described in Baldwin 2011 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3987820/ The best design for analyzing pre-post outcome data with one follow-up data point is an ANCOVA model where one adjusts for baseline values as a covariate in the model. The residuals of such a model are conditionally independent of one another. The test-statistic for the models which do and do not adjust for the indicator of receipt of intervention are best compared to an F distribution with 1 numerator degree of freedom and 2 denominator degrees of freedom which is very low power but appropriate to the design.
