This looks like a 2x2x4 (group)(visit)(time) factorial design. The groups are glaucoma and control. The visits are the two overnight visits and the 4 times 0.00-2.00, 2.00-4.00, 4.00-6.00 and 6.00-8.00. Intraocular pressure is the response. The ANOVA may be performed and appropriate inferences made.

I believe that your initial thoughts are correct. This is an area of longitudinal data analysis. My fav ref in this area is Prof. Marie Davidian's course notes. The link to those notes is :

https://www.stat.ncsu.edu/people/davidian/courses/st790/notes.html

If you look through these I believe you will find your answer.

Best of luck, David

Thanks very much for all suggestions. Just to clarify the main outcome here (level 1) is to compare pre and post intervention measurements of the intraocular pressure (continuous variable) in the whole cohort, so to compare 5 correlated measurements taken at specific time points. We have multiple within subject comparisons taken pre and post intervention. I should say that the eye pressure does not remain constant over night for an individual, typically we get higher readings towards morning hours.

So I would be comparing repeated paired measurements e.g. visit 1 2am with visit 2 2am etc. I am struggling to see how I could fit this into ANOVA. Comparing the glaucoma group with the control group is not a problem. I can simply derive between visits difference for each time point and use mixed design ANOVA with between subjects factor but this would only tell me whether both groups differ in response to CPAP and not whether CPAP increases the eye pressure between the visits. There is an additional problem of having measurements on two correlated eyes for each subject. Ideally, I would like to include both eyes into the model with a random intercept but I cannot think of any model which would allow for all these adjustments. The alternative here is to analyse both eyes separately, chose only one eye, a random eye or take a mean of the two eyes.

The link provided by David is very useful (thank you!) and I suspect this is the way to go but these models look quite complex for somebody who is not a statistician.

So far I simply derived the mean of the 5 measurements for each individual for each visit and compared between visits means with the t test. There is a significant difference regardless of how the eye is chosen which indicates that CPAP increases the eye pressure as I expected. I also compared means between two visits for each time point separately and noticed a higher mean difference towards morning hours. Is this simple approach a criminal offence?

Thanks a lot for your thoughts.

Dariusz

No, ofc it is not a criminal offense. As long as the repeated measure is accounted for the analysis is fine with the appropriate t-tests. The question is is there more information in the data that would be of interest and value to physicians and patients. The point of the models that Davidian develops is to try and get access to all of information in the data. I would encourage you to give it a try. Wish you the best, David