Since it is basically a linear statistical model, I would suggest as a minimum, n>5*(the number of IVs in the model). More would probably be better. See an expert, Prof. Marie Davidian's work on the subject at:

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

Best wishes, David Booth

Thanks, David. Much appreciated.

Hi Evan.

If the groups are at random, then why are you adjusting for covariates in the first place - any differences in the demographics have to be random!

If you do want to adjust, then the rules about over-fitting are a bit tricky for linear mixed effects models since each individual is measured more than once. Techniques like bootstrapping can help avoid the problem of over-fitting. I tend to use the Stata procedure swboot which undertakes bagging, or aggregated bootstrapped stepwise regression.

When you have just 2 time points I would not use a mixed model but standard regression of the post value on the pre value to model change; unless you have additional structure above the individual

for some orientation see

https://www.researchgate.net/post/What_are_the_Longitudinal_Data_Analyses_Options_for_just_Two_Time_Points

Adrian Esterman Good question (and something I'm still wrestling with). Several of the demographic covariates in this study may be prognostic with respect to the DVs in this particular sample (persons with dementia). Given my small sample size, though, I'd like to keep the number of covariates to a minimum--hence the original question.

Kelvyn Jones This approach seems very sensible. Thank you!

This is all excellent advice and I'm underqualified to comment too deeply. I would say, however, that the biology of the system should also be thought about and included in your model. If there are known risk factors then possibly these should also be reflected in your analysis to ensure more easy translation to wider populations.

Also, have you thought about interactions between covariates? These might be more meaningful than assessing the covariates themselves?

I can understand that if the numbers are small that randomization doe not guarantee equipoise.

Have you thought about using a propensity score? So that all the potential covariates can be reduced to one score

Article Propensity score matching and randomisation

And remember including covariates changes the meaning of the group difference comparisons. For decades many have urged caution when choosing to use covariates (e.g., http://meehl.umn.edu/sites/g/files/pua1696/f/084nuisancevariables.pdf), but at least in my little brain this has come into more focus in recent decades with the popularity of graphs for exploring causation (e.g., http://bayes.cs.ucla.edu/BOOK-09/causality2-excerpts.htm). So following from Joseph V Moxon comment, I would recommend thinking about how the different variables relate before just using them to increase power (or whatever other reasons you may use them). I am not saying don't use them, but be careful.

Also, with just two groups, as Kelvyn Jones says, the data can be treated with simpler analysis. Think whether it is appropriate to predict T2 from T1 (ancova) or model that gain score (T2-T1) or something else. There is a lot written on this topic (google Lord's paradox) and there are circumstances where one model is preferred to the other (e.g., Preprint How Students are Allocated to Schools Should Inform the Mode...

Thanks to everyone for the excellent feedback!

I am sending you one of my papers. However, the responses we have considered are binary and not normal. We have 3 time points. Small samples are considered and simulation studies have been carried out.