How to analyze the data for multiply measuring result from the mice pass the machine for Gait Analysis? We want to compare the difference of the data from Gait Analysis between normal group and treatment group in mice.
There are 6 mice in the normal group and treatment group, respectively.  We plan to conduct all mice pass the machine of Shuttle-Box for Gait Analysis one by one.
Due to the data varied widely from itself, we arrange each mice passes the Shuttle-Box four times (round1~round4).
Why the data varied widely? We suspect that the emotional state of mice may play a role in the results. Mice are naturally very timid and shy animals. The result of gait analysis might be influenced by even mild stimulus. Thus, the data was much different every round (round1~round4) for each mice.
So, how to analyze the data for this study?
1、Firstly, we calculated the average for each mice (round1~round4) in normal group and the average for each mice (round1~round4) in treatment group, respectively. We compared the average between two groups by t tests.
2、Alternatively, could the study also be considered as repeated measure design? And we conduct the study by using GLMM or GEE approach.  However, in the study, we arrange each mice passes the Shuttle-Box four times (round1~round4).
Is it different from the traditional time factor for repeated measure study? (Such as, the patients take a new antihypertensive drug, we measured their blood pressure at 7days, 14days, 21days, 28days).
Which method should we choose for the present study?
Thanks!


Dear Prof. Robert Long, thank you very much for your help.
We have read your suggestion and we prefer the linear mixed effects model. But how to estimate the “round” factor? As your mentioned, “If there is no temporal aspect to Round then you might consider not including it in the model at all - or just treating it as a potential confounder.”
Firstly, we repeat the test for the mice pass the machine due to the data was much different every round (round1~round4) for each mice. If only do it once or twice (per mice), we think it is difficult to explain the result. Secondly, why we choose four times? Actually, there is really no reason. It looks like we can choose three times or five time, even ten times. Thus, the “round” might not be considered as a traditional time factor which might influence the results in a repeated measures research.
So, we think there is no temporal aspect to Round and we treat it as a potential confounder. Am I understanding right? What is the random factor and fixed factor in the study, respectively? how to conduct the analysis using R or other software?
Thanks a lot!
 A: Averaging the data is going to lose information and statistical power, so it is not a good idea.
A linear mixed effects model with random intercepts for mice ID should take account of the repeated measures within mice. Then you can use all the data.
You mentioned a GLMM approach, but from what I can see a generalised model is not indicated. However, if it is a GLMM that you are fitting then you could choose a GEE instead, but if not, then a linear mixed model and a GEE should produce the same results.

Is it different from the traditional time factor for repeated measure study?

It is very similar. There are different ways to handle time in a repeated measures longitudinal model: it can be numeric or categorical. If numeric then it can be centred. In your case, if there is a temporal aspect to Round, then it can be handled in the same ways. So a model such as:
measurement ~ Group + Round + covariates + (1|mice_id)

would be a good place to start. If you code Round as numeric (eg 0,1,2,3) then the model will estimate a linear trend. If you code it as categorical then the model will produce 3 seperate estimates - all being a contrast with whichever level of Round you set as the reference (0 would make most sense in my opinion).
If there is no temporal aspect to Round then you might consider not including it in the model at all - or just treating it as a potential confounder.
If there is a temporal aspect, and you want the response to the treatment to differ over Rounds, then you might consider the interaction Group:Round
If you decide fit random slopes for Round (with Round as numeric) then you might consider centering Round which will improve interpretation.
