# Is a three-way mixed anova suitable here?

I have a question about what's the ideal test to run for my study design. I would appreciate any advice!

I have:

• One within-subjects factor: time (5 levels)

• 2 between-subjects factors: group (2 levels) and treatment (2 levels)

• And one dependent variable which is the levels of a biomarker in the blood.

I would like to see if the change in the biomarker levels significantly differ between the groups in response to the treatment over time.

Is it okay if I do a three-way(2x2x5) mixed ANOVA on this? A colleague told me that it is completely wrong to use an ANOVA and that I should do a linear mixed model instead.

Edit: The same individuals were measured over 5 timepoints. So, it's a repeated measures design. Each group (2 groups in total) of individuals were divided into 2 sub-groups. First sub-group received treatment A, the second group received treatment B. Each sub-group is around 20 individuals. So, 40 individuals per group, and 80 individuals in the whole experiment. The timepoints are evenly spaced (every week).

• Welcome to cv, Clarissa! Did you use the same individuals to measure over time, or do all data points come from different individuals? Please include this information in you (otherwise fine!) question. It is crucial for the decision if you should use a mixed model.
– Ute
Aug 25 at 22:06
• Thanks for pointing this out, Ute. I've edited my post. It was the same individuals tested over 5 timepoints. So, it's a repeated measures design. But each individual took either treatment A or treatment B, never both. Aug 25 at 22:17
• Thank you, and oops, sorry I overlooked that you had mentioned mixed ANOVA already. How many individuals do you have in each subgroup? And the time points, are they equally spread or is it like in some medical studies "after one week, a month, 3 months, a year"
– Ute
Aug 25 at 22:23
• No problem! Each sub-group is around 20 individuals. So, 40 individuals per group, and 80 individuals in the whole experiment. The timepoints are evenly spaced (every week). Aug 25 at 22:26
• Carissa, I believe that your critical colleague only heard "ANOVA", not mixed ANOVA. I can understand their concern on this background an have edited my answer accordingly. You are probably both right with correctnes of the models you propose, and it is a misunderstanding - I also did not see "mixed" on first read, it is not so common :-)
– Ute
Aug 27 at 11:29

Linear mixed models are the technique to go for, since you are interested in the change in biomarker levels over time. Your experimental design is perfect for this purpose.

Linear mixed models require that you carefully think about how to specify the model. Use your biological knowledge beforehand to clarify if you would expect differences in the rate at which the biomarker level changes only between groups, or between treatments, or even between individuals in each subgroup, and the same for the intercept. Also think about if a straight line would be a good approximation for the evolution of biomarker level within the five weeks, or if you expect something largely different, such as exponential growth.