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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.

Any advice or opinions about this would be helpful!

Thanks in advance!

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).

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  • $\begingroup$ 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. $\endgroup$
    – Ute
    Commented Aug 25, 2023 at 22:06
  • $\begingroup$ 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. $\endgroup$
    – Carissa
    Commented Aug 25, 2023 at 22:17
  • $\begingroup$ 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" $\endgroup$
    – Ute
    Commented Aug 25, 2023 at 22:23
  • $\begingroup$ 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). $\endgroup$
    – Carissa
    Commented Aug 25, 2023 at 22:26
  • $\begingroup$ 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 :-) $\endgroup$
    – Ute
    Commented Aug 27, 2023 at 11:29

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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.

[Edit: further information about ANOVA]
There is a big difference between (independent) ANOVA and mixed ANOVA. Ordinary three way (independent) ANOVA assumes that you have measured the data on different individuals for each combination of group, treatment and time. Thus all data points are independent. However, you have longitudinal data: you measured the biomarker level for the same individuals at all five time points. It would be completely wrong to analyze the data with an independent three way ANOVA, but mixed ANOVA allows you to specify which datapoints belong to the same individuum. Your colleague probably only heard the word "ANOVA", therefore their reaction.

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  • $\begingroup$ Hi Ute! Thanks for your response! Is an ANOVA completely wrong for this study design then? Or is a linear mixed model just better and more accurate, but both can be used? $\endgroup$
    – Carissa
    Commented Aug 26, 2023 at 14:01
  • $\begingroup$ I don't know why your colleague said this - they may have some reason? I understood you as you want to use time as a factor variable, while your colleague says you should treat it as continuous. There are many users here who would agree with your colleague, but I don't see it as "completely wrong", rather as "very different". It really depends on the scientific story that you want to tell in the end. Then you can see if your data support that story, and to that end, you have to chose a model that reflects your story. ... maye the whole thing is just a confusion of names for methods. $\endgroup$
    – Ute
    Commented Aug 26, 2023 at 17:28
  • $\begingroup$ I have added a paragraph about completely wrong version ANOVA - maybe this is why your colleague reacted so alarmedly, and remember, I also overlooked the word "mixed" in context with ANOVA. $\endgroup$
    – Ute
    Commented Aug 26, 2023 at 17:43
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    $\begingroup$ That might indeed be the reason, Ute. Thanks for your lengthy response. It's really very helpful!! You mention that both methods are different and it depends on the scientific story I want to tell. That's a very interesting point. In which circumstances does it make more sense to use a linear mixed model then, in your opinion? $\endgroup$
    – Carissa
    Commented Aug 27, 2023 at 21:17
  • $\begingroup$ This is quite complex to describe in words. Can you post graphs that for each of the four subgroups show biomarker vs time as a curve fir each participant? $\endgroup$
    – Ute
    Commented Aug 28, 2023 at 1:59

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