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I have a small sample size of participants (n=8) who were enrolled in a study to evaluate the change in one of the urine metabolites over time. The concentration of this metabolite in the urine was measured in three different occasions (baseline or time zero, after three months and then after six months.

I would like to study the change in this metabolite concentration over time. I am uncertain about the utility of the mixed effect model in such a small sample size, especially since there were concerns raised in the literature about the accuracy of this type of analysis.

http://www.joophox.net/publist/methodology05.pdf

In addition:

Snijders, T.A.B. & Bosker, R.J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. London: Sage Publishers.

Hox, J. (2010). Multilevel Analysis: Techniques and Applications. New York: Routledge.

I would like to inquire about the correct method to be used in such case. Is the mixed effect model still the best approach? Is ANOVA a better choice for the difference over time in such a small sample size?

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8 groups is not great for a random effect, but it's probably better than the alternative of using a fixed effect for each of them - especially if you are expecting group-level variation in more than the intercept. Perhaps more appropriate would be to switch to a Bayesian framework and specify your priors; the lack of data would just mean that the data will (probably) have a weak effect on your posterior, and you would have less cause to be concerned that the error estimates are poor.

But that would not be my biggest concern with this analysis. With 3 data points through time, you would have to be very confident that the metabolite will change in a specific way (e.g. linearly, exponential decay, etc). Deviation from this expected shape would be very difficult to pick up in your analysis.

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