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I have two different study groups (A: intervention, B: no intervention/control), each around n~220 patients. Now, every patient has had monthly check-ups for 12 months where blood was drawn, so for each patient, I have 12 metric values of lab values. I ran tests to see whether the data (i.e. the lab values) was normally distributed; it was not, therefore I am looking for a non-parametric test.

My null hypothesis would be: "There is no significant difference between Group A and Group B in terms of lab values over the course of 12 months of follow up."

What test should I use?

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  • $\begingroup$ Data do not need to be normally distributed. It is helpful (but often not necessary if you have "enough" data) for residuals to be normally distributed and homoskedastic. Best to check that first. $\endgroup$ Dec 16, 2023 at 12:39
  • $\begingroup$ That said, you will need to be much more precise in your null hypothesis, whether you go with a parametric or a nonparametric test. Repeated measurements and especially time series are complex. Are you looking for differences at the last time point, differences at any time point, differences between the time series dynamics (one would expect autocorrelation between your measurements; do you posit a fixed AR(p) model or is the order to be determined by the data? In any case, differences in dynamics could mean differences in the first AR coefficient, or in multiple ones), or something else? $\endgroup$ Dec 16, 2023 at 12:42

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Welcome to CrossValidated Simon.

Consider stating the goals in terms of what you'd like to estimate. Here it may be to estimate the longitudinal trajectories, by group A vs. B. This can be done by modeling the fixed effect of time flexibly (e.g., using a regression spline) and using a longitudinal model that does not assume a distribution. An example model is a proportional odds ordinal logistic semi parametric model, which can be extended to the longitudinal case using a Markov process, random effects, or GEE. More information may be found here. Any of these 3 approaches capitalizes on the proportional odds model being a generalization of the Wilcoxon test (a test you might have used were there to be only one time point).

If you want to do an analysis on the original scale in order to obtain mean trajectories, you may have to spend time transforming Y so that the residuals have a symmetric and Gaussian-like distribution.

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