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I have a data set that includes seven patients. Each patient is administered one of two different treatment modalities over follow-up. Several metrics were calculated at each visit, and I now wish to compare these.

Patients attended a baseline visit, then 6 weekly follow-up visits. So each patient has 7 repeated measures (separated by one week) where the treatment is administered each time.

So my idea was, for the second statistical analysis, to use a Wilcoxon test on the repeated measures of all patients, and set them as paired of course. So I take all values for one metrics for treatment 1, and compare it to all values for the same metric for treatment 2. Is that way off ?

However, I'm a bit uncertain what to do about the first one. I have 7 patients, and several metrics. Each metric should be compared between the two modalities. Is that just a t.test, an ANOVA, or something else ?

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There is no inherent rationale to apply a rank test to these data. You must do more preliminary analyses before anything can be said in certain.

The most accepted type of analysis for this design is a repeated measures ANCOVA. Here, random intercepts control for intra-individual effects in each of the 6 follow-up visits, and adjustment is performed for the baseline value. The baseline is inherently not a function of the treatment, so should be dropped as an observation and included as a covariate. Typically separate models are ran for each outcome.

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  • $\begingroup$ What if my data not normally distributed ? Would that be the same approach, or...? $\endgroup$ – Denver Dang Dec 15 '17 at 15:40
  • $\begingroup$ @DenverDang You have to find that out first, per my first remark. There are many relevant posts about this topic on the forum. This one for instance: stats.stackexchange.com/questions/6350/…. Make good use of the search. $\endgroup$ – AdamO Dec 15 '17 at 15:47
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With a balanced design, which seems to be your case, the ANOVA decomposition into sums of squares is unique. This means that the estimatives by restrict maximum likelihood (in another words, a mixed effects model) and the ANOVA method will be the same. More about this can be found in the book "Extending the linear model with R".

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