# Longitudinal analysis with a small sample

I have a small dataset with 7 subjects only.

Each subject got a treatment for a disease. Before getting the treatment, some measure of the disease was taken, let's call it "outcome". This is a continuous variable.

After the treatment, the "outcome" was measures several more times (1 day after, 1 week after, 1 month after).

I need to analyze this data, to see if there are differences after the treatment. I understand that a full longitudinal analysis is not feasible because I have N=7, and there is not enough power.

I thought to make specific comparisons, i.e. paired t-test (or non-parametric equivalent) per time point, for example, to compare 1 week to baseline, and then 1 months to baseline, and so on.

My question is, should I analyze the absolute change from baseline, or the percentage change from baseline? If this was a longitudinal model, the baseline would have been a covariate. But with a simple test, the value of the baseline can vary from one subject to another.

Should I take outcome - baseline or (outcome-baseline)/baseline? In the latter case, how exactly do I perform a paired t-test? Do you have a better suggestion?

My data contains the following variables: ID, time (baseline, 1 day, 1 week, 1 month), outcome.

• If I had enough power for a proper model, would it be correct to model the absolute change from baseline as DV with the time being IV and the baseline being a covariate? – BlueSigma Feb 6 '17 at 9:38
• With the sparsity of your data, I'd say any hypothesis test, be it in a longitudinal analysis (which would be some kind of mixed model?) or 'simple' T-test are equally 'powerless'. Of course this is also dependent on the differences between baseline and further measurements, but other model or test assumptions are bound to be violated. As a suggestion, you might want to look into permutation tests (where you randomly reorder values and test the different distributions across all/a lot of possible reorderings). Although I dare not predict whether such tests would give a clearer picture. – IWS Feb 6 '17 at 10:21
• The differences, especially in the first post treatment time point, are fairly large (would might actually be statistically significant). Which permutation test is suitable for paired data ? – BlueSigma Feb 6 '17 at 10:24
• – IWS Feb 6 '17 at 10:34
• ps. if you think this comment is an appropriate answer to your question, I'll make an answer out of it. – IWS Feb 6 '17 at 10:39