Paired data when observations are not independent

Question

I am working on a study that is analyzing changes in subjects with Cleft lip and palate before and after a surgery that advances the mid-face forward. The subject's cleft lips and palates have already been repaired years before. The investigators would like to know how the surgery that advances the mid-face affects the nose shapes in these subjects.

One of the study questions presented to me asks "for cleft lip and palate patients, does nostril change more or less on the cleft than the non-cleft side?". The data contains about 8 measurements of different areas of the nose, all continuous, before and after surgery. Because the question is asking to compare the outcomes between the left and right side, rather than the pre and post within each side, I don't think a paired t-test would work as the observations are not independent (because the cleft side of the nose can affect how the normal side of the nose is shaped). What statistical test should I perform in order to answer this question?

Thank you!

Answer 1

I suggest that the simplest thing you can do is to take the difference between the cleft side measurement and the non-cleft side and then do a paired t-test on the difference between pre- and post-scores. If there is some way in which you can combine the eight areas into a single score before the differencing operation that would probably (a) give you a more precise and meaningful comparison, (b) avoid the problem of having 8 bites at the cherry (officially known as the problem of multiple comparisons). I am not knowledgeable enough about maxillofacial studies to advise further.