# Longitudinal data analysis with a single group

I need you assistance with finding the right model to analyze longitudinal data with a single group. My data comes from the ophthalmic field, i.e. eyes. I have n subjects. For each subject, one eye was chosen by random, and some treatment was applied to reduce the pressure inside the eye (a continuous scale).

The second eye was not treated, but the pressure was measured there as well. I have several time periods: Before treatment was applied, after 1 week, after 2 weeks and after a month.

I want to know if the treatment works, and basically could settle for a paired t-test using 1 time period and comparing it to the before values. However, I have noticed a correlation between the treated and untreated eyes. The correlation is 0.8!

So I thought that maybe, using the untreated eye, I could explain some of the variability. To sum it up, I have one group of treatment, I have 4 time periods and I have another eye for control. How do I analyze this for the best?

• It is not clear if the pressure in second eye was tested at each time period or only once? – rnso Oct 19 '14 at 12:19
• at each time period – user58892 Oct 19 '14 at 12:39
• Well of course there is correlation between left and right eye: in spite of the intervention, the two eyes in the same head tend to be more similar than to eyes in different heads. That's why you use a paired design. – AdamO Nov 29 '16 at 0:52

Following is a suggestion. I am not sure if it is the best way. Difference between eyes at each period can be analyzed:

ddf
subject_id     time left right_active difference_bet_eyes
1          1 baseline   10           12                   2
2          1      1wk   11           13                   2
3          1      2wk   12           12                   0
4          1      4wk   10           12                   2
5          2 baseline   11           13                   2
6          2      1wk   12           12                   0
7          2      2wk   10           12                   2
8          2      4wk   10           10                   0
...

aov.out = aov(difference_bet_eyes ~ time + Error(subject_id/time), data=ddf)
summary(aov.out)


One would be interested to compare it with result of right_active without taking left eye into consideration:

aov.out = aov(right_active ~ time + Error(subject_id/time), data=ddf)

• interesting idea. thanks. Alternatively, can I add the value of the untreated eye as a covariate to a GEE or mixed model, of Y vs time ? – user58892 Oct 19 '14 at 13:21