# One factor repeated measures where first time point is a control

Patients were randomized to two groups (control and intervention). Each patient is evaluated at 3 time points. The first time point is taken pre-intervention, so it should have the same mean response in both intervention and control groups.

The idea is to test for different slopes in the two groups. I can do this with a repeated measures anova, testing for the group x time interaction.

I am wondering if a stronger test would involved constraining the mean effects for time 1 to be equal, but I am unsure how to set this up (either in R or SPSS).

$$y_{gkti}=\mu+\alpha_g+\tau_{gt}+\eta_{k}+\epsilon_{gkti}$$

subject to $\tau_{11}=\tau_{21}$

Where the $\alpha$ are the group effects for groups 1 and 2, and the $\tau$ are the time effects and the $\eta$ are the patient effects.

Any ideas?

• Repeated measures ANOVA makes strong assumptions, especially sphericity, that are unlikely to be met in longitudinal data. Have you considered a multi-level model? – Peter Flom Oct 3 '13 at 14:28
• Yes, but the sample size is very small, the data are balanced, so it seems that an ANOVA would be fine. The basic multi-level model has a simple error structure that implies sphericity. Any model that would model the covariance structure in more detail is going to cost power. – Placidia Oct 4 '13 at 12:27