In a hypothetical PET study, my sample consists of a clinical population which exhibit brain hypermetabolism. I divide my sample into two homogenous groups. One receives a treatment whereas the other does not (control). My analysis is a 2 x 2 mixed factorial design with treatment (receive treatment, doesn't receive treatment) as the between groups factor and treatment status (pretest, postest) as the within-subjects factor.
The treatment group complete a cognitive task which is expected to reduce the brain hypermetabolism to almost nothing but return to elevated hypermetabolism in up to 2 minutes. In other words, the cognitive task reduces the activity for a short amount of time but slowly the brain hypermetabolism will return to the elevated levels that distinguish our clinical sample. It is not known whether this regression to pretreatment levels will be linear or non linear.
In my design I compare group averages in brain hypermetabolism in the treatment vs. control group pretest and posttest. There should be no difference in our control group in the pretest and posttest stages, but there should be a significant difference in the treatment group.
My question is, is there a standard procedure for obtaining group averages on a linear function? If we know that the brain hypermetabolism returns in <2 minutes, should we average the value of the line across 2 minutes? 1 minute? At the participant level? At the group level?
Alternatively, instead of working out an average, should one calculate the slope of the lines in treatment vs. non-treatment conditions and compare these?
I would much appreciate citations to handle such procedures.