Compare variance across time I have an analysis question. Unfortunately my biostats collaborator is no longer involved in the project.
We have a dataset of n=6 people. the study was terminated early due to covid but we are still required to report results despite the very small number of subjects. For each subject we have measured our variable of interest weekly. Subjects then began a 3-month intervention and continued the weekly survey. We want to know if variability in our outcome changed with the intervention. In our SAP my collaborator wrote, “we will compare weekly variance estimates of variable of interest (frequency of a specific behavior occurring)” to test this question. This is asked by a single question where the subject indicates the number or times the behavior occurred during the past week. This question is asked for 16-weeks. The first 4 are pre intervention, the final 12 weeks are during an intervention. This is the only behavior we are asking about regarding variability/variance.
It’s not clear to me how to do this statistically given the repeated measure design.
 A: As you only have one weekly report of the number of behaviors, you don't have the usual measure of variance within a week for an individual. I suspect that the statistician had in mind a Poisson regression model.
For such a model, the variance in the number of counts equals the number of counts, so modeling the counts is the same as modeling the variance. It's possible to test that assumption of variance = mean, and use a negative binomial or a "quasi-Poisson" model instead if the assumption isn't tenable, as explained in the above link and in many pages on this site.
There is no problem accounting for the repeated-measure design. Most simply, with only 6 individuals you can include individual as a categorical, fixed-effect predictor in your model to account for differences in baseline counts. You could also include interactions of individual with intervention to allow for differences in responses to the intervention. An alternative would be to account for individual with a random term or terms in a mixed model. Your sample of 6 individuals is at the point where either fixed or random effects might be used.
What isn't clear from your description is how the effect of intervention was going to be teased apart from time. Unless the intervention has an immediate and constant effect, the intervention would presumably change the trajectory over time of the behavior. Thus simply averaging pre- and post-intervention counts per week might not use your data fairly.
My guess is that a simple plot of your counts over time for each individual, with some simple smooth curve for each as produced by LOESS, will provide useful hints.
