# Cumulative predictors in longitudinal mixed-effects models

I am conducting an mixed effects for repeated measures regression where I want to estimate the effect of a pharmacological treatment and therapy on severity of mental health symptoms. Participants had mental health symptoms measured on a continuous scale on four occasions over 12 weeks, at baseline (0 weeks), 4, 8, and 12 weeks. I am treating the pharmacological treatment as a two-level categorical time-invariant predictor, placebo vs active. That is reasonably straightforward.

The conceptual issue I am having is with the therapy predictor. Participants could take up to six therapy sessions during the twelve weeks, but therapy was not compulsory, so the timing and number of sessions within each 4-week measurement wave varied a lot across participants. My original thought was to include number of sessions in the previous 4-week period as a simple time-varying predictor. However, it occurred to me just now that the efficacy of therapy is cumulative/additive. So perhaps it would make more sense to make this predictor cumulative, i.e. total number of sessions engaged in up to whatever point the measurement is taken. This predictor would still be time-varying but it would be cumulative.

My question is Is there anything wrong statistically with using this sort of cumulative variable in this sort of longitudinal growth model? Some redundancy maybe? Like each session is sort of counted twice in successive waves.

• (+1) Interesting ! So, if the therapy variable was, say 0, 2, 2, 6 for a participant, that would mean they undertook 0, 2, 0 and 4 sessions, respectively in the previous periods ? Dec 3, 2020 at 19:49
• Yes @Robert Long that is correct. I do peer inside the black box from time to time but I will never explore all its dimensions, and this sort of thing is beyond my current knowledge of what is kosher in a mixed-effects growth model. Dec 3, 2020 at 23:26

## 1 Answer

I don't think there is anything wrong with using a cumulative measure of therapy sessions, especially if you theorize that the response is associated with the cumulative number of sessions. Cumulative measurements happen all the time - weight and height for example - but we don't (usually) think about stripping it back to the change in weight or height in the previous period.

• Thanks @Robert Long. Nice analogy and makes perfect sense. Really appreciate your allaying my fears. Dec 4, 2020 at 21:11
• Hey Robert Long - can you please check this out? stats.stackexchange.com/questions/592352/… Oct 15, 2022 at 19:17