Best procedure? PrePost - TreatmentControl | negative slope for low Post, positive slope for high post expected. + control variables

Question

I'm looking for the best procedure for my case. I have a Pre and Post measurement in Treatment and control group. I have a couple of demographic variables which need to be controlled for.

The catch here is, that I expect a very extreme Mathew Effect to the point where it is possible to see a very low or even negative slope for individuals with low Pre-measurement (baseline) and a positive slope for individuals with a high baseline.

So the average in Post-measurement (outcome) in the treatment group may even remain the same as in the control. Because some individuals go up, others go down, depending on their baseline.

The groups are relatively similar at baseline. There is age related change in the outcome measurement to be expected in both groups I'm interested in the change between Pre and Post. Is it bigger in the treatment group?

However, given that the baseline measurement may influence this I'm also interested if there is an interaction between baseline and treatment.

Normally without control variables I'd do an ANOVA to look for differences in the mean change between baseline and outcome. But I don't see that capturing my complexities.

I could also do an ANCOVA, but I believe this is rather to look for a difference in outcome means adjusted for baselines.

I could also do a regression on the outcome and add an interaction Condition*Baseline to account for the baseline. I'm not sure what speaks against this.

Or I could do some sort of Multi Level Regression. Given my expectation this would need to be a random coefficient model.

Here I could do either a model with, analyzing the trends for each individual. Level 1 - Outcome, PrePost (Time 1 or Time 2) Level 2 - (condition 0/1), Age, Sex, Income, ID (identifies an individual uniquely)

analyzing the trends for each individual.

Or I could do a model with Level 1 - Outcome Level 2 - (condition 0/1), Age, Sex, Income, baseline

Or I could, supposedly do something called a Generalized Estimating Equations (GEE) model, which I just read about today.

So, this is what I came up with, given my training and the ressources I found on the internet and in my books.

The normal regression with Condition*Baseline is the one I understand intuitively, but I'm not sure if it is correct for me to use it.

The MLR to analyze the trends seems to be a good thing to use, but as a random coefficient model it only runs with nmle not lme4 without error in R with my data. (too many slopes, error)

I'm looking for advice in justifying to use one method or the other...

Answer 1

I have no great insight, but since nobody else has answered I figured I'd say something. So it sounds like you have two issues here: you want to find out the treatment effect but you think baseline may be very strongly related to post-treatment outcome, possibly strong enough to "outshadow" the treatment effect?

But if it is indeed so that the outcome you are studying is very stable, so much so that intervention effects - or at least the one you have used - are negligible, there's really not much to do statistically. You'd need to plan a different kind of intervention, or maybe conclude that this outcome is not amendable to interventions?

In practice, in my understanding, if your randomization was successful (and your samples are large enough), and it sounds like it was (you say the control and intervention groups were similar), the above issue will be taken into account by any suitable modeling approach, such as ANCOVA, RM-ANOVA, multilevel regression or GEE. If there is very little treatment-related change, then your time*intervention effect will be weak and likely non-significant. And this will reflect the way things are in the world (or at least in your data).

So, in my opinion, you can model your data using any of the modelling approaches you list that are suitable for pre-post testing (I like multilevel regression with random intercept, but GEE or a suitable ANOVA will do) and see the treatment effect you get. Then, you could visualize the change for each participant from baseline to post-treatment by treatment group. This visualization is likely to tell you a lot about the possible issue of the within-person stability of your outcome.

A detail: As you noticed, lmer won't estimate random slopes when you have only 2 observations per cluster. nlme will.