# can I use a multilevel model for my situation? Pre/post, no control group

I have a question about whether multilevel modeling is appropriate in my situation. I’m working on an analysis looking at the effect of a treatment for patients with a disease. There is one pre measurement and one post measurement, and no control group. I have several covariates (e.g., demographics). Outcome is continuous.

Research questions: • what is effect of the treatment? • How do covariates such as demographics influence the outcome?

I was thinking of a linear mixed model: • random intercept for subject • dummy variable: 1 for post period, 0 for pre period. interpreted as the treatment effect • covariates as themselves in model (i.e., not interacted with any other variables)

None of the covariates are time-varying.

Seems that an alternative approach would be to run a normal linear regression, with the outcome being the post period measurement, and the pre period measurement as an independent variable. Other variables would be included as they are. I haven't been able to easily find examples of doing multilevel modeling with pre/post data, so I’m wondering if a multilevel modeling approach really requires more measurements (e.g. 3 or more time points).

There were some subjects who withdrew from the study, but I can’t get their data. Sample size isn't great - 34 for one set of people, and 19 for another set. (I have 2 groups of people that need to be analyzed separately). Note: the two group are analyzed separately because one of them represents patients with the disease and in the second case, the patients don’t have the disease.

Any thoughts?

Thank you!

• Why do you need to analyse the two groups separately ? Can you explain a little more about how the study was designed and how the data were collected ? Please edit the question with this info. – Robert Long Mar 23 at 21:06

## 1 Answer

If I understand the study correctly you have just two outcome measurements per patient: one before treatment and one after. If that's the case then you can simply compute a single score, Post - Pre, for each patient. Then you can run a normal regression model with that score as your dependent variable and the covariates you mentioned as your independent variables (regressors):

In R syntax that would be (R automatically includes the intercept):

Post - Pre Score ~ Intercept + B1*Covariate 1 + B2*Covariate 2 + ...

The beta values and t-statistics for each covariate will tell you how much each covariate was a good predictor of the efficacy of the treatment. The intercept of the model will be the effect of the treatment alone. That's because the intercept is a test of whether the mean of the dependent variable (Post - Pre Score)!= 0. Asking if the difference score != 0, is the same as asking if there was a difference between the mean Post score and the mean Pre score, accounting for the fact that each patient was measured twice (i.e. repeated measures design which is why I'm inferring you thought about multi-level modeling in your question).

• Thank you!!! Would the treatment effect be the same here as in the approach I described above - specifically, normal linear regression, with the outcome being the post period measurement, and the pre period measurement as an independent variable? I think the interpretation with the covariates would be different (they would predict post period value rather than change). – Marissa Mar 31 at 19:36
• No, the interpretation would change in the same way the interpretation changes for the covariates (as you pointed out). Specifically, the coefficient for the pre-period measurement IV in the model you're suggesting would estimate, "What is the expected increase/decrease in the post-period measurement, for every unit increase in the pre-period measurement?" This is different than asking, "Is there a difference between the mean pre-period measurement and mean post-period measurement?" – ejolly Mar 31 at 21:23
• Another way to think about this that the model you suggest estimates the correlation between the pre and post measures (accounting for the other covariates; technically called the semi-partial correlation), whereas the model suggested in my answer estimate the mean difference between the pre and post measures (accounting for other covariates). – ejolly Mar 31 at 21:26