# Assessing bivariate change (pre- and post-intervention) when sample size is small and there is no control group?

I have data from a randomised control trial of approximately 60 people (30 people in the intervention group, 30 in the control group). I would like to assess whether change in one variable (M) is associated with change in another (Y), which are continuous variables. Ideally I'd run a mediation analysis to see if M mediates the effect of the intervention on the outcome Y, however I am low in power.

Therefore instead I am planning to assess the association between change in M and change in Y within the intervention group only (i.e., ignoring data from the control group). To do this, I am thinking of:

1. Creating "change scores" for M and Y by using the post-intervention score for each variable and regressing out the respective baseline score and covariates (i.e., residuals from post-intervention score ~ pre-intervention score + age + sex + other baseline covariates). I will use the same set of covariate for both.
2. Then I plan to use a regression to assess whether change in M predicts change in Y. That is, "change in Y" ~ "change in M".
3. I have quite a lot of missing data at follow-up so plan to address missing data I am thinking of using multiple imputation, though I am unsure whether to apply this or when, probably at stage 1.

Questions: Does this sound like a reasonable approach that would have greater power than a mediation analysis? Is there a way to complete a similar anlysis using linear mixed models so that I can use MLE to address missing data?

I should probably mention that in the above plan, I use data from two-timepoints. However, for my variable M I have three timepoints (i.e., an additional measurement mid-intervention at 6 months). I also plan to run analyses for several outcomes (Ys) some of which have 3 measures (baseline, 6 months, 12 months), others only have two (baseline, 12 months).

This is the within-participant mediation approach describes in

Montoya, A. K., & Hayes, A. F. (2017). Two-condition within-participant statistical mediation analysis : a path-analytic framework. Psychological Methods, 22(1), 6-27. https://doi.org/10.1037/met0000086.

coming from

Judd, C. M., Kenny, D. A., & McClelland, G. H. (2001). Estimating and testing mediation and moderation in within-subject designs. Psychological Methods, 6, 115–134.10. https://doi.org/1037/1082-989x.6.2.115

Images from Montoya & Hayes (2017), p. 13

• Thank you so much for your response and the references! Is this analysid likely to be better powered than a mediation analysis in the whole sample (N = ~60) with X = intervention vs. control group? Commented Mar 27 at 13:05
• You can use the 60 subjects, so it will be as powerful as it can get. Using the differences will certainly help as it increases power.
– POC
Commented Mar 27 at 14:01