We are going to do a mixed-effect model to examine the time-group interaction
Study design: A pilot 2-arm, parallel RCT, 18 sbj in each group.
2 Time points: Baseline, Post-tx
Results: Baseline: Tx = 35.6 (SD: 24) vs Control = 44.5 (SD: 23);
while at Post-tx: Tx = 17.2 (SD:24) vs. Control = 22.9 (SD: 24). The lower the score, the better the condition is. Mixed effect model showed no group by time interaction. P = 0.98.
The lower the score, the better the condition is. Mixed effect model showed no group by time interaction. P = 0.98.
Problem: There is a visual difference at baseline but no sig difference. We want to calculate the between-group effect size, which is 0.27 favoring the tx group. However, it seems not very make sense as both groups showed improvement, but Tx group showed a lower score may attribute to the lower score at baseline.
We would like to find a more appropriate way to illustrate such group difference, and would like to ask which of the following is more appropriate:
(1) include the baseline score as covariates although no significant baseline difference is identified, and then examine a 2X2 group by time interaction.
(2) use the change scores (changes from baseline) for group comparison in mixed effect model (but it seem group-by-time interaction is not feasible as the time points become one change score only)
(3) any other approach?
Thank you very much for your help.
(1) is the best choice. It is an ANCOVA.
In a GLM procedure the model is: Postx = baseline + group
-One of the problems with an ANCOVA is that the covariates are assumed to be unaffected by treatment; the baseline should be measured before the treatments are assigned. (They therefore are sometimes names pre-measure.)
-Another problem is that the relationship between the outcome (i.c., Postx) and the covariate (i.c., baseline) must be the same in all groups, i.e. the regression lines of each group should have the same slope.The correlation between baseline and Postx should be (about) the same for both groups. There should be no 'baseline x group' interaction.
I agree with Jos that ANCOVA is usually the preferred way to analyze such data. E.g., see the short article by Vickers & Altman linked below.
But note that the ANCOVA model appropriate for this design does not include a 2x2 (group x time) interaction (as mentioned in the original question). The post-treatment value of the variable of interest is the outcome variable, the pre-treatment value of that same variable is the covariate, and the group variable is a factor variable--and that is it. There is no time factor, and no treatment x time interaction term.
Also, if Ss were randomly assigned to groups, there is no point in comparing them on the covariate, because any difference you see is due to chance (because of the random allocation to groups). See what the CONSORT guidelines say about that (2nd link below).
HTH.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1121605/
http://www.consort-statement.org/checklists/view/32--consort-2010/510-baseline-data
Assuming a correct mixed model analysis, I don't believe in a valid visual result when we have a p-value like this (0.98). Both groups (Tx and Control) fall in similar way. In my opinion, this test fail in detect any kind of effect, the statistics only evidentiate this lack of effect and any other statistical approach will show the same result, unless some kind of mistake in the mixed model be corrected.
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