What is the best way to compare changes between two groups? Given we have two equal-sized groups, each with a continuous pre and post-measure. E.g., in an RCT with a treatment and a placebo group and a pre and post-intervention outcome measure, and no drop-out.

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*What would be the best way to test if the pre-post changes between the two groups differ?

*What would be the best way to quantify the effect size if they differ?

*How could we handle different-sized groups?


The purpose of a parallel-group RCT is to compare parallel groups, not to see how patients change from baseline.  There are huge disadvantages to computing change from baseline, chief among them being that the assumptions required for change to work well (and lead to efficient analysis) are seldom satisfied.  E.g. post vs. pre is not linear or it is linear and the slope of post on pre is not 1.0 due to measurement error, regression to the mean, and loss of impact of pre as post gets further out in time.
So think of the pre measurement as a baseline covariate, and adjust for it flexibly.  I've seen several cases where post on pre is not even linear, e.g., in a depression drug RCT where patients starting with severe depression get much more relieve than those started with mild depression.  For more information see this.
