Sample size calculation - repeated measures, two groups We want to calculate sample size for detecting the difference between mean depression scores of two groups of patients after three months of treatment - i.e. those who received a specialized mental health intervention ("treatment group") and those received routine treatment ("control group"). These patients are randomly assigned to the two groups. Also, the mean scores are differences between the baseline (pre-treatment) and end-line (post-treatment or at 3 months) scores of the respective groups. So, we wanted to calculate the sample size for detecting the difference in differences. Which is the best approach to follow for this situation?
 A: A parallel-group randomized trial is design to compare parallel groups, not to compare change from baseline.  You need to be using ANCOVA with Y=post score and X=baseline score.  Change from baseline assumes linearity and a slope of 1.0 for post-pre.  In depression studies I've seen strong nonlinearity.  The most general analysis that is powerful is a generalization of the Wilcoxon test: the proportional odds ordinal logistic model with Y=post score and using a cubic spline function to adjust for X.  More details are here.
That being said, for planning purposes, when we don't have pilot data that allows us to do ANCOVA, we assume linearity and a slope of 1.0 and use the unpaired t-test on change from baseline for power calculation when there are no intermediate measurements between baseline and 3m.  This will underestimate power because the mean squared error assuming a slope of 1.0 will be higher than the mean squared error that estimates the slope from the data.  But it is better to use the two-sample t-test to analyze change from baseline than it is to get a much bigger mean squared error by using a two-sample t-test without baseline subtraction, which assumes a slope of 0.0.
A: Thanks Frank, we also found the following paper that may help. Would you recommend following either of the methods explained in 3.1 and 3.2, if not the ANCOVA, due to strong assumptions in the latter.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6297128/#appsec1
