Say I have a study with n individuals, and measure some outcome, Y, at three time points (baseline, 1 week and 4 weeks). I now calculate the relative changes Y1/Ybaseline and Y4/Y1. The correlation between these changes (
corr(Y1/Ybaseline, Y4/Y1)) will be biased towards a negative value (-0.5 if the 3 measurements are independent) because of the shared term, Y1 (Spurious correlation of ratios - Wikipedia).
Is there a way to “correct” for this spurious correlation?
The problem is similar to the spurious correlation between a baseline value and a subsequent change, for which a number of approaches have been suggested (Assessing the Relationship between the Baseline Value of a Continuous Variable and Subsequent Change Over Time).