# Power Calculations using “Percent Change” vs. “Absolute Values”

Percent change can be extremely misleading for a number of reasons (e.g. regression to the mean), even though in the medical literature percent change is used quite frequently to "normalize" clinical data. In a regression model it is better to put the baseline value in the overall model, as opposed to transforming the data to "percent change".

However, I'm trying to understand what pitfalls one might encounter if you use percent change in power calculations for prospective studies.

Is it better to use absolute values for power calculations? Would using percent change lead to erroneous calculations the same way it would for normalizing clinical data?

Very good question, and it depends on whether $Y$ is binary or continuous. For binary $Y$ many speak of % change on the odds scale, e.g. a 25% increase in the odds of an event = an odds ratio of 1.25 and we plug 1.25 into a power calculation (we also need the control group probability).
For continuous $Y$ percent change is an improper measure when it is used on individual subjects, because of asymmetry in the way the measure behaves. But percent change on overall summary measures is OK. But we work backwards to solve for the absolute change corresponding to that. For example one might have a 2-sample $t$-test designed to detect a 15% decrease in mean $Y$ from a control group mean of 90 to a mean of $90 \times 0.85 = 76.5$ on the original scale, for a difference of 13.5. We compare 13.5 to SD$(Y)$.