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I'm designing a prospective study trying to detect a change in the performance of a particular group of patients on a specific cognitive reasoning exam after an intervention longitudinally. Our research team is going to be studying the patients at baseline (prior to treatment), and then again at 1, 3, 6 and 12 months. I am trying to calculate a sample size based on previous data that the collaborator has collected.

The collaborator that I'm working with has validated this specific test on thousands of participants over a wide range of ages. Thus, the scores of the individuals in the study are always expressed as a percentile for where they are in the overall population (in other words, a collection of historical data).

I don't have much experience working with these percentile scores, but I'm wondering it there would be a difference in the ability to power the study if we base our power calculation on the percentiles compared to the raw scores? My collaborators state that all the previous studies they have published use these same historical controls that represent the total population.

I don't necessarily like the historical controls and comparing to historical data. Thus, for the current study we are going to include a real-time control group that we do not expect to have any change in cognitive score over time.

Is there a problem basing our power and sample size calculations on percentiles, and detecting a change in a particular number of percentiles on this test over time? Would it potentially be better or advantageous if we were to use the raw scores instead? Or, alternatively, would it be worse?

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