Estimating and testing an index of responsiveness and the relationship of the index to power

Responsiveness has been proposed as a criterion, in addition to reliability and validity, to evaluate instruments that measure quality of life or functional status. The responsiveness index measures the change in a quality of life score due to a treatment relative to the variability of changes in that score within a stable control group. We derive the expected value, variance and distribution of the responsiveness index and give a large sample distribution for comparing the responsiveness of two different instruments. We also give the relationship between the responsiveness index and the power of a test of treatment effect.