Estimating the responsiveness of an instrument using more than two repeated measures

The responsiveness of a measuring instrument is its ability to detect change over time. A commonly used index of responsiveness is the effect size for paired differences. This paper generalizes the effect size for paired differences to more than two repeated observations per subject. The sampling distribution of the generalized responsiveness statistic, Rt, is simulated for a range of plausible parameter values and for a range of sample sizes varying both the number of subjects (n) and the number of observations per subject (t). The coverage properties of confidence intervals constructed by four methods are compared. Confidence intervals based on jackknife estimates of the standard error and bias of Rt have good coverage properties even when n and t are small. The methods are used to determine which of two standard quality-of-life measures is more responsive to improvements in quality of life following surgery for early-stage breast cancer.