Importance of Reproducibility in Responsiveness Issues

In cohort studies, longitudinal changes in individuals are often studied. The sample size requirements are then directly related to the responsiveness of the measuring instrument/scale, which is defined as the ability to detect a clinically meaningful change over time. We demonstrate that whatever the index used to assess responsiveness (effect size, standardized response mean, Guyatt's index), it is enhanced by an increase in the intraclass correlation coefficient (ICC), which assesses the reproducibility of the measuring instrument/scale. Therefore, an improvement in reproducibility leads to an increase in responsiveness and thus an increase in power. In the special case of one observation per subject and time, we also prove that an increase in the ICC reduces the coefficient of variation of the estimators of the standardized response mean and of Guyatt's index. This result has also been observed for the effect size on an example. Such a result implies that the better the reproducibility, the lower the sample size requirements for confident statistical inference of responsiveness results.