Clinically Meaningful Change: False Negatives in the Estimation of Individual Change

In a recent paper, Ferrer and Pardo (2014) tested several distribution-based methods designed to assess when test scores obtained before and after an intervention reflect a statistically reliable change. However, we still do not know how these methods perform from the point of view of false negatives. For this purpose, we have simulated change scenarios (different effect sizes in a pre-post-test design) with distributions of different shapes and with different sample sizes. For each simulated scenario, we generated 1,000 samples. In each sample, we recorded the false-negative rate of the five distribution-based methods with the best performance from the point of view of the false positives. Our results have revealed unacceptable rates of false negatives even with effects of very large size, starting from 31.8% in an optimistic scenario (effect size of 2.0 and a normal distribution) to 99.9% in the worst scenario (effect size of 0.2 and a highly skewed distribution). Therefore, our results suggest that the widely used distribution-based methods must be applied with caution in a clinical context, because they need huge effect sizes to detect a true change. However, we made some considerations regarding the effect size and the cut-off points commonly used which allow us to be more precise in our estimates.