Quantifying responsiveness of quality of life measures without an external criterion

The responsiveness of a quality of life measure has received considerable attention in the literature. A two time-point (pre-/post-) study design is usually adopted to evaluate this property when a gold standard is not available. Among many indices, Cohen's effect size and the standardized response mean (SRM) are usually computed. To interpret the results, researchers commonly appeal to an arbitrary criterion for both indices even though they are different by definition. In this paper, we demonstrate their close algebraic relationship and conceptual differences, showing that only the SRM is necessary to quantify responsiveness. To facilitate interpretation, we transform the SRM to the 'probability of change' with a value of 0.5 denoting null responsiveness and 1.0 perfect responsiveness. Simple confidence interval procedures are provided and evaluated. We also discuss the possibility of applying the results to the analysis of data from a two independent groups pre-/post- design. Two examples are provided.