# The mathematical relationship among different forms of responsiveness coefficients

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## Abstract

### Background

Little consensus exists regarding the most appropriate measure of responsiveness. While most indices are variants on Cohen’s effect size, the mathematical relationships among these indices have not been elucidated. Consequently, the health-related quality of life (HRQL) literature contains many publications in which a variety of different indices are computed and differences among them noted. These differences are completely predictable when the underlying analytical form of each coefficient is explicated.

### Methods

In this paper, we begin with a mathematical analysis of the variance components underlying an observed change score. From this, we determine analytically the relationships among the more commonly used indices of responsiveness.

### Conclusions

Based on this analysis, we conclude that Cohen’s effect size and the Standardized Response Mean are the two most appropriate measures, as each provides unique information and each best captures an important relation between treatment effect and variability in response. However, the latter should be interpreted with caution, as under some circumstances, any measure based on variability in change scores can give misleading information. On this basis, we recommend that future analysis of responsiveness be restricted to the Cohen effect size to ensure interpretability and comparability with treatment effects in other domains.

## Keywords

Responsiveness HRQL Equivalence Mathematics## References

- 1.American Psychological Association. (1999). Standards for educational and psychological tests.Google Scholar
- 2.Anderson, J. J., Firschein, H. E., & Meenan, R. F. (1989). Sensitivity of a health status measure to short-term clinical changes in arthritis.
*Arthritis and Rheumatism, 32*, 844–850.PubMedCrossRefGoogle Scholar - 3.Chren, M. M., Lasek, R. J., Flocke, S. A., & Zyzanski, S. J. (1997). Improved discriminative and evaluative capability of a refined version of Skindex, a quality-of-life instrument for patients with skin diseases.
*Archives of Dermatology, 133*, 1433–40.PubMedCrossRefGoogle Scholar - 4.Cohen, J. J. (1988).
*Statistical power analysis for the behavioral sciences*(p. 8). Erlbaum: Hillsdale, NJ.Google Scholar - 5.Crosby, R. D., Kolotkin, R. L., & Williams, G. R. (2003). Defining clinically meaningful change in health related quality of life.
*Journal of Clinical Epidemiology, 56*, 395–407PubMedCrossRefGoogle Scholar - 6.Deyo, R. A., & Centor, R. M. (1986). Assessing the responsiveness of functional scales to clinical change: An analogy to diagnostic test performance.
*Journal of Chronic Diseases, 39*, 897–906.PubMedCrossRefGoogle Scholar - 7.Deyo, R. A., Diehr, P., & Patrick, D. L. (1991). Reproducibility and responsiveness of health status measures: Statistics and strategies for evaluation.
*Controlled Clinical Trials, 2*, 142S–158SCrossRefGoogle Scholar - 8.Fitzpatrick, R., Ziebland, S., Jenkinson, C., & Mowat, A. (1992). Importance of sensitivity to change as a criterion for selecting health status instruments.
*Quality in Health Care, 1*, 89–93.PubMedGoogle Scholar - 9.Guyatt, G. H., Walter, S. D., & Norman, G. R. (1987). Measuring change over time: Assessing the usefulness of an evaluative instrument.
*Journal of Chronic Diseases, 40*, 171–178.PubMedCrossRefGoogle Scholar - 10.Hays, R. D., & Hadorn, D. (1992). Responsiveness to change: An aspect of validity, not a separate dimension.
*Quality of Life Research, 1*, 73–75PubMedCrossRefGoogle Scholar - 11.Kirshner, B., & Guyatt, G. (1985). A methodological framework for assessing health indices.
*Journal of Chronic Diseases, 38*, 27–36.PubMedCrossRefGoogle Scholar - 12.Liang, M. J., Fossel, A. H., & Larson, M. G. (1990). Comparison of five health status instruments for orthopedic evaluation.
*Medical Care, 28*, 632–642.PubMedCrossRefGoogle Scholar - 13.Lindebloom, R., Sprangers, M. A. G., & Zwinderman, A. (2005). Responsiveness: A reinvention of the wheel?
*Health and Quality of Life Outcomes, 3*, 8.CrossRefGoogle Scholar - 14.Norman, G. R., Stratford, P., & Regehr, G. (1997). Methodological problems in the retrospective computation of responsiveness to change: The lesson of Cronbach.
*Journal of Clinical Epidemiology, 50*, 869–879PubMedCrossRefGoogle Scholar - 15.Norman, G. R., Stratford, P., & Regehr, G. (1997) Methodological problems in the retrospective computation of responsiveness to change: The lesson of Cronbach.
*Journal of Clinical Epidemiology, 50*, 869–879.PubMedCrossRefGoogle Scholar - 16.Norman, G. R., Wyrwich, K. W., & Sloan, J. A. (2003). Interpretation of changes in health-related quality of life: The remarkable universality of half a standard deviation.
*Medical Care, 41*, 582–592.PubMedCrossRefGoogle Scholar - 17.O’Keeffe, S. T., Lye, M., Donnellan, C., & Carmichael, D. N. (1998). Reproducibility and responsiveness of quality of life assessment and six minute walk test in elderly heart failure patients.
*Heart, 80*, 377–382.PubMedGoogle Scholar - 18.Pickard, A. S., Johnson, J. A., & Feeny, D. H. (2005). Responsiveness of generic health related quality of life measures in stroke.
*Quality of Life Research, 14*, 207–219PubMedCrossRefGoogle Scholar - 19.Reilly, M. C., & Zbrozek, A. S. (1992). Assessing the responsiveness of a quality-of-life instrument and the measurement of symptom severity in essential hypertension.
*Pharmacoeconomics 2*, 54–66.PubMedGoogle Scholar - 20.Sprangers, M. A. G., Moinpour, C. M., Moynihan, T. J., Patrick, D. L., & Revecki, D. A. (2002). Assessing meaningful change in quality of life over time: A user’s guide for clinicians.
*Mayo Clinic Proceedings, 77*, 561–571PubMedCrossRefGoogle Scholar - 21.Stratford, P. W., Binkley, J. M., & Riddle, D. L. (1996). Health status measures: strategies and analytical methods for assessing change scores.
*Physical Theraphy, 76*, 1109–1123.Google Scholar - 22.Streiner, D. L., & Norman, G. R. (1993).
*Health measurement scales: A practical guide to their development and use*(p. 142). Oxford University PressGoogle Scholar - 23.Streiner, D. L., & Norman, G. R. (2003).
*Health measurement scales: A practical guide to their development and use,*3rd ed. (p. 141). Oxford University PressGoogle Scholar - 24.Terwee, C. B., Dekker, F. W., Wiersinga, W. M., Prummel, M. F., & Bossuyt, P. M. M. (2003). On assessing responsiveness of health-related quality of life instruments: Guidelines for instrument evaluation.
*Quality of Life Research, 12*, 349–362.PubMedCrossRefGoogle Scholar - 25.Ware, J. E., Kemp, J. P., Buchner, D. A., Singer, A. E., Nolop, K. B., & Goss, T. F. (1998). The responsiveness of disease-specific and generic health measures to changes in the severity of asthma among adults.
*Quality of Life Research, 7*, 235–244PubMedCrossRefGoogle Scholar - 26.Wells, G., Beaton, D., Shea, B., Boers M., Simon, L., Strand, V., Brooks, P., & Tugwell, P. (2001). Minimal clinically important differences: Review of methods.
*The Journal of Rheumatology, 28*, 406–412.PubMedGoogle Scholar - 27.Wright, J. G., & Young, N. L. (1997). A comparison of different indices of responsiveness.
*Journal of Clinical Epidemiology, 50*, 239–246PubMedCrossRefGoogle Scholar - 28.Wyrwich, K. W., Tierney, W. M., & Wolinsky, F. D. (2002). Using the standard error of measurement to identify important changes on the Asthma Quality of Life Questionnaire.
*Quality of Life Research, 11*, 1–7.PubMedCrossRefGoogle Scholar