Analysis of the short form‐36 (SF‐36): the beta‐binomial distribution approach

Health‐related quality of life (HRQoL) is an important indicator of health status and the Short Form‐36 (SF‐36) is a generic instrument to measure it. Multiple linear regression (MLR) is often used to study the relationship of HRQoL with patients' characteristics, though HRQoL outcomes tend to be not normally distributed, skewed and bounded (e.g. between 0 and 100). A sample of 193 patients with eating disorders has been analysed to assess the performance of the MLR under non‐normality conditions. Normal distribution was rejected for seven out of the eight domains. A beta‐binomial distribution is suggested to fit the SF‐36 scores. The beta‐binomial distribution is not rejected for five out of the eight domains. Thus, a beta‐binomial regression (BBR) is suggested to analyse the SF‐36 scores. Results using MLR and BBR have been compared for real and simulated data. Performance of the BBR is shown to be better than MLR in the HRQoL domains with few ordered categories and very similar to MLR in the more continuous domains. Moreover, the interpretation of the estimates obtained with BBR is clinically more meaningful. A common technique of statistical analysis is preferable for all the HRQoL dimensions. Therefore, the BBR approach is recommended not only to detect significant predictors of HRQoL when SF‐36 is used, but also to analyse and interpret the effect of several explanatory variables on HRQoL. Further work is required to test the better performance of BBR against standard methods for other HRQoL outcomes, populations or interventions. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  J. G. Skellam.  A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable between the Sets of Trials , 1948 .

[2]  G. J. Goodhardt,et al.  The Beta‐Binomial Model for Consumer Purchasing Behaviour , 1970 .

[3]  C. S. Weil.  Selection of the valid number of sampling units and a consideration of their combination in toxicological studies involving reproduction, teratogenesis or carcinogenesis. , 1970, Food and cosmetics toxicology.

[4]  S. Goldsmith.  The status of health status indicators. , 1972, Health services reports.

[5]  S. Goldsmith.  A reevaluation of health status indicators. , 1973, Health services reports.

[6]  Griffiths Da.  Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease. , 1973 .

[7]  Williams Da,et al.  The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. , 1975 .

[8]  Martin Crowder,et al.  Beta-binomial Anova for Proportions , 1978 .

[9]  D. Garner,et al.  The Eating Attitudes Test: an index of the symptoms of anorexia nervosa , 1979, Psychological Medicine.

[10]  D. A. Williams,et al.  Extra‐Binomial Variation in Logistic Linear Models , 1982 .

[11]  R. Snaith,et al.  The Hospital Anxiety and Depression Scale , 1983 .

[12]  S. Katz.  The science of quality of life. , 1987, Journal of chronic diseases.

[13]  W O Spitzer,et al.  State of science 1986: quality of life and functional status as target variables for research. , 1987, Journal of chronic diseases.

[14]  G W Torrance,et al.  Utility approach to measuring health-related quality of life. , 1987, Journal of chronic diseases.

[15]  T Heeren,et al.  Robustness of the two independent samples t-test when applied to ordinal scaled data. , 1987, Statistics in medicine.

[16]  M Schumacher,et al.  Statistical analysis of quality of life data in cancer clinical trials. , 1990, Statistics in medicine.

[17]  M. Schumacher,et al.  Assessment of quality of life in clinical trials. , 1991, Statistics in medicine.

[18]  C. Sherbourne,et al.  The MOS 36-Item Short-Form Health Survey (SF-36) , 1992 .

[19]  J. E. Brazier,et al.  Validating the SF-36 health survey questionnaire: new outcome measure for primary care. , 1992, BMJ.

[20]  David R. Cox,et al.  Quality‐Of‐Life Assessment: Can We Keep it Simple? , 1992 .

[21]  J. Fleishman,et al.  Quality of Life in Persons with Human Immunodeficiency Virus Infection: Measurement by the Medical Outcomes Study Instrument , 1992, Annals of Internal Medicine.

[22]  Byron J. T. Morgan.  Analysis of Quantal Response Data , 1992 .

[23]  R B D'Agostino,et al.  Robustness and power of analysis of covariance applied to data distorted from normality by floor effects: homogeneous regression slopes. , 1996, Statistics in medicine.

[24]  D. Simonson,et al.  Assessment of quality-of-life outcomes. , 1996, The New England journal of medicine.

[25]  J. Brazier,et al.  Comparison of outcome measures for patients with chronic obstructive pulmonary disease (COPD) in an outpatient setting. , 1997, Thorax.

[26]  C. Clancy,et al.  Outcomes Research: Measuring the End Results of Health Care , 1998, Science.

[27]  R M Kaplan,et al.  Comparison of the Quality of Well-being Scale and the SF-36 results among two samples of ill adults: AIDS and other illnesses. , 1998, Journal of clinical epidemiology.

[28]  Normative comparisons for the evaluation of clinical significance. , 1999 .

[29]  R. Sheldon,et al.  Statistical issues encountered in the comparison of health-related quality of life in diseased patients to published general population norms: problems and solutions. , 1999, Journal of clinical epidemiology.

[30]  F D Wolinsky,et al.  Identifying meaningful intra-individual change standards for health-related quality of life measures. , 2000, Journal of evaluation in clinical practice.

[31]  P. Fayers,et al.  Quality of Life: Assessment, Analysis, and Interpretation , 2000 .

[32]  M J Campbell,et al.  DESIGN AND ANALYSIS OF TRIALS WITH QUALITY OF LIFE AS AN OUTCOME: A PRACTICAL GUIDE , 2001, Journal of biopharmaceutical statistics.

[33]  Mounir Mesbah,et al.  Statistical Methods for Quality of Life Studies , 2002, Springer US.

[34]  M. Mesbah,et al.  Statistical methods for quality of life studies : design, measurements and analysis , 2002 .

[35]  M J Campbell,et al.  A review of ordinal regression models applied on health-related quality of life assessments , 2002, Statistical methods in medical research.

[36]  I. White,et al.  Choice of test for comparing two groups, with particular application to skewed outcomes , 2003, Statistics in medicine.

[37]  R. D'Agostino,et al.  Robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials , 2003, Statistics in Medicine.

[38]  Michael J Campbell,et al.  The use of bootstrap methods for analysing health-related quality of life outcomes (particularly the SF-36) , 2004, Health and quality of life outcomes.

[39]  I. Arostegui,et al.  Changes in health related quality of life among patients treated for eating disorders , 2002, Quality of Life Research.

[40]  D. Machin,et al.  Modelling Variability of Quality of Life Scores: A Study of Questionnaire Version and Bilingualism , 2004, Quality of Life Research.

[41]  I. Arostegui,et al.  The health-related quality of life in eating disorders , 2004, Quality of Life Research.

[42]  S. Stansfeld,et al.  Assessing the validity of the SF-36 General Health Survey , 1997, Quality of Life Research.

[43]  M. Splaine,et al.  Use of the Reliable Change Index to evaluate clinical significance in SF-36 outcomes , 2002, Quality of Life Research.

[44]  J. A. Sacristán,et al.  Los medicamentos en la Unin Europea: el tndem comercio-salud , 2005 .

[45]  Gaietà Permanyer-Miralda,et al.  El Cuestionario de Salud SF-36 español: una década de experiencia y nuevos desarrollos , 2005 .

[46]  Michael J Campbell,et al.  The use of bootstrap methods for estimating sample size and analysing health‐related quality of life outcomes , 2005, Statistics in medicine.