The analysis of repeated multivariate binary quality of life data: a hierarchical model approach

Abstract

Many quality of life measuring instruments consist of a number of questions that are answered on ordinal scales. Often these responses are then totalled to give a summary score for each quality of life domain within the instrument. This, however, may lose valuable information about individual aspects of patient quality of life and also can have little intuitive meaning. Here we present an alternative analysis, in which dichotomized individual items of the questionnaire are analyzed. We first show how a hierarchical logistic regression model for repeated binary data can be extended to the multivariate case. We then use such a model for analyzing the prevalence of six symptoms in a palliative treatment trial in non-small-cell lung cancer. The analysis provides information about the correlations between symptoms, both between and within person. If appropriate, it also permits the estimation of a treatment effect common to all symptoms. Methods for model checking are discussed. We conclude that this methodology can provide a more intuitive and informative analysis of quality of life data than that obtained by considering summary scores.

Get full access to this article

View all access options for this article.

References

Bergner M , Bobbit RA , Carter WB , Gilson BS. The sickness impact profile: development and final revision of a health status measure . Medical Care 1981; 19: 787-806 .

de Haes JCJM , van Knippenberg FCE , Neijt JP. Measuring psychological and physical distress in cancer patients: structure and application of the Rotterdam Symptom Checklist . British Journal of Cancer 1990; 62: 1034-1038 .

Bowling A. Measuring Health: a review of quality of life measurement scales. Milton Keynes: Open University Press , 1983.

Beacon HJ , Thompson SG. Multi-level models for repeated measurement data: application to quality of life data in clinical trials . Statistics in Medicine 1996; 15: 2717-2732 .

Longford NT. Random coefficient models. Oxford: Oxford Science 1995.

Goldstein H. Multilevel statistical models. London: Arnold , 1995.

Fayers PM , Jones DR. Measuring and analyzing quality of life in cancer clinical trials: a review . Statistics in Medicine 1983; 2: 429-446 .

Little RJA , Rubin DB. Statistical analysis with missing data. New York: Wiley , 1987.

Goldstein H , Rasbash J , Plewis I , Draper D , Browne W , Yang M , Woodhouse G , Healy MJR. A user’s guide to MLwiN. London: Institute of Education , 1998.

10.

Stiratelli R , Laird N , Ware JH. Random effects models for serial observations with binary response . Biometrics 1984; 40: 961-971 .

11.

Zeger SL , Karim MR. Generalized linear models with random effects; a Gibbs sampling approach . Journal of the American Statistical Association 1991; 86: 79-86 .

12.

Breslow NE , Clayton DG. Approximate inference in generalized linear mixed models . Journal of the American Statistical Association 1993; 88: 9-25 .

13.

Gilks WR , Clayton DG , Spiegelhalter DJ , Best NG , Sharples LD , Kirby AJ. Modelling complexity: application of Gibbs sampling in medicine . Journal of the Royal Statistical Society Series B 1993; 55: 39-102 .

14.

Goldstein H. Nonlinear multilevel models with an application to discrete response data . Biometrika 1991; 78: 45-51 .

15.

Rodriguez G , Goldman N. An assessment of estimation procedures for multilevel models with binary responses . Journal of the Royal Statistical Society Series A 1995; 158: 73-89 .

16.

Goldstein H , Rasbash J. Improved approximations for multilevel models with binary responses . Journal of the Royal Statistical Society Series A 1996; 159: 505-513 .

17.

Goldstein H. Multilevel mixed linear model analysis using iteratively generalized least squares . Biometrika 1986; 73: 43-56 .

18.

Goldstein H. Restricted unbiased iterative generalized least squares estimation . Biometrika 1989; 76: 622-623 .

19.

Zigmond AS , Snaith RP. The hospital anxiety and depression scale . Acta Psychiatrica Scandinavica 1983; 67: 361-370 .

20.

Johnson RA. Applied multivariate statistical analysis. Wichern , 1988, pp 148-153.

21.

Hopwood P , Stephens RJ , Machin D. Approaches to the analysis of quality of life data: experiences gained from a Medical Research Council Lung Cancer Working Party palliative chemotherapy trial . Quality of Life Research 1994; 3: 339-352 .

22.

Curran D , Bacchi M , Hsu Schmitz SF , Molenburghs G , Sylvester RJ. Identifying types of missingness in quality of life data from clinical trials . Statistics in Medicine 1998; 17: 739-756 .

23.

Park T , Lee SY. A test of missing completely at random for longitudinal data with missing observations . Statistics in Medicine 1997; 16: 1859-1872 .

24.

Fairclough DL. Summary measures for comparison of quality of life in clinical trials of cancer therapy . Statistics in Medicine 1997; 16: 1197-1210 .

25.

Mole TR. The analysis of representative surveys of coronary diseases. PhD thesis, London University, 2000, pp 137-50.

26.

Lee Y , Nelder JA. Hierarchical generalized linear models . Journal of the Royal Statistical Society Series B 1996; 58: 656-678 .

27.

Liang K-L , Zeger SL. Longitudinal data analysis using generalized linear models . Biometrika 1986; 73: 13-22 .

28.

Neuhaus JM , Kalbfleisch JD , Hauck WW. A comparison of cluster-specific and population averaged approaches for analyzing correlated binary data . International Statistical Review 1991; 59: 25-35 .

29.

Diggle PJ , Liang K-Y , Zeger SL. Analysis of longitudinal data. Oxford: Oxford Science , 1994.

30.

Hastie TJ , Tibshirani RJ. Generalized additive models. London: Chapman and Hall , 1990.

31.

Beacon HJ , Thompson SG. The analysis of complex patterns of binary response: an example of transient dysphagia following radiotherapy . Statistics in Medicine 1998; 17: 2551-2561 .

32.

Ten Have TR , Landis JR , Hartzel J. Population-averaged and cluster specific models for clustered ordinal response data . Statistics in Medicine 1996; 15: 2573-2588 .

33.

Ribaudo HJ , Bacchi M , Bernhard J , Thompson SG. A multilevel analysis of longitudinal ordinal data: evaluation of the level of physical performance of women receiving adjuvant therapy for breast cancer . Journal of the Royal Statistical Society (Series A, Statistics in Society) 1999; 162: 349-360 .

34.

Lunn DJ , Wakefield J , Racinen-Poon A. Cumulative logit models for ordinal data: a case study involving allergic rhinitis severity scores . Statistics in Medicine 2001; 20: 2261-2285 .