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Calculating ordinal regression models in SAS and S-Plus. (English) Zbl 0971.62035

Summary: Although a number of regression models for ordinal responses have been proposed, these models are not widely known and applied in epidemiology and biomedical research. Overviews of these models are either highly technical or consider only a small part of this class of models so that it is difficult to understand the features of the models and to recognize important relations between them.
We give an overview of logistic regression models for ordinal data based upon cumulative and conditional probabilities. We show how the most popular ordinal regression models, namely the proportional odds model and the continuation ratio model, are embedded in the framework of generalized linear models. We describe the characteristics and interpretations of these models and show how the calculations can be performed by means of SAS and S-Plus. We illustrate and compare the methods by applying them to data of a study investigating the effect of several risk factors on diabetic retinopathy. A special aspect is the violation of the usual assumption of equal slopes which makes the correct application of standard models impossible. We show how to use extensions of the standard models to work adequately with this situation.

MSC:

62J12 Generalized linear models (logistic models)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Agresti, Psychological Bulletin 105 pp 290– (1989)
[2] Ananth, International Journal of Epidemiology 26 pp 1323– (1997)
[3] Anderson, Journal of the Royal Statistical Society 46 pp 1– (1984)
[4] Armstrong, American Journal of Epidemiology 129 pp 191– (1989)
[5] Ashby, Applied Statistics 35 pp 289– (1986)
[6] Ashby, Statistics in Medicine 8 pp 1317– (1989)
[7] Bender, Journal of Clinical Epidemiology 51 pp 809– (1998)
[8] Berridge, Statistics in Medicine 10 pp 1703– (1991)
[9] Cox, Statistics in Medicine 14 pp 1191– (1995)
[10] Cox, Statistics in Medicine 7 pp 435– (1997)
[11] Greenland, Biometrical Journal 27 pp 189– (1985)
[12] Greenland, Statistics in Medicine 13 pp 1665– (1994)
[13] Greenwood, Canadian Journal of Statistics 16 pp 325– (1988)
[14] 1998a: Design: S functions for biostatistical/epidemiologic modeling, testing, estimation, validation, graphics, and prediction. Functions available on the Web in the StatLib repository of statistical software at ”http://lib.stat.cmu.edu/S/Harrell/”.
[15] Harrell, Statistics in Medicine 17 pp 909– (1998b)
[16] Hastie, Statistics in Medicine 8 pp 785– (1989)
[17] Holtbrügge, Applied Statistics 40 pp 249– (1991)
[18] Hosmer, Communications in Statistics - A: Theory and Methods 9 pp 1043– (1980)
[19] Jörgens, Diabetologia 36 pp 99– (1993)
[20] Läärä, Biometrika 72 pp 206– (1985)
[21] Lee, Computer Applications in Biosciences 8 pp 555– (1992) · Zbl 05392655 · doi:10.1093/bioinformatics/8.6.555
[22] McCullagh, Journal of the Royal Statistical Society - B 42 pp 109– (1980)
[23] and , 1989: Generalized Linear Models. Chapman and Hall, New York.
[24] Mühlhauser, Diabetic Medicine 13 pp 536– (1996)
[25] Peterson, Applied Statistics 39 pp 205– (1990)
[26] Pregibon, Annals of Statistics 9 pp 705– (1981)
[27] 1987: SAS/STAT Guide for Personal Computers, Version 6 Edition. SAS Institute Inc., Cary, NC.
[28] 1990: SAS Technical Report P-200, SAS/STAT Software: CALIS and LOGISTIC Procedures, Release 6.04. SAS Institute Inc., Cary, NC.
[29] Scott, Journal of Clinical Epidemiology 50 pp 45– (1997)
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