Using Binary Logistic Regression Models for Ordinal Data with Non-proportional Odds

  • Ralf Bender
    Address for correspondence: Ralf Bender, Ph.D., Department of Metabolic Diseases and Nutrition, Heinrich-Heine-University of Düsseldorf, P.O. Box 101007, D-40001, Düsseldorf, Germany
    Department of Metabolic Diseases and Nutrition, Heinrich-Heine-University of Düsseldorf, Düsseldorf, Germany
    Search for articles by this author
  • Ulrich Grouven
    Department of Anesthesiology, Research Group Informatics and Biometry, Hannover Medical School, Hospital Oststadt, Hannover, Germany
    Search for articles by this author


      The proportional odds model (POM) is the most popular logistic regression model for analyzing ordinal response variables. However, violation of the main model assumption can lead to invalid results. This is demonstrated by application of this method to data of a study investigating the effect of smoking on diabetic retinopathy. Since the proportional odds assumption is not fulfilled, separate binary logistic regression models are used for dichotomized response variables based upon cumulative probabilities. This approach is compared with polytomous logistic regression and the partial proportional odds model. The separate binary logistic regression approach is slightly less efficient than a joint model for the ordinal response. However, model building, investigating goodness-of-fit, and interpretation of the results is much easier for binary responses. The careful application of separate binary logistic regressions represents a simple and adequate tool to analyze ordinal data with non-proportional odds.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Journal of Clinical Epidemiology
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • McCullagh P.
        Regression models for ordinal data (with discussion).
        J R Stat Soc B. 1980; 42: 109-142
        • Anderson J.A.
        Regression and ordered categorical variables (with discussion).
        J R Stat Soc B. 1984; 46: 1-30
        • Armstrong B.G.
        • Sloan M.
        Ordinal regression models for epidemiologic data.
        Am J Epidemiol. 1989; 129: 191-204
        • Agresti A.
        Tutorial on modeling ordered categorical response data.
        Psych Bull. 1989; 105: 290-301
        • Greenland S.
        Alternative models for ordinal logistic regression.
        Stat Med. 1994; 13: 1665-1677
        • Cox C.
        Location-scale cumulative odds models for ordinal data.
        Stat Med. 1995; 14: 1191-1203
        • Cox C.
        Multinomial regression models based upon continuation ratios.
        Stat Med. 1997; 16: 435-441
        • Scott S.C.
        • Goldberg M.S.
        • Mayo N.E.
        Statistical assessment of ordinal outcomes in comparative studies.
        J Clin Epidemiol. 1997; 50: 45-55
        • Bender R.
        • Grouven U.
        Ordinal logistic regression in medical research.
        J R Coll Physic London. 1997; 31: 546-551
        • Bender R.
        • Grouven U.
        Logistic regression models used in medical research are poorly presented (Letter).
        Br Med J. 1996; 313: 628
        • Engel J.
        Polytomous logistic regression.
        Stat Neerl. 1988; 42: 233-252
        • Peterson B.
        • Harrell Jr, F.E.
        Partial proportional odds models for ordinal response variables.
        Appl Stat. 1990; 39: 205-217
        • Jörgens V.
        • Grüsser M.
        • Bott U.
        • Mühlhauser I.
        • Berger M.
        Effective and safe translation of intensified insulin therapy to general internal medicine departments.
        Diabetologia. 1993; 36: 99-105
        • Mühlhauser I.
        • Bender R.
        • Bott U.
        • Jörgens V.
        • Grüsser M.
        • Wagener W.
        • et al.
        Cigarette smoking and progression of retinopathy and nephropathy in type 1 diabetes.
        Diabetic Med. 1996; 13: 536-543
      1. SAS. SAS Technical Report P-200 SAS/STAT® Software: CALIS and LOGISTIC Procedures, Release 6.04. Cary, NC: SAS Institute Inc.; 1990.

        • Harrell Jr, F.E.
        • Margolis P.A.
        • Gove S.
        • Mason K.E.
        • Mulholland E.K.
        • Lehmann D.
        • et al.
        Tutorial in biostatistics.
        Stat Med. 1998; 17: 909-944
        • Brant R.
        Assessing proportionality in the proportional odds model for ordinal logistic regression.
        Biometrics. 1990; 46: 1171-1178
        • Harrell Jr, F.E.
        • Lee K.L.
        • Califf R.M.
        • Pryor D.B.
        • Rosati R.A.
        Regression modelling strategies for improved prognostic prediction.
        Stat Med. 1984; 3: 143-152
        • Hosmer D.W.
        • Lemeshow S.
        Goodness-of-fit tests for the multiple logistic regression model.
        Comm Stat A. 1980; 9: 1043-1069
        • Hosmer D.W.
        • Lemeshow S.
        Applied Logistic Regression. Wiley, New York1989
        • Hosmer D.W.
        • Hosmer T.
        • le Cessie S.
        • Lemeshow S.
        A comparison of goodness-of-fit tests for the logistic regression model.
        Stat Med. 1997; 16: 965-980
        • Pregibon D.
        Logistic regression diagnostics.
        Ann Stat. 1981; 9: 705-724
      2. SAS. SAS Procedures Guide for Personal Computers, Version 6 Edition. Cary, NC: SAS Institute Inc.; 1985.

      3. SAS. SAS/STAT Guide for Personal Computers, Version 6 Edition. Cary, NC: SAS Institute Inc.; 1987.

      4. SAS. SAS Technical Report P-229 SAS/STAT Software: Changes and Enhancements, Release 6.07. Cary, NC: SAS Institute Inc.; 1992.

      5. Hedeker D, Gibbons D. DOS versions of MIXOR, MIXREG, and MIXGSUR programs (plus some SPSS and SAS macro programs). Internet Web Page, URL:∼hedeker/mixdos.html, October 1997.

        • Woodward M.
        • Laurent K.
        • Tunstall-Pedoe H.
        An analysis of risk factors for prevalent coronary heart disease by using the proportional odds model.
        Statistician. 1995; 44: 69-80
        • Koch G.G.
        • Amara I.A.
        • Singer J.M.
        A two-stage procedure for the analysis of ordinal categorical data.
        in: Sen P.K. Biostatistics Statistics in Biomedical, Public Health and Environmental Sciences. Elsevier, North-Holland1985
        • Begg C.B.
        • Gray R.
        Calculation of polychotomous logistic regression parameters using individualized regressions.
        Biometrika. 1984; 71: 11-18
        • Mühlhauser I.
        Cigarette smoking and diabetes.
        Diabetic Med. 1994; 11: 336-343
        • Chase H.P.
        • Garg S.K.
        • Marshall G.
        • Berg C.L.
        • Harris S.
        • Jackson W.E.
        • Hamman R.E.
        Cigarette smoking increases the risk of albuminuria among subjects with type 1 diabetes.
        JAMA. 1991; 265: 614-617
        • Marshall G.
        • Jones R.H.
        Multi-state models and diabetic retinopathy.
        Stat Med. 1995; 14: 1975-1983