Ordinal regression models for epidemiologic data

Our plain-English summary of Ordinal regression models for epidemiologic data, by B.G. Armstrong, M. Sloan (American Journal of Epidemiology, 1989).

The study

• Authors: B.G. Armstrong, M. Sloan
• Journal: American Journal of Epidemiology
• Published: 1989;129(1):191-204
• Cited by: 193 articles, as counted by NIH iCite
• Read it: PubMed · Publisher

Abstract

Health status is often measured in epidemiologic studies on an ordinal scale, but data of this type are generally reduced for analysis to a single dichotomy. Several statistical models have been developed to make full use of information in ordinal response data, but have not been much used in analyzing epidemiologic studies. The authors discuss two of these statistical models--the cumulative odds model and the continuation ratio model. They may be interpreted in terms of odds ratios, can account for confounding variables, have clear and testable assumptions, and have parameters that may be estimated and hypotheses that may be tested using available statistical packages. However, calculations of asymptotic relative efficiency and results of simulations showed that simple logistic regression applied to dichotomized responses can in some realistic situations have more than 75% of the efficiency of ordinal regression models, but only if the ordinal scale is collapsed into a dichotomy close to the optimal point. The application of the proposed models to data from a study of chest x-rays of workers exposed to mineral fibers confirmed that they are easy to use and interpret, but gave results quite similar to those obtained using simple logistic regression after dichotomizing outcome in the conventional way.

In plain English

This was a statistical methods article. The authors described two models for health outcomes graded on an ordered scale: the cumulative odds and continuation ratio models. Using theoretical calculations, they compared the cumulative odds model with the usual approach of splitting the scale in two and using simple logistic regression. A simulation tested all three, although the authors said the continuation ratio model cannot be compared directly with the others. They applied the methods to an earlier cross-sectional study of 244 miners exposed to tremolite fibers, whose chest x-rays were graded for small opacities. In that example, profusion score was significantly associated with age, smoking and cumulative fiber exposure under all three methods. The odds ratio per 100 fiber/ml-years was 1.42 (95% confidence interval 1.12-1.80) with simple logistic regression, 1.46 (1.23-1.74) with cumulative odds and 1.27 (1.12-1.44) with continuation ratio. The authors explained that the continuation ratio odds ratio has a different meaning. No major interpretation depended on the model chosen. The authors concluded that ordinal methods are indicated where avoiding loss of information matters or where choosing a split point is arbitrary.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Statistical methods article: description of two ordinal regression models, theoretical efficiency calculations, a small simulation study, and an illustrative application to existing cross-sectional chest x-ray data
• Who was studied: Illustrative example: 244 past and present miners exposed to tremolite fibers, from an earlier cross-sectional study of radiographic abnormalities
• Exposure: Exposure to fibers measured as a cumulative exposure index in fiber/ml-years. Age and smoking habit were treated as potential confounders.
• Main results:
  • In the miners, profusion of small opacities on chest x-ray was significantly associated with age, smoking and cumulative exposure under all three methods of analysis.
  • In the miners, odds ratios per 100 fiber/ml-years of cumulative exposure were as follows: simple logistic 1.42 (95% CI 1.12-1.80); cumulative odds 1.46 (1.23-1.74); continuation ratio 1.27 (1.12-1.44).
  • The odds ratio from the continuation ratio model has a different interpretation from that of the cumulative odds model. The authors described its lower values as an expected result of that different meaning.
  • In the miners, the global likelihood ratio for age, smoking and cumulative exposure together was 57.0 for simple logistic, 75.1 for cumulative odds and 76.8 for continuation ratio models.
  • In the miners and in subsets of their data, no major issue of interpretation depended on the choice of model.
  • In theoretical calculations with equally probable outcome categories, simple logistic regression split near the optimal point had 75 to 80 per cent of the efficiency of the cumulative odds model.
  • Using the category distribution of the miners' x-rays, simple logistic regression at the conventional cut-point was 77 per cent as efficient as cumulative odds regression.
  • In the simulation, simple logistic regression was 83 per cent as efficient as the cumulative odds model, close to the predicted 82 per cent.
  • In the simulation, the continuation ratio model could not be compared directly with the other two methods because its parameter has a different interpretation.
• The authors' conclusion: The authors concluded that ordinal regression methods are indicated where avoiding loss of information is a major consideration, or where choosing a single cut-point involves an arbitrary choice. They also judged that splitting the scale costs only slightly less power if the cut-point is close to its optimal point.
• Limitations the authors state:
  • Computational difficulties arose with sparse higher x-ray categories, so scores of 2/3 and above were combined into one category.
  • Overall likelihoods could not be read as measures of goodness of fit because continuous exposure variables were used.
  • The simulated data followed the cumulative odds model; the authors expected results less favorable to that model if the data followed another model.
  • The conventional chest x-ray cut-point might not be close to the one that is optimal for statistical power.

Topics

The National Library of Medicine indexes this study under subjects our site covers: Tremolite.

Medical terms in this study, explained in our Lexicon: Odds Ratio, Confounding, Chest X-Ray, Mineral Fiber.

Related studies

• Availability of epidemiologic data for chemicals known to cause cancer in animals: an update — M. Karstadt (1998)
• Asbestos Fiber Concentrations in the Lungs of Brake Repair Workers: An Updated Analysis Using Several Regression Methods to Handle Nondetectable Measurements — Y. Liu, G.M. Marsh, et al. (2018)
• Occam's razor pares the choice among statistical models — K.J. Rothman (1978)
• A reanalysis of the Stanton et al. pleural sarcoma data — G.W. Oehlert (1991)
• Fiber burden and patterns of asbestos-related disease in chrysotile miners and millers — A. Churg, J.L. Wright, et al. (1993)
• Indirect corrections for confounding under multiplicative and additive risk models — M.H. Gail, S. Wacholder, et al. (1988)

Browse more research in American Journal of Epidemiology, or return to medical research.