Standardized binomial models for risk or prevalence ratios and differences

David B. Richardson, Alan C. Kinlaw, Richard F. MacLehose, Stephen R. Cole

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


Background: Epidemiologists often analyse binary outcomes in cohort and cross-sectional studies using multivariable logistic regression models, yielding estimates of adjusted odds ratios. It is widely known that the odds ratio closely approximates the risk or prevalence ratio when the outcome is rare, and it does not do so when the outcome is common. Consequently, investigators may decide to directly estimate the risk or prevalence ratio using a log binomial regression model. Methods: We describe the use of a marginal structural binomial regression model to estimate standardized risk or prevalence ratios and differences. We illustrate the proposed approach using data from a cohort study of coronary heart disease status in Evans County, Georgia, USA. Results: The approach reduces problems with model convergence typical of log binomial regression by shifting all explanatory variables except the exposures of primary interest from the linear predictor of the outcome regression model to a model for the standardization weights. The approach also facilitates evaluation of departures from additivity in the joint effects of two exposures. Conclusions: Epidemiologists should consider reporting standardized risk or prevalence ratios and differences in cohort and cross-sectional studies. These are readily-obtained using the SAS, Stata and R statistical software packages. The proposed approach estimates the exposure effect in the total population.

Original languageEnglish (US)
Article numberdyv137
Pages (from-to)1660-1672
Number of pages13
JournalInternational journal of epidemiology
Issue number5
StatePublished - Oct 1 2015

Bibliographical note

Publisher Copyright:
© The Author 2015; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association.


  • Risk
  • prevalence
  • regression models
  • standardizations


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