Log-binomial methodology

The risk ratio (relative risk) is the ratio measure of choice for summarising the impact of exposure on the incidence proportion (“risk”) in epidemiologic studies (Greenland, 1987). Fitting a log binomial regression model with binomial errors and a logarithmic link to binary outcome data makes it possible to estimate risk and risk ratios in longitudinal studies (as opposed to odds ratios), and prevalence ratios in cross-sectional studies. However, standard methods for fitting the model can result in numerical difficulties typified by failure of the fitting algorithm to converge.  This has prompted some practitioners to resort to one of several improvised methods, none of which are fully satisfactory.

Deddens, Petersen and Lei (2003) proposed a method for solving the problem of non-convergence when fitting the log binomial model using SAS. Further details are given in Petersen and Deddens (2010). However, their method is difficult to navigate and has remained relatively unknown since its publication. Associate Professor Leigh Blizzard and PhD student Chao Zhu have succeeded in implementing this method for use in the Stata and R statistical packages.

Current work is focusing on:

  • Developing documentation and publications demonstrating the implementation of the new software.
  • Applying a mixed model approach to the Petersen Deddens method to enable it to be applied to correlated response data

References:

Deddens, J., Petersen, M., & Lei, X. (20030). Estimation of prevalence ratios when PROC GENMOD does not converge.  Proceedings of the 28th annual SAS users group international conference, 30 270-28.

Greenland, S (1987) Interpretation of choice of effect measures in epidemiologic analysis. American Journal of Epidemiology 125, 761-768

Petersen, MR and Deddens JA (2010) Maximum likelihood estimation of the log-binomial model. Communications in Statistics - Theory and Methods, 39, 874-883

Team Members:

  • Prof Leigh Blizzard
  • Zhu Chao
  • Imogen Jones
  • Dr Karen Wills

External Collaborators:

  • Dr Jim Stankovich
  • Prof David Hosmer