Log-binomial models: exploring failed convergence
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Log-binomial models: exploring failed convergence Emerging Themes in Epidemiology 2013, 10:14
doi:10.1186/1742-7622-10-14
Tyler Williamson ([email protected]) Misha Eliasziw ([email protected]) Gordon Hilton Fick ([email protected])
ISSN
1742-7622
Article type
Methodology
Submission date
23 April 2013
Acceptance date
5 December 2013
Publication date
13 December 2013
Article URL
http://www.ete-online.com/content/10/1/14
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© 2013 Williamson et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Log-binomial models: exploring failed convergence Tyler Williamson1∗ ∗ Corresponding author Email: [email protected] Misha Eliasziw2 Email: [email protected] Gordon Hilton Fick3 Email: [email protected] 1 Departments of Family Medicine and Public Health Sciences, Queen’s University, Kingston,
ON, Canada 2 Department
of Public Health and Community Medicine, Tufts University, Boston, MA,
USA 3 Department
of Community Health Sciences, University of Calgary, Calgary, AB, Canada
Abstract Background Relative risk is a summary metric that is commonly used in epidemiological investigations. Increasingly, epidemiologists are using log-binomial models to study the impact of a set of predictor variables on a single binary outcome, as they naturally offer relative risks. However, standard statistical software may report failed convergence when attempting to fit log-binomial models in certain settings. The methods that have been proposed in the literature for dealing with failed convergence use approximate solutions to avoid the issue. This research looks directly at the log-likelihood function for the simplest log-binomial model where failed convergence has been observed, a model with a single linear predictor with three levels. The possible causes of failed convergence are explored and potential solutions are presented for some cases.
Results Among the principal causes is a failure of the fitting algorithm to converge despite the log-likelihood function having a single finite maximum. Despite these limitations, log-binomial models are a viable option for epidemiologists wishing to describe the relationship between a set of predictors and a binary outcome where relative risk is the desired summary measure.
Conclusions Epidemiologists are encouraged to continue to use log-binomial models and advocate for improvements to the fitting algorithms to promote the widespr
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