Williamson Tyler, Eliasziw Misha, Fick Gordon Hilton
Departments of Family Medicine and Public Health Sciences, Queen's University, Kingston, ON, Canada.
Emerg Themes Epidemiol. 2013 Dec 13;10(1):14. doi: 10.1186/1742-7622-10-14.
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.
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.
Epidemiologists are encouraged to continue to use log-binomial models and advocate for improvements to the fitting algorithms to promote the widespread use of log-binomial models.
相对风险是流行病学调查中常用的一个汇总指标。越来越多的流行病学家使用对数二项式模型来研究一组预测变量对单个二元结局的影响，因为这些模型自然会给出相对风险。然而，在某些情况下，当尝试拟合对数二项式模型时，标准统计软件可能会报告收敛失败。文献中提出的处理收敛失败的方法使用近似解来避免这个问题。本研究直接考察了在观察到收敛失败的最简单对数二项式模型（即具有三个水平的单个线性预测变量的模型）的对数似然函数。探讨了收敛失败的可能原因，并针对某些情况提出了潜在的解决方案。
主要原因之一是尽管对数似然函数有一个单一的有限最大值，但拟合算法仍未能收敛。尽管有这些局限性，对数二项式模型对于希望描述一组预测变量与二元结局之间关系（其中相对风险是期望的汇总度量）的流行病学家来说是一个可行的选择。
鼓励流行病学家继续使用对数二项式模型，并倡导改进拟合算法，以促进对数二项式模型的广泛应用。
