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Log-binomial models: exploring failed convergence

机译：对数二项式模型：探索失败的收敛

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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 widespread use of log-binomial models.
机译：背景相对风险是一种流行病学调查中常用的汇总指标。流行病学家越来越多地使用对数二项式模型来研究一组预测变量对单个二进制结果的影响，因为它们自然会带来相对风险。但是，当尝试在特定设置中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。文献中提出的用于解决收敛失败的方法使用了近似解决方案来避免该问题。这项研究直接着眼于最简单的对数二项式模型的对数似然函数，该模型已观察到收敛失败，该模型具有三个水平的单个线性预测变量。探索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。结果尽管对数似然函数只有一个有限的最大值，但主要原因是拟合算法无法收敛。尽管存在这些局限性，对数二项式模型仍然是流行病学家的可行选择，他们希望描述一组预测变量与二元结果之间的关系，其中相对风险是所需的汇总指标。结论鼓励流行病学家继续使用对数二项式模型，并提倡改进拟合算法以促进对数二项式模型的广泛使用。

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