标题： 互补对数-对数模型改进的风险比近似：与逻辑模型的比较 显示英文标题

标题： Improved Risk Ratio Approximation by Complementary Log-Log Models: A Comparison with Logistic Models

摘要： 由逻辑回归模型得到的几率比无法近似常见结果的风险比，这可能导致从业者对暴露效应产生潜在的误解。 本文研究了互补对数-对数模型作为一种实用的替代方法来生成风险比近似值。 我们证明，互补对数-对数模型对应的效应测量指标（本文称为互补对数比），始终比几率比更接近风险比。 为了比较近似准确性，我们采用了单参数Aranda-Ordaz联结函数族，该族函数包括logit和互补对数-对数联结函数作为特例。 在这个统一框架内，我们对互补对数比与几率比之间的近似准确性进行了理论比较，结果显示前者总是产生较小的近似偏差。 模拟研究进一步巩固了我们的理论发现。 鉴于互补对数-对数模型在R和SAS等标准统计软件中易于实现，我们鼓励在目标是更准确地近似风险比时，更多地使用此模型作为逻辑回归模型的简单而有效的替代方案。 显示英文摘要

摘要： Odds ratios obtained from logistic models fail to approximate risk ratios with common outcomes, leading to potential misinterpretations about exposure effects by practitioners. This article investigates the complementary log-log models as a practical alternative to produce risk ratio approximation. We demonstrate that the corresponding effect measure of complementary log-log models, called the complementary log ratio in this article, consistently provides a closer approximation to risk ratios than odds ratios. To compare the approximation accuracy, we adopt the one-parameter Aranda-Ordaz family of link functions, which includes both the logit and complementary log-log link functions as special cases. Within this unified framework, we implement a theoretical comparison of approximation accuracy between the complementary log ratio and the odds ratio, showing that the former always produces smaller approximation bias. Simulation studies further reinforce our theoretical findings. Given that the complementary log-log model is easily implemented in standard statistical software such as R and SAS, we encourage more frequent use of this model as a simple and effective alternative to logistic models when the goal is to approximate risk ratios more accurately.