Lin Tuo, Zhao Rongzhe, Tu Shengjia, Wu Hao, Zhang Hui, Tu Xin M
Division of Biostatistics and Bioinformatics, Herbert Wertheim School of Public Health and Human Longevity Science, UC San Diego, La Jolla, California, USA.
College of Environmental Science and Engineering, Tongji University, Shanghai, China.
Gen Psychiatr. 2023 Mar 7;36(2):e100977. doi: 10.1136/gpsych-2022-100977. eCollection 2023.
Although logistic regression is the most popular for modelling regression relationships with binary responses, many find relative risk (RR), or risk ratio, easier to interpret and prefer to use this measure of risk in regression analysis. Indeed, since Zou published his modified Poisson regression approach for modelling RR for cross-sectional data, his paper has been cited over 7 000 times, demonstrating the popularity of this alternative measure of risk in regression analysis involving binary responses. As longitudinal studies have become increasingly popular in clinical trials and observational studies, it is imperative to extend Zou's approach for longitudinal data. The two most popular approaches for longitudinal data analysis are the generalised linear mixed-effects model (GLMM) and generalised estimating equations (GEE). However, the parametric GLMM cannot be used for the extension within the current context, because Zou's approach treats the binary response as a Poisson variable, which is at odds with the Bernoulli distribution for the binary response. On the other hand, as it imposes no mathematical model on data distributions, the semiparametric GEE is coherent with Zou's modified Poisson regression. In this paper, we develop a GEE-based longitudinal model for binary responses to provide inference about RR.
尽管逻辑回归是用于对二元响应的回归关系进行建模最常用的方法，但许多人发现相对风险（RR）或风险比更易于解释，并且更倾向于在回归分析中使用这种风险度量。事实上，自从邹发表了他用于对横断面数据的RR进行建模的修正泊松回归方法以来，他的论文被引用了7000多次，这表明这种替代风险度量在涉及二元响应的回归分析中很受欢迎。随着纵向研究在临床试验和观察性研究中越来越普遍，扩展邹的方法以适用于纵向数据势在必行。纵向数据分析中两种最常用的方法是广义线性混合效应模型（GLMM）和广义估计方程（GEE）。然而，参数化GLMM在当前情况下不能用于扩展，因为邹的方法将二元响应视为泊松变量，这与二元响应的伯努利分布不一致。另一方面，由于半参数GEE不对数据分布施加数学模型，它与邹的修正泊松回归是一致的。在本文中，我们开发了一个基于GEE的二元响应纵向模型，以提供关于RR的推断。
