Relative risk regression: reliable and flexible methods for log-binomial models
Relative risk regression: reliable and flexible methods for log-binomial models
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DOI：
10.1093/biostatistics/kxr030
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发表时间：
2012-01-01
期刊：
影响因子：
2.1
通讯作者：
Gillett, Alexandra C.
中科院分区：
文献类型：
--
作者：
Marschner, Ian C.;Gillett, Alexandra C.
在前瞻性研究中，相对危险度（rr）通常被认为比比值比更可取。然而，与比值比的逻辑回归不同，RR回归的标准对数二项模型不考虑自然参数约束，因此经常受到数值不稳定性的影响。本文提出了一种可靠、灵活的对数二项模型拟合方法。我们使用期望最大化（EM）算法，其中乘法事件概率被视为潜在二进制结果集合的联合概率。这给出了一个简单的迭代方案，提供了稳定的收敛到最大似然估计。除了可靠性外，该方法还提供了一些灵活的推广，包括未指定等渗回归函数的模型。我们通过对心脏病发作后死亡率的年龄特异性RR的模拟和数据分析来检验该方法的性能。这些分析证明了RR回归中数值不稳定性的潜力，并展示了如何使用所提出的方法来克服这种不稳定性。用R语言实现该方法的源代码作为补充材料提供在Biostatistics网站上。
Relative risks (RRs) are generally considered preferable to odds ratios in prospective studies. However, unlike logistic regression for odds ratios, the standard log-binomial model for RR regression does not respect the natural parameter constraints and is therefore often subject to numerical instability. In this paper, we develop a reliable and flexible method for fitting log-binomial models. We use an Expectation-Maximization (EM) algorithm where the multiplicative event probability is viewed as the joint probability for a collection of latent binary outcomes. This gives a simple iterative scheme that provides stable convergence to the maximum likelihood estimate. In addition to reliability, the method offers some flexible generalizations, including models with unspecified isotonic regression functions. We examine the method's performance using simulations and data analyses of the age-specific RR of mortality following heart attack. These analyses demonstrate the potential for numerical instability in RR regression and show how this can be overcome using the proposed approach. Source code to implement the method in R is provided as supplementary material available at Biostatistics online.