Logistic regression is widely used to evaluate the association between risk factors and a binary outcome. The logistic curve is symmetric around its point of inflection. Alternative families of curves, such as the additive Gompertz or Guerrero-Johnson models, have been proposed in various scenarios due to their asymmetry: disease risk may initially increase rapidly and be followed by a longer period where the rate of growth slowly decreases. When modeling binary outcomes in relation to risk factors, an additive logistic model may not provide a good fit to the data. Suppose the outcome and an additive function of the risk factors are indeed related through an asymmetric function, but we model the relationship using a logistic function. We illustrate - both from a mathematical framework and through a simulation-based evaluation - that higher-order terms, such as pairwise interactions and quadratic terms, may be required in a logistic regression model to obtain a good fit to the data. Importantly, as significant higher-order terms may be a manifestation of model misspecification, these terms should be cautiously interpreted; a more pragmatic approach is to develop contrasts of disease risk coming from a good fitting model. We illustrate these concepts in 2 cohort studies examining early death for late-stage colorectal and pancreatic cancer cases, and 2 case-control studies investigating NAT2 acetylation, smoking, and advanced colorectal adenoma and bladder cancer.

中文翻译：

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从增长曲线角度进行统计交互。

Logistic回归广泛用于评估风险因素与二元结果之间的关联。逻辑曲线在其拐点附近对称。由于它们的不对称性，已在其他各种情况下提出了替代曲线系列，例如加性Gompertz或Guerrero-Johnson模型：疾病风险最初可能会迅速增加，然后是更长的时期，增长率会缓慢降低。当对与风险因素相关的二元结果进行建模时，加法逻辑模型可能无法很好地拟合数据。假设风险因素的结果和加性函数确实通过不对称函数相关，但是我们使用逻辑函数对关系进行建模。我们从数学框架和通过基于仿真的评估中都说明，逻辑回归模型可能需要更高阶的项（例如，成对交互和二次项）才能很好地拟合数据。重要的是，由于重要的高阶术语可能表示模型规格不正确，因此应谨慎解释这些术语。一种更实用的方法是通过良好的拟合模型得出疾病风险的对比。我们在两项研究晚期结直肠癌和胰腺癌病例的早期死亡的队列研究以及两项研究NAT2乙酰化，吸烟和晚期结直肠腺瘤和膀胱癌的病例对照研究中阐明了这些概念。逻辑回归模型中可能需要使用它以获得与数据的良好拟合。重要的是，由于重要的高阶术语可能表示模型规格不正确，因此应谨慎解释这些术语。一种更实用的方法是通过良好的拟合模型得出疾病风险的对比。我们在两项研究晚期结直肠癌和胰腺癌病例的早期死亡的队列研究以及两项研究NAT2乙酰化，吸烟和晚期结直肠腺瘤和膀胱癌的病例对照研究中阐明了这些概念。逻辑回归模型中可能需要使用它以获得与数据的良好拟合。重要的是，由于重要的高阶术语可能表示模型规格不正确，因此应谨慎解释这些术语。一种更实用的方法是通过良好的拟合模型得出疾病风险的对比。我们在两项研究晚期结直肠癌和胰腺癌病例的早期死亡的队列研究以及两项研究NAT2乙酰化，吸烟和晚期结直肠腺瘤和膀胱癌的病例对照研究中阐明了这些概念。