Summary Many methods have recently been proposed for efficient analysis of case‐control studies of gene‐environment interactions using a retrospective likelihood framework that exploits the natural assumption of gene‐environment independence in the underlying population. However, for polygenic modelling of gene‐environment interactions, which is a topic of increasing scientific interest, applications of retrospective methods have been limited due to a requirement in the literature for parametric modelling of the distribution of the genetic factors. We propose a general, computationally simple, semiparametric method for analysis of case‐control studies that allows exploitation of the assumption of gene‐environment independence without any further parametric modelling assumptions about the marginal distributions of any of the two sets of factors. The method relies on the key observation that an underlying efficient profile likelihood depends on the distribution of genetic factors only through certain expectation terms that can be evaluated empirically. We develop asymptotic inferential theory for the estimator and evaluate its numerical performance via simulation studies. An application of the method is presented.

中文翻译：

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病例对照研究中复杂多基因基因-环境相互作用的半参数分析

总结最近提出了许多方法来有效分析基因-环境相互作用的病例对照研究，这些方法使用回顾性似然框架，该框架利用了潜在人群中基因-环境独立性的自然假设。然而，对于基因-环境相互作用的多基因建模，这是一个越来越受科学关注的话题，由于文献中需要对遗传因素的分布进行参数建模，回顾性方法的应用受到了限制。我们提出了一种通用的、计算简单的、半参数的方法来分析病例对照研究，该方法允许利用基因-环境独立性假设，而无需对两组因子中任何一个的边际分布进行任何进一步的参数建模假设。该方法依赖于关键观察，即潜在的有效轮廓似然取决于遗传因素的分布，仅通过可以经验评估的某些期望项。我们为估计器开发渐近推理理论，并通过模拟研究评估其数值性能。介绍了该方法的应用。