We study the benefit of exploiting the gene–environment independence (GEI) assumption for inferring the joint effect of genotype and environmental exposure on disease risk in a case–control study. By transforming the problem into a constrained maximum likelihood estimation problem we derive the asymptotic distribution of the maximum likelihood estimator (MLE) under the GEI assumption (MLE‐GEI) in a closed form. Our approach uncovers a transparent explanation of the efficiency gained by exploiting the GEI assumption in more general settings, thus bridging an important gap in the existing literature. Moreover, we propose an easy‐to‐implement numerical algorithm for estimating the model parameters in practice. Finally, we conduct simulation studies to compare the proposed method with the traditional prospective logistic regression method and the case‐only estimator. The Canadian Journal of Statistics 47: 473–486; 2019 © 2019 Statistical Society of Canada

中文翻译：

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基因-环境独立性在病例对照研究中的益处的新观点

在病例对照研究中，我们研究了利用基因-环境独立性（GEI）假设来推断基因型和环境暴露对疾病风险的联合影响的益处。通过将问题转化为受约束的最大似然估计问题，我们可以得出封闭形式的GEI假设（MLE-GEI）下最大似然估计器（MLE）的渐近分布。我们的方法揭示了在更一般的情况下利用GEI假设获得的效率的透明解释，从而弥合了现有文献中的重要空白。此外，我们提出了一种易于实现的数值算法，用于在实践中估算模型参数。最后，《加拿大统计杂志》 47：473–486；2019©2019加拿大统计学会