Case-control mother–offspring pair design has been widely adopted for studying early-life and women’s pregnancy health. It allows assessment of pre- and perinatal environmental risk factors as well as both maternal and offspring genetic risk factors. Data arising from this design is routinely analyzed using standard prospective logistic regression. Such data has two unique features: the offspring genotypes are not correlated with maternal environmental risk factors given maternal genotypes, and offspring and maternal genotypes are related through mendelian transmission. In this work, built upon a novel regression model relating maternal genotypes to environmental risk factors, we proposed a novel retrospective likelihood method that effectively utilized the two data features to increase statistical efficiency for detecting maternal and offspring genetic effects. The inference procedure was based on a profile likelihood derived using the Lagrange multiplier method, but we replaced the multipliers with their large sample limits to enable highly efficient and computationally stable estimation. We showed that our proposed estimates of odds ratio association parameters are consistent and asymptotically normally distributed and demonstrated the finite sample performance through extensive simulation studies and application to genetic association studies of birth weight and gestational diabetes mellitus.

中文翻译：

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一种有效且计算稳健的统计方法，用于分析病例对照的母子对遗传关联研究

病例对照母对子设计已被广泛用于研究早期生命和妇女怀孕健康。它可以评估产前和围产期的环境危险因素以及孕产妇和后代的遗传危险因素。使用标准前瞻性逻辑回归对来自该设计的数据进行常规分析。这样的数据有两个独特的特征：后代基因型与母亲的基因型与母亲的环境危险因素无关，而后代和母亲的基因型通过孟德尔传播相关。在这项工作中，建立在将孕产妇基因型与环境危险因素相关联的新型回归模型的基础上，我们提出了一种新颖的回顾性似然方法，该方法有效利用了这两个数据特征，以提高统计效率，以检测母体和后代的遗传效应。推理过程基于使用拉格朗日乘数法得出的轮廓似然，但是我们将乘数替换为它们的大样本限制，以实现高效且计算稳定的估计。我们表明，我们提出的比值关联参数估计值是一致的，并且呈渐近正态分布，并通过广泛的模拟研究并将其应用于出生体重和妊娠糖尿病的遗传关联研究，证明了有限的样本性能。但是我们将乘法器替换为其较大的样本数限制，以实现高效且计算稳定的估算。我们表明，我们提出的比值关联参数估计值是一致的，并且呈渐近正态分布，并通过广泛的模拟研究并将其应用于出生体重和妊娠糖尿病的遗传关联研究，证明了有限的样本性能。但是我们将乘法器替换为其较大的样本数限制，以实现高效且计算稳定的估算。我们表明，我们提出的比值关联参数估计值是一致的，并且呈渐近正态分布，并通过广泛的模拟研究并将其应用于出生体重和妊娠糖尿病的遗传关联研究，证明了有限的样本性能。