Case‐control sampling is frequently used in genetic association studies to examine the relationship between disease and genetic exposures. Such designs usually collect extensive information on phenotypes beyond the primary disease, whose associations with the genetic exposures are also of great interest. Because the cases are over‐sampled, appropriate analysis of secondary phenotypes should take into account this biased sampling design. We previously introduced a weighting‐based estimator for appropriate secondary analysis, but have not thoroughly explored its statistical properties. In this article, we revisit our previous estimator to offer new insights and methodological extensions. Specifically, we extend our previous estimator and construct its more general form based on generalized least squares (GLS). Such an extension allows us to connect the GLS estimator with the generalized method of moments and motivates a new specification test designed to assess the adequacy of the disease model or the weights. The specification test statistic measures the weighted discrepancy between the case and control subsample estimators, and asymptotically follows a central Chi‐squared distribution under correct disease model specification. We illustrate the GLS estimator and specification test using a case‐control sample of peripheral arterial disease, and use simulations to further shed light on the operating characteristics of the specification test.

中文翻译：

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案例控制关联研究的二级分析：对基于加权的推理的洞察力激发了新的规范测试。

病例对照抽样经常用于遗传关联研究中，以检查疾病与遗传暴露之间的关系。这样的设计通常会收集除原发性疾病以外的表型信息，这些信息与遗传暴露的关联也引起了人们的极大兴趣。由于病例被过度抽样，因此对次要表型的适当分析应考虑这种偏倚的抽样设计。之前，我们引入了基于加权的估算器来进行适当的二次分析，但尚未彻底探索其统计特性。在本文中，我们将重新审视先前的估算器，以提供新的见解和方法扩展。具体来说，我们扩展了先前的估计量，并基于广义最小二乘（GLS）构造了其更一般的形式。这样的扩展使我们能够将GLS估计器与广义矩方法联系起来，并激发了一项新的规范测试，旨在评估疾病模型或权重的适当性。规范检验统计量度了案例与对照子样本估计量之间的加权差异，并在正确的疾病模型规范下渐近遵循中心卡方分布。我们使用外周动脉疾病的病例对照样本说明了GLS估计量和规范测试，并使用模拟进一步阐明了规范测试的操作特性。规范检验统计量度了案例与对照子样本估计量之间的加权差异，并在正确的疾病模型规范下渐近遵循中心卡方分布。我们使用外周动脉疾病的病例对照样本说明了GLS估计量和规范测试，并使用模拟进一步阐明了规范测试的操作特性。规范检验统计量度了案例与对照子样本估计量之间的加权差异，并在正确的疾病模型规范下渐近遵循中心卡方分布。我们使用外周动脉疾病的病例对照样本说明了GLS估计量和规范测试，并使用模拟进一步阐明了规范测试的操作特性。