Selection bias is a common concern in epidemiologic studies. In the literature, selection bias is often viewed as a missing data problem. Popular approaches to adjust for bias due to missing data, such as inverse probability weighting, rely on the assumption that data are missing at random and can yield biased results if this assumption is violated. In observational studies with outcome data missing not at random, Heckman's sample selection model can be used to adjust for bias due to missing data. In this paper, we review Heckman's method and a similar approach proposed by Tchetgen Tchetgen and Wirth (2017). We then discuss how to apply these methods to Mendelian randomization analyses using individual-level data, with missing data for either the exposure or outcome or both. We explore whether genetic variants associated with participation can be used as instruments for selection. We then describe how to obtain missingness-adjusted Wald ratio, two-stage least squares and inverse variance weighted estimates. The two methods are evaluated and compared in simulations, with results suggesting that they can both mitigate selection bias but may yield parameter estimates with large standard errors in some settings. In an illustrative real-data application, we investigate the effects of body mass index on smoking using data from the Avon Longitudinal Study of Parents and Children.

中文翻译：

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使用选择工具调整孟德尔随机化中的选择偏差

选择偏倚是流行病学研究中普遍关注的问题。在文献中，选择偏差通常被视为缺失数据问题。调整因缺失数据导致的偏差的流行方法（例如逆概率加权）依赖于数据随机缺失的假设，如果违反此假设，可能会产生有偏差的结果。在结果数据不是随机缺失的观察性研究中，Heckman 的样本选择模型可用于调整因数据缺失导致的偏差。在本文中，我们回顾了 Heckman 的方法和 Tchetgen Tchetgen 和 Wirth (2017) 提出的类似方法。然后，我们讨论如何将这些方法应用于使用个体水平数据的孟德尔随机化分析，缺少暴露或结果或两者的数据。我们探索与参与相关的遗传变异是否可以用作选择的工具。然后，我们描述了如何获得调整缺失的 Wald 比率、两阶段最小二乘法和逆方差加权估计。在模拟中对这两种方法进行了评估和比较，结果表明它们都可以减轻选择偏差，但在某些情况下可能会产生具有较大标准误差的参数估计。在一个说明性的真实数据应用程序中，我们使用来自雅芳父母和儿童纵向研究的数据来调查体重指数对吸烟的影响。结果表明它们都可以减轻选择偏差，但在某些设置中可能会产生具有较大标准误差的参数估计。在一个说明性的真实数据应用程序中，我们使用来自雅芳父母和儿童纵向研究的数据来调查体重指数对吸烟的影响。结果表明它们都可以减轻选择偏差，但在某些设置中可能会产生具有较大标准误差的参数估计。在一个说明性的真实数据应用程序中，我们使用来自雅芳父母和儿童纵向研究的数据来调查体重指数对吸烟的影响。