Most of the existing Mendelian randomization (MR) methods are limited by the assumption of linear causality between exposure and outcome, and the development of new non-linear MR methods is highly desirable. We introduce two-stage prediction estimation and control function estimation from econometrics to MR and extend them to non-linear causality. We give conditions for parameter identification and theoretically prove the consistency and asymptotic normality of the estimates. We compare the two methods theoretically under both linear and non-linear causality. We also extend the control function estimation to a more flexible semi-parametric framework without detailed parametric specifications of causality. Extensive simulations numerically corroborate our theoretical results. Application to UK Biobank data reveals non-linear causal relationships between sleep duration and systolic/diastolic blood pressure.

翻译：现有孟德尔随机化（MR）方法大多受限于暴露与结局间线性因果关系的假设，亟需发展新的非线性MR方法。我们将计量经济学中的两阶段预测估计和控制函数估计引入MR，并将其拓展至非线性因果关系。本文给出了参数识别的条件，从理论上证明了估计量的一致性和渐近正态性。在线性和非线性因果关系下对两种方法进行了理论比较。进一步将控制函数估计推广至更灵活的半参数框架，无需对因果关系进行详细参数化设定。大量模拟实验佐证了理论结果。应用于英国生物银行（UK Biobank）数据揭示了睡眠时长与收缩压/舒张压之间的非线性因果关系。