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2021; 36(5): 465–478.
Eur J Epidemiol.2021; 36(5):465-478.
Published online 2021 May 7. doi: 10.1007/s10654-021-00757-1
doi: 10.1007/s10654-021-00757-1
PMCID: PMC8159796
PMID: 33961203

Mendelian randomisation for mediation analysis: current methods and challenges for implementation

Alice R. Carter,corresponding author1,2 Eleanor Sanderson,1,2 Gemma Hammerton,1,2,3 Rebecca C. Richmond,1,2 George Davey Smith,1,2,4 Jon Heron,1,2,3 Amy E. Taylor,1,2,4 Neil M. Davies,1,2,5 and Laura D. Howe1,2
爱丽丝-R-卡特, corresponding author 1, 2 埃莉诺-桑德森, 1, 2 杰玛-哈默顿, 1, 2, 3 丽贝卡-C-里士满, 1, 2 乔治-戴维-史密斯, {{10} 2, 4 乔恩-希伦, {{13} 2, 3 艾米-E-泰勒, 1, 2, 4 尼尔-戴维斯(Neil M. Davies), {{{19} 2, 5 和劳拉-D-豪 1, 2

Associated Data 相关数据

Supplementary Materials 补充材料
Data Availability Statement

Abstract 摘要

Mediation analysis seeks to explain the pathway(s) through which an exposure affects an outcome. Traditional, non-instrumental variable methods for mediation analysis experience a number of methodological difficulties, including bias due to confounding between an exposure, mediator and outcome and measurement error. Mendelian randomisation (MR) can be used to improve causal inference for mediation analysis. We describe two approaches that can be used for estimating mediation analysis with MR: multivariable MR (MVMR) and two-step MR. We outline the approaches and provide code to demonstrate how they can be used in mediation analysis. We review issues that can affect analyses, including confounding, measurement error, weak instrument bias, interactions between exposures and mediators and analysis of multiple mediators. Description of the methods is supplemented by simulated and real data examples. Although MR relies on large sample sizes and strong assumptions, such as having strong instruments and no horizontally pleiotropic pathways, our simulations demonstrate that these methods are unaffected by confounders of the exposure or mediator and the outcome and non-differential measurement error of the exposure or mediator. Both MVMR and two-step MR can be implemented in both individual-level MR and summary data MR. MR mediation methods require different assumptions to be made, compared with non-instrumental variable mediation methods. Where these assumptions are more plausible, MR can be used to improve causal inference in mediation analysis.
中介分析旨在解释暴露影响结果的途径。传统的、非工具变量的中介分析方法在方法学上存在许多困难,包括暴露、中介和结果之间的混杂以及测量误差造成的偏差。孟德尔随机化(MR)可用于改善中介分析的因果推断。我们介绍了两种利用 MR 估算中介分析的方法:多变量 MR(MVMR)和两步 MR。我们概述了这两种方法,并提供代码演示如何将它们用于中介分析。我们回顾了可能影响分析的问题,包括混杂、测量误差、弱工具偏差、暴露与中介之间的相互作用以及多中介分析。模拟和真实数据实例对方法的描述进行了补充。虽然MR依赖于大样本量和强有力的假设,如具有强有力的工具和不存在横向多效途径,但我们的模拟证明,这些方法不受暴露或介导因素和结果的混杂因素以及暴露或介导因素的非差异性测量误差的影响。MVMR 和两步 MR 均可在个体水平 MR 和汇总数据 MR 中实施。与非工具变量中介方法相比,工具变量中介方法需要做出不同的假设。如果这些假设更合理,则 MR 可用于改进中介分析中的因果推断。

Supplementary Information

The online version contains supplementary material available at 10.1007/s10654-021-00757-1.
在线版本包含补充材料,见 10.1007/s10654-021-00757-1。

Keywords: Mendelian randomisation, Mediation analysis, Multivariable Mendelian randomisation, Two-step Mendelian randomisation

Introduction 导言

Mediation analysis can improve aetiological understanding and identify intermediate variables as potential intervention targets, when intervening on an exposure is not feasible. However, in order to make causal inference, non-instrumental variable (IV) regression based mediation analysis requires strong assumptions. Mendelian randomisation (MR) is an alternative causal inference approach using genetic variants as an IV for a phenotype []. In this paper we compare non-IV regression-based methods for mediation analysis with MR methods for mediation analysis, and describe the assumptions required for MR mediation methods to make valid causal inference.
中介分析可以提高对病因的认识,并在对暴露进行干预不可行的情况下,将中间变量确定为潜在的干预目标。然而,为了进行因果推断,基于非工具变量(IV)回归的中介分析需要强有力的假设。孟德尔随机化(Mendelian randomisation,MR)是一种可供选择的因果推断方法,它使用基因变异作为表型的IV[1]。在本文中,我们将非基于 IV 回归的中介分析方法与 MR 中介分析方法进行了比较,并描述了 MR 中介方法进行有效因果推断所需的假设条件。

Mediation analysis 调解分析

Methods for mediation analysis emerged in the early twentieth-century, although often not described as such at the time, with formal methods developed by Baron and Kenny in the 1980s [, ]. More recently, a large amount of research has built on and improved mediation methods for better causal inference [].
中介分析的方法出现于二十世纪初,尽管当时通常没有这样的描述,但 Baron 和 Kenny 在二十世纪八十年代开发了正式的方法[2, 3]。最近,大量研究在中介分析方法的基础上进行了改进,以更好地进行因果推断[4]。

Three parameters are typically estimated in a traditional mediation analysis i) the total effect (the effect of the exposure on the outcome through all potential pathways) ii) the direct effect, either controlled or natural (the remaining effect of the exposure on the outcome that acts through pathways other than the specified mediator or set of mediators) and iii) the natural indirect effect (the path from exposure to outcome that acts through the mediator(s)). In situations where the total effect, direct effect and indirect effect all act in the same direction, an estimate of the “proportion mediated” (i.e., proportion of the total effect explained by the mediator) can be calculated. Two common approaches to estimate the indirect effect are; the product of coefficients method and the difference in coefficients method [] (see Fig. 1a).
在传统的中介分析中,通常会估算三个参数:i) 总效应(暴露通过所有潜在途径对结果产生的效应);ii) 直接效应(受控效应或自然效应)(暴露通过特定中介或中介集合以外的途径对结果产生的其余效应);iii) 自然间接效应(从暴露到结果之间通过中介产生效应的路径)。如果总效应、直接效应和间接效应的作用方向相同,则可以计算出 "中介比例"(即中介解释的总效应比例)。估算间接效应的两种常用方法是:系数乘积法和系数差法[5](见图 1a)。

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The decomposed effects in a non-IV regression-based mediation analysis where c represents the total effect, c' represents the direct effect and the indirect effect can be calculated by subtracting c’ from c (difference method) or multiplying A times B (product of coefficients method) b multivariable Mendelian randomisation, using a combined genetic instrument for both the exposure and mediator of interest, to estimate the direct effect c' of the exposure and c two-step Mendelian randomisation, where the effect of the exposure on the mediator (A) and mediator on the outcome b are estimated separately, using separate genetic instrumental variables for both the exposure and mediator. These estimates are then multiplied together to estimate the indirect effect of the mediator (A*B)
基于非 IV 回归的中介分析中的分解效应,其中 c 代表总效应,c'代表直接效应,间接效应可通过从 c 中减去 c'(差值法)或将 A 乘以 B(系数乘积法)来计算 b 多变量孟德尔随机法、使用相关暴露因子和中介因子的综合遗传工具,估算暴露因子的直接效应 c'; c 两步孟德尔随机法:使用暴露因子和中介因子的单独遗传工具变量,分别估算暴露因子对中介因子 (A)和中介因子对结果 b 的效应。然后将这些估计值相乘,估算出中介效应的间接效应(A*B)

Traditional non-IV mediation methods, such as Baron and Kenny methods, rely on several strong, untestable assumptions including, (i) no unmeasured confounding between the exposure, mediator and outcome (ii) no exposure-caused confounders of the mediator and outcome (intermediate confounders, see Fig. 2a) and (iii) no exposure-mediator interaction [, , ]. Furthermore, measurement error in either the exposure or mediator can introduce bias [].
传统的非 IV 中介方法,如 Baron 和 Kenny 方法,依赖于几个强有力的、无法检验的假设,包括:(i)暴露、中介和结果之间没有未测量的混杂因素(ii)中介和结果没有暴露引起的混杂因素(中间混杂因素,见图 2a)和(iii)没有暴露-中介相互作用[4, 6, 7]。此外,暴露因子或中介因子的测量误差也会带来偏差[8]。

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Schematic diagram illustrating the causal assumptions (dashed lines) in a non-IV regression-based mediation methods and b Mendelian randomisation mediation analysis with the measured associations in solid black lines. Additional assumptions: in non-IV mediation there is no measurement error in the exposure or mediator; in Mendelian randomisation mediation there is no exposure-mediator interaction. In Mendelian randomisation, the exclusion restriction criteria mean there are no alternative pathways from the instrument to the outcome other than via the exposure (or mediator) of interest
示意图说明了 a 基于非 IV 回归的中介方法和 b 孟德尔随机中介分析中的因果假设(虚线),黑色实线表示测量到的关联。其他假设:在非回归中介分析中,暴露因子或中介因子不存在测量误差;在孟德尔随机中介分析中,暴露因子与中介因子之间不存在交互作用。在孟德尔随机化中,排除限制标准意味着从工具到结果之间除了通过相关暴露(或中介)之外,没有其他途径可供选择

Baron and Kenny methods were introduced to estimate mediation with a continuous exposure, mediator and outcome, although they are also now often applied to binary variables. In the presence of a continuous or rare binary outcome the estimates from the difference in coefficients and the product of coefficients method should coincide [, ].
巴伦法和肯尼法是用来估计连续暴露、中介和结果的中介作用的,不过现在也经常用于二元变量。在存在连续或罕见二元结果的情况下,系数差法和系数乘积法的估计值应该是一致的[4, 9]。

Counterfactual reasoning has been used to develop confounder adjusted methods that can address some of the previously described strong assumptions in non-IV mediation methods []. The assumptions made by these counterfactual approaches, mean mediation can be estimated in the presence of exposure-mediator interactions and account for measured intermediate confounders. Additionally, these more flexible approaches can allow for binary mediators and outcomes. However, these methods remain biased in the presence of unmeasured confounding, measurement error in the exposure or mediator, or in a mis-specified model with reverse causality [, ]. Here, the estimated direct effect is described as being a “controlled direct effect” if the value of the mediator is controlled at a certain value for all individuals in the population, or a “natural direct effect”, when the value of the mediator is allowed to take the value for each person that it would have taken naturally had they been unexposed, in a counterfactual scenario. The “natural indirect effect” represents the average change in an outcome if the value of the exposure was fixed, but the value of the mediator changes from its natural value when exposed to its natural value when unexposed. If there is no interaction between the exposure and mediator, the estimate of the natural direct effect is equivalent to the controlled direct effect, and indeed would align with estimates from Baron and Kenny approaches to mediation [, , ].
反事实推理已被用于开发混杂因素调整方法,以解决之前描述的非 IV 中介方法中的一些有力假设[10- 14]。这些反事实方法所做的假设,意味着可以在存在暴露-中介相互作用的情况下估计中介作用,并考虑到测量的中间混杂因素。此外,这些更灵活的方法还允许使用二元中介和结果。但是,如果存在未测量的混杂因素、暴露因子或中介因子的测量误差,或者在具有反向因果关系的错误模型中,这些方法仍然存在偏差[4, 15]。在这里,如果对人群中的所有个体而言,中介因子的值被控制在某一特定值,则估计的直接效应被描述为 "受控直接效应";如果在反事实情况下,允许中介因子的值取自每个人未暴露时的自然值,则估计的直接效应被描述为 "自然直接效应"。自然间接效应 "是指如果暴露值固定不变,但调解因子的值从暴露时的自然值变为未暴露时的自然值时,结果的平均变化。如果暴露与中介物之间不存在交互作用,那么自然直接效应的估计值就等同于受控直接效应,事实上,这与巴伦和肯尼方法对中介效应的估计值是一致的[4, 9, 16]。

Mendelian randomisation 孟德尔随机化

In Mendelian randomisation (MR) randomly allocated genetic variants are used as instrumental variables (IV) for a phenotype [, , ]. Given the random allocation of genetic variants at conception, MR estimates are not biased by confounding between an exposure and outcome, reverse causation and measurement error []. Three core assumptions are required for a genetic variant to be a valid IV, these are (i) the genetic variants are associated with the exposure (the relevance assumption) (ii) genetic instruments are exchangeable with the outcome, across levels of the instrument (the independence assumption) and (iii) the genetic variants do not affect the outcome via any variable other than the exposure (the exclusion restriction criteria) (Online Resource 1: sFig. 1) []. Indeed, in the case of the independence assumption and exclusion restriction criteria, these are strong and unverifiable assumptions.
在孟德尔随机化(Mendelian randomisation,MR)中,随机分配的遗传变异被用作表型的工具变量(IV)[1, 17, 18]。由于基因变异体在受孕时随机分配,孟德尔随机化的估计值不会因暴露与结果之间的混杂、反向因果关系和测量误差而产生偏差[17]。基因变异体要成为有效的IV,需要三个核心假设,即(i)基因变异体与暴露相关(相关性假设);(ii)基因工具可与结果交换,跨工具水平(独立性假设);(iii)除暴露外,基因变异体不会通过任何变量影响结果(排除限制标准)(在线资料 1:图 1)[1]。事实上,就独立性假设和排除限制标准而言,这些都是无法验证的有力假设。

Rationale for using Mendelian randomisation in mediation analysis

MR can be used to overcome some of the previously described strong assumptions required for causal inference in mediation analysis. For example, estimates are not biased due to unmeasured confounding between an exposure, mediator or outcome.
MR 可以用来克服前面提到的中介分析中因果推断所需的一些有力假设。例如,估算值不会因暴露因子、中介因子或结果之间未测量的混杂而产生偏差。

In mediation terms, univariable MR estimates the total effect of the exposure on the outcome. Two differing MR approaches can then be used which broadly mirror traditional non-IV regression-based approaches to mediation to decompose the direct and indirect effects: multivariable MR (MVMR) [, ] and two-step MR [].
就中介作用而言,单变量中介作用估算暴露对结果的总效应。然后可以使用两种不同的 MR 方法来分解直接效应和间接效应,这两种方法大致反映了传统的基于非 IV 回归的中介方法:多变量 MR(MVMR)[ 19, 20] 和两步 MR[ 21- 23]。

In MVMR the controlled direct effect of the exposure on the outcome, controlling for the mediator, is estimated [, ]. The genetic instrument for both the primary exposure and the second exposure (mediator) are included as instruments in the analysis (Fig. 1b) [, ]. The indirect effect can then be estimated by subtracting the direct effect from the total effect (akin to the difference in coefficients method). MVMR assumes no interaction between the exposure and the mediator; therefore, the controlled direct effect estimated is equivalent to the natural direct effect where this assumption holds true. As such, we refer to this as the direct effect, without further distinction, throughout this manuscript.
在 MVMR 中,在控制中介因素的情况下,估计暴露对结果的直接控制效应[19, 23]。主要暴露和第二暴露(中介因子)的遗传工具都作为工具纳入分析(图 1b)[24, 25]。然后,从总效应中减去直接效应(类似于系数差法),即可估算出间接效应。MVMR 假设暴露与中介物之间没有交互作用;因此,估计的受控直接效应等同于这一假设成立时的自然直接效应。因此,我们在本手稿中将其称为直接效应,而不作进一步区分。

Two-step MR (also known as network MR) is akin to the product of coefficient methods. Two MR estimates are calculated i) the causal effect of the exposure on the mediator and ii) the causal effect of the mediator on the outcome (Fig. 1c) [, , ]. These two estimates can then be multiplied together to estimate the indirect effect. Two-step MR also assumes no interaction between the exposure and the mediator.
两步 MR(又称网络 MR)类似于系数乘积法。计算两个 MR 估计值:i) 暴露对中介因子的因果效应;ii) 中介因子对结果的因果效应(图 1c)[21、23、26]。然后将这两个估计值相乘就可以估算出间接效应。两步法 MR 还假定暴露与中介效应之间不存在交互作用。

These MR methods are increasingly being used in mediation analysis [, ]. In this paper, we demonstrate how MVMR, and two-step MR can be used to estimate the direct effect, indirect effect and the proportion mediated, and which assumptions are required for the resulting estimates to be unbiased []. We provide guidance about how to carry out each method, with code provided, and illustrate each method using both simulated and real data (see Online Resource 2), applied to an individual level MR analysis.
这些 MR 方法正越来越多地用于中介分析[19, 27-30]。在本文中,我们演示了如何使用 MVMR 和两步 MR 估算直接效应、间接效应和中介比例,以及估算结果无偏所需的假设条件[23- 25]。我们提供了关于如何执行每种方法的指导,并提供了代码,还使用模拟数据和真实数据(见在线资料 2)对每种方法进行了说明,并将其应用于个体水平的 MR 分析。

Methods 方法

Simulation study 模拟研究

We simulated data under the model illustrated in Fig. 1 with continuous, rare binary (5% prevalence) and common binary (25% prevalence) outcomes. We varied the total effect of our exposure and proportion mediated and obtained results using non-IV regression based mediation methods using both the difference and product of coefficients approaches, and MR methods using both MVMR and two-step MR. Additionally, we simulated results where the total effect of the exposure on the outcome is small, and where each of the exposure and mediator were subject to non-differential measurement error. Finally, we simulated how MR methods can estimate mediation in the presence of multiple mediators, these simulations are illustrated in Online Resource 1: sFig. 2. The full range of scenarios simulated are presented in sTable 1. Simulation analyses were carried out using R version 3.5.1 and the corresponding code for the simulation studies can be found at https://github.com/eleanorsanderson/MediationMR.
我们根据图 1 所示的模型模拟了连续、罕见二元(5% 发生率)和常见二元(25% 发生率)结果的数据。我们改变了暴露的总效应和中介比例,并使用基于非 IV 回归的中介方法(同时使用系数差法和系数乘积法)以及 MR 方法(同时使用 MVMR 和两步 MR)得出了结果。此外,我们还模拟了暴露对结果的总影响较小、暴露和中介均存在非差异性测量误差的结果。最后,我们模拟了 MR 方法如何在存在多个中介因子的情况下估计中介效应,这些模拟结果见在线资料 1:图 2。表 1 列出了所有模拟场景。模拟分析使用 R 3.5.1 版本进行,模拟研究的相应代码见 https://github.com/eleanorsanderson/MediationMR。

Applied example 应用实例

Using data from UK Biobank (N = 184 778), we investigate the role of body mass index (BMI) and low-density lipoprotein cholesterol (LDL-C) in mediating the associations between education and systolic blood pressure, cardiovascular disease (CVD) and hypertension (continuous, rare binary and common binary outcomes, respectively). The effects on binary outcomes (hypertension and incident CVD) were estimated on risk difference, log odds ratio, and odds ratio scales. Applied analyses were performed using Stata version 15 (StataCorp LP, Texas) and corresponding code is available at https://github.com/alicerosecarter/MediationMR. The full worked through example is available in Online Resource 2.
我们利用英国生物样本库(N = 184 778)的数据,研究了体重指数(BMI)和低密度脂蛋白胆固醇(LDL-C)在调解教育程度与收缩压、心血管疾病(CVD)和高血压(分别为连续、罕见二元和常见二元结果)之间关系中的作用。对二元结果(高血压和心血管疾病)的影响按风险差异、对数几率比例和几率比例进行估计。应用分析使用 Stata 15 版本(StataCorp LP,德克萨斯州)进行,相应代码可在 https://github.com/alicerosecarter/MediationMR 上获取。完整的工作示例见在线资料 2。

Statistical analysis 统计分析

The following approaches were applied to both applied analyses and simulated data. Equations describing each of these analyses are given in Online Resource 1.
以下方法适用于应用分析和模拟数据。描述每种分析方法的方程见在线资料 1。

Difference in coefficients method

Each outcome was regressed on the exposure adjusting for the mediator to estimate the direct effect of the exposure. The direct effect was subtracted from the total effect, estimated using multivariable regression, to estimate the indirect effect. In all simulation scenarios the standard deviation of the regression coefficients was calculated across repeats to evaluate precision.

系数差异法 将每个结果与暴露进行回归,并对中介因素进行调整,以估算暴露的直接效应。将直接效应从使用多变量回归估算的总效应中减去,以估算间接效应。在所有模拟方案中,都要计算各次回归系数的标准偏差,以评估精确度。

Product of coefficients method

Two regression models were estimated. Firstly, the mediator was regressed on the exposure. Secondly, the outcome was regressed on the mediator, adjusting for the exposure. These two estimates were multiplied together to estimate the indirect effect.

系数乘积法 估计了两个回归模型。首先,对中介因素进行回归。其次,将结果与中介因素进行回归,并对接触因素进行调整。将这两个估计值相乘,即可估算出间接效应。

Multivariable Mendelian randomisation

Using MVMR to estimate the direct effect, in the first stage regression, the effect of the instrument for the exposure and the polygenic score for the mediator are used to predict each exposure respectively. In the second stage regression, the outcome was regressed on the predicted values of each exposure. The direct effect was then subtracted from the total effect, estimated using two-stage least squares regression, to estimate the indirect effect.

多变量孟德尔随机使用 MVMR 估算直接效应,在第一阶段的回归中,分别使用暴露的工具效应和中介的多基因得分来预测每个暴露。在第二阶段回归中,将结果与每个暴露的预测值进行回归。然后从使用两阶段最小二乘法回归估算的总效应中减去直接效应,以估算间接效应。

Two-step Mendelian randomisation

A univariable MR model was carried out to estimate the effect of the exposure on the mediator. A second model estimating the effect of the mediator on each outcome was carried out using MVMR. Both the genetic variants for the mediator and the exposure were included in the first and second stage regressions in MVMR. Previous approaches in the literature have not used MVMR for this second step [, ] and propose carrying out a univariable MR of the effect of the mediator on the outcome. However, using MVMR ensures any effect of the mediator on the outcome is independent of the exposure. Additionally, this method provides an estimate of the direct effect of the exposure on the outcome. The two regression estimates from the second stage regression are multiplied together to estimate the indirect effect.

两步孟德尔随机法 采用单变量 MR 模型估计暴露对中介效应的影响。使用 MVMR 建立第二个模型,估计中介因子对每种结果的影响。在 MVMR 的第一和第二阶段回归中,中介因子和暴露因子的遗传变异都包括在内。以往文献中的方法没有将 MVMR 用于第二步[21, 23],而是建议对中介因子对结果的影响进行单变量 MR。然而,使用 MVMR 可以确保中介因子对结果的任何影响都与暴露无关。此外,这种方法还能估算暴露因素对结果的直接影响。将第二阶段回归的两个回归估计值相乘,即可估计出间接效应。

Multiple mediators

In non-IV mediation analyses, to estimate the direct effect attributable to multiple mediators, the outcome was regressed on the exposure, controlling for all mediators, using multivariable regression. Here, the coefficient for the exposure reflects the direct effect []. This direct effect was then subtracted from the total effect to estimate the indirect effect. Secondly, the product of coefficients method was used to estimate the indirect effect of each mediator individually. The combined effect of all mediators was then estimated by summing together each individual effect.

多重中介 在非静脉注射中介分析中,为了估算多重中介的直接影响,在控制所有中介的情况下,使用多变量回归法对结果与暴露进行回归。在此,暴露的系数反映了直接效应[31]。然后从总效应中减去直接效应,以估计间接效应。其次,使用系数乘积法估算每个中介因素的间接效应。然后,通过将每个单独效应相加,估算出所有中介效应的综合效应。

In MR analyses, the direct effect attributable to multiple mediators was assessed using MVMR, controlling for all mediators. This direct effect was then subtracted from the total effect to estimate the combined indirect effect. Secondly two-step MR was used, as previously described, considering each mediator individually and summing the effects together to obtain the indirect effect of all mediators combined.
在 MR 分析中,使用 MVMR 评估了可归因于多个中介因素的直接效应,并对所有中介因素进行了控制。然后从总效应中减去这一直接效应,估算出综合间接效应。其次,如前所述,采用两步 MR 法,分别考虑每个中介因子,然后将其效应相加,得出所有中介因子的综合间接效应。

Proportion mediated

The proportion mediated is calculated by dividing the indirect effect by the total effect. In individual-level MR, the confidence intervals can be estimated via bootstrapping.

中介比例 中介比例的计算方法是用间接效应除以总效应。在个体水平的 MR 中,置信区间可通过引导法估算。

Testing the assumptions of mediation analysis

In this analysis, we have simulated a number of scenarios where non-IV regression based methods or MR methods for mediation analysis may provide biased answers. In this section we outline these results and any implications for analyses.
在本分析中,我们模拟了一些情况,在这些情况下,非基于 IV 回归的方法或 MR 方法进行的中介分析可能会提供有偏差的答案。在本节中,我们将概述这些结果以及对分析的影响。

Unmeasured confounding between the exposure, mediator and outcome

Many of the key causal assumptions in non-IV mediation analysis relate to assumptions of no unmeasured confounding between all of the exposure, mediator and outcome, including where confounders of the mediator and outcome are descendants of the exposure (intermediate confounding). Controlling for confounders in multivariable regression analyses often leads to residual confounding because it is generally impossible to measure all confounders, and frequently those that are measured are measured with error.

Indeed, in our simulations where residual covariance was simulated to reflect confounding, both the non-IV difference method and non-IV product of coefficients method were equally biased (Fig. 3 and Online Resource 1: sTables 2). Where no confounding was simulated in the case of no true total effect, estimates from non-IV approaches were free from bias (Online Resource 1: sTable 3). In simulations both with and without residual covariance to reflect confounding, MVMR and two-step MR estimated the direct effect, indirect effect and proportion mediated with no bias (Fig. 2 and Online Resource 1: sTables 4 and 5).
事实上,在模拟残差协方差以反映混杂因素的情况下,非个体差异法和非个体系数乘积法同样存在偏差(图 3 和在线资料 1:表 2)。在没有真实总效应的情况下,模拟没有混杂因素时,非个体差异法的估计值没有偏差(在线资料 1:表 3)。在有和没有反映混杂因素的残差协方差的模拟中,MVMR 和两步 MR 对直接效应、间接效应和中介比例的估计均无偏差(图 2 和在线资料 1:表 4 和表 5)。

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Size of absolute bias for the indirect effect of an exposure on a continuous outcome, rare binary outcome and common binary outcome through a continuous mediator, for a range of fixed true total effect sizes (0.2, 0.5 and 1.0) and range of true indirect effect sizes using non-IV regression based mediation methods or Mendelian randomisation, on the relative scale (simulated N = 5000). In all scenarios, unmeasured confounding is simulated
在一系列固定真实总效应大小(0.2、0.5 和 1.0)和一系列真实间接效应大小范围内,使用基于非 IV 回归的中介方法或孟德尔随机化方法,通过连续中介效应,暴露对连续结果、罕见二元结果和常见二元结果的间接效应的绝对偏差大小(模拟 N = 5000)。在所有情况下,都模拟了未测量的混杂因素

Collider bias can be introduced by adjusting for the mediator in the presence of un- or mis-measured mediator-outcome confounders, where a backdoor path opens up between the exposure and the confounder (Online Resource 1: sFig. 3) [, , ]. Given that MR estimates are unbiased by unmeasured confounding of the exposure-outcome and mediator-outcome relationships [, ], this means that within MR analyses, adjusting for the mediator does not result in collider bias.
在存在未测量或测量误差的介导-结果混杂因素的情况下,对介导因素进行调整可能会引入对撞机偏差,即在暴露和混杂因素之间出现后门路径(在线资料 1:图 3)[ 6, 32, 33]。鉴于 MR 估计值不会受到暴露-结果和中介-结果关系中未测量到的混杂因素的影响[1, 17],这意味着在 MR 分析中,对中介因素进行调整不会导致碰撞偏差。

Analysis of binary outcomes

Mediation analysis of binary outcome is challenging because of the non-collapsibility of odds ratio. This means the association between an exposure and outcome would not be constant on the odds-ratio scale by strata of categorical covariate [, ]. In mediation analysis, including the mediator in the model estimating the direct effect, means the model is no longer comparable with that for the total effect.
二元结果的中介分析具有挑战性,因为几率比是不可比的。这意味着暴露与结果之间的关联在不同的分类协变量的几率范围内并不恒定[34, 35]。在中介分析中,将中介因素纳入估计直接效应的模型中,意味着该模型与总效应模型不再具有可比性。

The mediation literature indicates that to estimate the direct and indirect effects of a binary outcome, the outcome must be rare (less than 10% prevalence), so the odds ratio approximates the risk ratio, and the product of coefficients method should be used []. In the presence of a common binary outcome, estimates from the product of coefficients method and difference method are unlikely to align (and indeed the literature suggests both are likely biased) [].
中介文献表明,要估算二元结果的直接和间接影响,结果必须是罕见的(发生率低于 10%),因此几率近似于风险比,应使用系数乘积法[9]。如果存在常见的二元结果,系数乘积法和差值法的估计值不太可能一致(事实上,文献表明这两种方法都可能存在偏差)[4]。

In our simulations, both the difference in coefficients and the product of coefficients non-IV methods, with common and rare binary outcomes on a linear relative scale were biased as expected by unmeasured confounding (Fig. 3 and Online Resource 1: sTables 6–9). The size of bias was similar across the two non-IV methods. In simulated MR scenarios with common and rare binary outcomes on a linear relative scale, estimated effects were concordant between MVMR and two-step MR, with little to no bias (Fig. 3 and Online Resource 1: sTables 10–13).
在我们的模拟中,非静脉注射法的系数差值和系数乘积,以及线性相对尺度上的常见和罕见二元结果,都由于未测量的混杂因素而出现了预期的偏差(图 3 和在线资料 1:表 6-9)。两种非 IV 方法的偏差大小相似。在以线性相对比例计算常见和罕见二元结果的模拟 MR 情景中,MVMR 和两步 MR 的估计效应一致,几乎没有偏差(图 3 和在线资料 1:表 10-13)。

In the scenarios simulated, there was some bias when analysing binary outcomes on the log odds ratio scale using both MVMR and two-step MR, for both common and rare binary outcomes (Online Resource 1: sTables 14 and 15). This bias was small and typically would not alter conclusions made, although typically the size of absolute bias increased as the size of the true proportion mediated increased. However, the exact bias from non-collapsibility will be unique to each scenario, including depending on the strength of the mediators. Analyses in individual level MR can be conducted on the risk difference scale, which reduces bias due to non-collapsibility.
在模拟的情景中,使用 MVMR 和两步 MR 按对数几率表分析二元结果时,对于常见和罕见的二元结果都存在一些偏差(在线资料 1:表 14 和表 15)。这种偏差较小,通常不会改变所得出的结论,不过随着真实中介比例的增加,绝对偏差的大小通常也会增加。不过,非可比性带来的确切偏差在每种情况下都是独一无二的,包括取决于介导因素的强度。个体水平的 MR 分析可以按照风险差异尺度进行,这样可以减少非可比性带来的偏差。

In simulation scenarios explored, neither MVMR nor two-step MR were able to estimate the mediated effects without bias when using the odds ratio scale (Online Resource 1: sTables 16 and 17).
在所探讨的模拟方案中,无论是 MVMR 还是两步 MR,在使用几率比标度时都无法无偏差地估计中介效应(在线资料 1:表 16 和表 17)。

Measurement error in the exposure or mediator

Our results show that in non-IV approaches, with a continuous exposure and mediator, non-differential measurement error in the mediator leads to an underestimate of the mediated effect. This is consistent with previous methodological and applied work []. Where non-differential measurement error was simulated in the exposure, the mediated effect was over estimated (Online Resource 1: sTable 18).
我们的研究结果表明,在连续暴露和中介效应的非 IV 方法中,中介效应的非差异性测量误差会导致中介效应的低估。这与之前的方法学和应用研究一致[8]。如果模拟暴露中的非差异性测量误差,则会高估中介效应(在线资料 1:表 18)。

In MR simulations, both MVMR and two-step MR estimated the mediated effects with little bias when non-differential measurement error was simulated either in the exposure or the mediator (Online Resource 1: sTable 19). This is consistent with the previous literature demonstrating that MR estimates are less prone to bias by measurement error than conventional non-IV analyses [, ].
在MR模拟中,当模拟暴露或中介的非差异性测量误差时,MVMR和两步MR估计的中介效应几乎没有偏差(在线资料1:表19)。这与之前的文献一致,表明与传统的非 IV 分析相比,MR 估计值不易受测量误差的影响[1, 17]。

Weak instrument bias 弱仪器偏差

In order to obtain valid causal inference for mediation, all standard MR assumptions must be met. This includes having strong instruments, typically determined through an F-statistic or conditional F-statistic of greater than 10. The conditional instrument strength in multivariable MR can be tested using the Sanderson-Windmeijer F-statistic []. When the instruments in the simulation were weakly associated with the exposure, both MVMR and two-step MR estimates of the indirect effect and proportion mediated were biased. The size of bias was greatest for a common binary outcome. When weak instruments were simulated for the mediator, estimates of the indirect effect and proportion mediated from both MVMR and two-step MR were biased (Online Resource 1: sFig. 4 and sTable 19). Bias due to weak instruments have been discussed extensively in the literature [], and methods are now available for testing for weak instrument bias in MVMR [].
为了获得有效的中介因果推断,必须满足所有标准的 MR 假设。这包括要有强有力的工具,通常通过大于 10 的 F 统计量或条件 F 统计量来确定。多变量 MR 中的条件工具强度可以使用 Sanderson-Windmeijer F 统计量进行检验[ 36]。当模拟中的工具与暴露呈弱相关时,MVMR 和两步 MR 对间接效应和中介比例的估计都有偏差。对于常见的二元结果,偏差最大。当模拟的中介因子为弱中介因子时,MVMR 和两步 MR 对间接效应和中介比例的估计值都存在偏差(在线资料 1:图 4 和表 19)。文献中对弱工具导致的偏差进行了广泛讨论[37-39],目前已有方法可用于检测 MVMR 中的弱工具偏差[40]。

Pleiotropy 多型性

One of the core MR assumptions is that the genetic variants used as instruments do not affect the outcome other than via the exposure of interest, known as pleiotropy. Bias can be introduced to MR mediation analyses if any of the associations between the exposure and outcome, exposure and mediator or mediator and outcome are pleiotropic. In simulations with pleiotropy in the association between the exposure and outcome, estimates of the total effect and direct effect are biased (Online resource 1: sTable 20). In this scenario, no pleiotropy is present for the association between the exposure and mediator or mediator and outcome, therefore no bias is present for the indirect (mediated) effect. In simulations with pleiotropy in the association between the mediator and the outcome estimates of the direct effect and indirect effect are biased (Online resource 1: sTable 21).
MR 的核心假设之一是,作为工具的基因变异除通过相关暴露影响结果外,不会影响其他结果,这被称为多向性。如果暴露与结果、暴露与介导因素或介导因素与结果之间的任何关联是多向性的,那么 MR 中介分析就会出现偏差。在暴露与结果之间存在多向关联的模拟中,总效应和直接效应的估计值会出现偏差(在线资料 1:表 20)。在这种情况下,暴露因子与中介因子或中介因子与结果之间的关联不存在多向性,因此间接(中介)效应不存在偏差。在中介效应与结果之间的关联存在多向性的模拟中,直接效应和间接效应的估计值会出现偏差(在线资源 1:sTable 21)。

Bias due to pleiotropy has been discussed extensively in the literature [, ]. Methods are available for testing for and assessing for pleiotropy, including in MVMR [, ]. Indeed, MVMR was developed as a method to account for pleiotropic variants [, , ].
文献中对多义性造成的偏差进行了广泛讨论[ 41, 42]。有一些方法可用于检测和评估多效性,包括 MVMR [ 40, 43- 45]。事实上,MVMR 是作为一种考虑多效变异的方法而开发的[24, 25, 46]。

Small total effects 总效应小

In simulation studies with no true total effect the MR estimate of the proportion mediated is implausible (Online Resource 1: sTable 4). Where there is no evidence of a total effect, consideration should be given as to whether it is appropriate to continue with mediation analyses. Although an indirect effect can be estimated in the absence of a significant total effect, or absence of total effect when the indirect effect and direct effect act in opposing directions and cancel each other out, these estimates are prone to inflated type 1 errors (i.e. false positive results) [].
在没有真正总效应的模拟研究中,中介比例的 MR 估计值是不可信的(在线资料 1:表 4)。如果没有证据表明存在总效应,则应考虑继续进行中介分析是否合适。虽然在总效应不显著的情况下,或在间接效应和直接效应作用方向相反并相互抵消的情况下,可以估算出间接效应,但这些估算很容易出现夸大的 1 型误差(即假阳性结果)[47]。

Where the total effect is weak or estimated imprecisely, simulations show the indirect effect and the proportion mediated using MR can be estimated but have large standard deviations (Online Resource 1: sTables 22–25). In this case, results should be interpreted with caution, especially considering the bounds of error.
在总效应较弱或估算不精确的情况下,模拟结果表明,间接效应和使用 MR 调解的比例可以估算,但标准偏差较大(在线资料 1:表 22-25)。在这种情况下,应谨慎解释结果,特别是考虑到误差范围。

Interactions between the exposure and mediator

In simulation scenarios with an interaction between the exposure and mediator present, the estimate of the direct effect of the exposure from both the difference in coefficients method and MVMR method was biased. In our simulations, as the size of the interaction increased, the size of both the absolute and relative bias of the direct effect increased (Online Resource 1: sTable 26). The size of the bias was typically larger in the non-IV analyses compared with MR analyses.
在暴露因子与中介因子之间存在交互作用的模拟情景中,系数差法和 MVMR 法对暴露因子直接效应的估计都存在偏差。在我们的模拟中,随着交互作用大小的增加,直接效应的绝对偏差和相对偏差也随之增加(在线资料 1:表 26)。与 MR 分析相比,非 IV 分析的偏差通常更大。

Analysis of multiple mediators

The direct effect of an exposure controlling for multiple mediators in a single model can be assessed using MVMR. Where all MR specific assumptions are satisfied, the direct effect of multiple mediators is estimated with no evidence of bias (Online Resource 1: sTable 27). Here, non-overlapping SNPs for all exposures and mediators are included in one set of instruments. The estimated direct effect attributable to multiple mediators is unbiased, even when one mediator causes another mediator, which in our simulations was demonstrated by M2 causing M3 (Online Resource 1: sFig. 2).
在单个模型中控制多个中介因子的暴露的直接效应可通过 MVMR 进行评估。在满足所有 MR 特定假设的情况下,估算多个中介因子的直接效应时不会出现偏差(在线资料 1:表 27)。在这里,所有暴露因子和中介因子的非重叠 SNPs 都包含在一组工具中。即使一个中介因子会导致另一个中介因子,我们的模拟也证明了这一点(在线资料 1:图 2)。

Where the mediators do not cause each other, estimates of the indirect effects and proportion mediated from both MVMR (mutually adjusting for all mediators) and two-step MR (considering each mediator individually and summing together) will coincide (Online Resource 1: sTable 27). In our simulations, both MR methods estimated the indirect effect of each mediator, and the three mediators jointly, with no bias (Online Resource 1: sTable 27). This is consistent with the existing literature on analyses with multiple mediators [].
在中介因子互不影响的情况下,MVMR(对所有中介因子进行相互调整)和两步 MR(单 独考虑每个中介因子并将其相加)对间接效应和中介比例的估计值是一致的(在线资料 1:表 27)。在我们的模拟中,两种 MR 方法都能估算出每个中介因子以及三个中介因子的间接效应,且没有偏差(在线资料 1:表 27)。这与现有文献对多个中介因素的分析结果一致[31]。

Where one mediator causes another mediator, the indirect effect estimated via two-step MR captures both the amount of the association explained by the mediator of interest, and the amount of the mediator-outcome association captured by related mediators. In our example, this means that the effect of M3 is estimated twice, once directly and once via M2. As such, the estimate for the proportion mediated summing all three mediators together will likely be an overestimate of the combined proportion mediated, but the estimated direct effects remain unbiased. In our simulations, the combined proportion mediated was over-estimated by 6% (Online Resource 1: sTable 27), which is equivalent to the proportion explained by M3 via M2. The indirect effect of M2 estimated using two-step MR is however unbiased and reflects both the direct effect of M2 on the outcome and the indirect effect via M3 (Online Resource 1: sFig. 2).
当一个中介因子引起另一个中介因子时,通过两步 MR 估算的间接效应既能反映相关中介因子所解释的关联程度,也能反映相关中介因子所反映的中介因子-结果关联程度。在我们的例子中,这意味着 M3 的效应要估算两次,一次是直接估算,一次是通过 M2 估算。因此,将所有三个中介因子相加得出的中介比例估计值很可能会高估综合中介比例,但直接效应估计值仍然是无偏的。在我们的模拟中,综合中介比例被高估了 6%(在线资料 1:表 27),这相当于 M3 通过 M2 所解释的比例。然而,使用两步 MR 估算的 M2 间接效应是无偏的,既反映了 M2 对结果的直接效应,也反映了通过 M3 产生的间接效应(在线资料 1:图 2)。

Limitations of Mendelian randomisation applied to mediation analysis

Instrument selection 仪器选择

When using MR for mediation, SNPs included in the instruments for the exposure and mediator should be independent. Contrastingly, when MVMR is being used to test for potential pleiotropic pathways, SNPs associated with the two exposures under consideration can be included [, , ]. This is not the case when MVMR is being used to test for mediation. Should non-independent SNPs be included as instruments it would not be possible to distinguish whether an attenuation in the direct effect, compared with the total effect, was due to mediation or pleiotropy.
在使用MR进行中介研究时,暴露和中介的工具中包含的SNP应该是独立的。与此相反,当 MVMR 用于检验潜在的多效应途径时,可以包括与所考虑的两种暴露相关的 SNP [ 24, 25, 48]。当 MVMR 用于检验中介作用时,情况就不是这样了。如果将非独立的 SNPs 作为工具包括在内,就无法区分与总效应相比,直接效应的衰减是由于中介作用还是多重效应。

In a two-step MR mediation analysis, the mediator is considered as both an exposure (of the outcome) and as an outcome (of the exposure) and therefore any instruments for the exposure that are also instruments for the mediator are pleiotropic in the estimation of the effects of the exposure on the mediator and should be excluded. Where there are no independent SNPs, or the SNPs had a perfectly proportional effect on both the exposure and the mediator, then it would not be possible to use MR methods to estimate mediation.
在两步 MR 中介分析中,中介因子既被视为(结果的)暴露因子,也被视为(暴露因子的)结果,因此,在估计暴露因子对中介因子的影响时,任何暴露因子的工具同时也是中介因子的工具都是多效性的,应排除在外。如果没有独立的 SNPs,或者 SNPs 对暴露因子和中介因子的影响完全成比例,那么就不可能使用 MR 方法来估计中介效应。

The exclusion restriction criteria assuming no pleiotropic pathway is an important assumption of standard univariable MR, which applies equally when MR is used for mediation analysis. Some methods are available to assess pleiotropy including for the use of MVMR [].
假设无多向性途径的排除限制标准是标准单变量 MR 的一个重要假设,在 MR 用于中介分析时同样适用。有一些方法可用于评估多效性,包括使用 MVMR [ 43-45]。

Binary exposures and/or mediators

Very few binary exposures will be truly binary and are likely a dichotomization of an underlying liability, changing the interpretation of an MR analysis []. For example, smoking is often defined as ever versus never smokers, when the underlying exposure is a latent continuous variable reflecting smoking heaviness and duration. As a result, the exclusion restriction criteria are violated, where the genetic variant can influence the outcome via the latent continuous exposure, even if the binary exposure does not change []. In a mediation setting, the same would apply to a binary mediator. In these scenarios, two-step MR could be used to test whether there is evidence of a causal pathway between the binary exposure and/or mediator. However, the estimates of mediation would likely be biased.
极少数二元暴露是真正的二元暴露,很可能是潜在责任的二分法,从而改变了磁共振分析的解释[49]。例如,吸烟通常被定义为 "曾经吸烟 "和 "从不吸烟",而潜在的暴露是一个反映吸烟量和持续时间的潜在连续变量。因此,就违反了排除限制标准,即使二元暴露不发生变化,遗传变异也会通过潜在的连续暴露影响结果[49]。在中介设置中,这同样适用于二元中介。在这些情况下,可以使用两步 MR 来检验是否有证据表明二元暴露和/或中介因子之间存在因果关系。但是,对中介作用的估计可能会有偏差。

Interactions between the exposure and mediators

Within non-IV methods based on counterfactual assumptions, exposure-mediator interactions can be accommodated when estimating mediation parameters. This is not possible in the non-IV mediation methods assessed here (difference in coefficients and product of coefficients) or in the MR methods, MVMR or two-step MR.
在以反事实假设为基础的非IV 方法中,在估算中介参数时可以考虑暴露-中介相互作用。本文所评估的非个体因素中介方法(系数差和系数乘积)或 MR 方法(MVMR 或两步 MR)都无法做到这一点。

Methods are available for estimating interactions in an MR framework with individual level data, but these do not currently extend to estimating mediation in the presence of exposure-mediator interactions [, , ]. Estimates of mediation from MR mediation methods will be assuming effect homogeneity of both the exposure on the mediator and outcome, and mediator on the outcome. This means that the effect of either the exposure or the mediator on the outcome is not modified by the genetic instrument []. For estimates of the direct effect and indirect effect from two-step MR to be unbiased, the homogeneity assumption must be satisfied between the exposure-mediator association and mediator-outcome association and there should be no interaction between the exposure and mediator [, ]. Similarly, where MVMR is used, the effects between the exposure, mediator and outcome should all be homogenous []. Where the homogeneity assumption cannot be satisfied, the causal estimates from MR analyses will provide a valid test of the causal null hypothesis, but not the local average treatment effect [, ]. Developing MR methods which can account for these interactions will be important areas of future research.
在 MR 框架下,可以用个体水平数据估算交互作用,但这些方法目前还不能用于估算暴露-中介交互作用的中介作用[13, 50, 51]。MR中介方法对中介的估计将假定暴露对中介和结果的影响以及中介对结果的影响都是同质的。这意味着遗传工具不会改变暴露因子或中介因子对结果的影响[52]。要使两步 MR 对直接效应和间接效应的估计无偏,必须满足暴露-中介相关性和中介-结果相关性之间的同质性假设,并且暴露和中介之间不存在交互作用[23, 53]。同样,在使用 MVMR 的情况下,暴露因子、中介因子和结果之间的效应都应该是同质的[45]。如果同质性假设无法满足,则磁共振分析的因果估计值将提供因果零假设的有效检验,但不能提供局部平均治疗效果[45, 54]。开发能够考虑这些相互作用的 MR 方法将是未来研究的重要领域。

Non-linear effects of an exposure or mediator

A further limitation of MR methods are where the effects of the exposure or mediator are non-linear. Although some methods are emerging for carrying out MR analysis with non-linear exposures [, ], these methods have not yet been extended to MR mediation analyses. Current MR methods for mediation analysis will assume a linear association between the exposure and outcome. As above, where the linearity assumption cannot be satisfied, the causal estimates would be a valid test of the causal null hypothesis, but not the local average causal effect. Where non-linear effects are of interest in a mediation model, non-IV methods should be considered.
磁共振方法的另一个局限是暴露或中介效应是非线性的。虽然目前出现了一些对非线性暴露进行磁共振分析的方法[55, 56],但这些方法尚未扩展到磁共振中介分析。目前用于中介分析的 MR 方法会假设暴露与结果之间存在线性关系。如上所述,当线性假设无法满足时,因果估计值将是对因果零假设的有效检验,而不是局部平均因果效应。如果在中介模型中需要考虑非线性效应,则应考虑非 IV 方法。

Time varying exposures or mediators

In non-IV mediation analyses, the effects of exposures and mediators throughout the life course can be investigated by analysing prospective longitudinal data. In a simple model, the exposure, mediator and outcome should all be measured at separate, sequential, time points. This approach is preferred even when time varying effects are not a focus of the analysis, as cross-sectional data does not reflect the implied temporality suggested by mediation analysis []. In a more complex model, the longitudinal time varying relationships between exposures and mediators can be modelled using structural equation models []. However, all of these approaches assume the direction of the effect between the exposure, mediator and outcome has been correctly specified, and is not due to reverse causality. Where this is incorrectly specified, or there are bidirectional relationships over time, estimates of the mediated effects can be biased. Additionally, where prospective data are used, the length of the interval between the exposure and mediator measurement is typically not accounted for []. Therefore, these analyses assume all variables have been measured at the critical time point and interval lengths for the associations between the exposure, mediator and outcome to exist. Here, the indirect effect estimated will be dependent upon the timing of these three measurements.
在非 IV 中介分析中,可以通过分析前瞻性纵向数据来研究暴露和中介因素在整个生命过程中的影响。在一个简单的模型中,暴露因子、中介因子和结果都应在不同的、连续的时间点进行测量。即使时间变化效应不是分析的重点,这种方法也是首选,因为横截面数据不能反映中介分析所暗示的时间性[57-59]。在更复杂的模型中,可以使用结构方程模型来模拟暴露和中介因素之间的纵向时变关系[60]。然而,所有这些方法都假定暴露、中介和结果之间的效应方向是正确的,而不是由于反向因果关系造成的。如果指定的方向不正确,或者随着时间的推移存在双向关系,那么中介效应的估计值就会出现偏差。此外,在使用前瞻性数据时,通常不会考虑暴露与中介测量之间的时间间隔[61]。因此,这些分析假定所有变量都已在关键时间点和时间间隔长度上进行了测量,暴露、中介效应和结果之间的关联才会存在。在此,估计的间接效应将取决于这三个测量的时间。

Mediation estimates from MR represent lifetime effects of the exposure and mediator measured at a single point in time []. As with non-IV approaches for this model to be valid, the assumptions must be made that the temporal relationship between the exposure and mediator has been correctly specified, that these relationships do not change throughout the life course and that the exposure and mediator have been measured at the relevant time points. However, as the genetic variants used as IVs for the exposure and mediator used in MR represent lifetime effects cross-sectional data collection can be applied here. Where time varying effects are not accounted for, the direct effect from an MR mediation analysis can be thought of as the effects of a one unit change in the lifetime exposure, not explained by a change in the mediators.
MR 估算的中介效应代表了暴露和中介效应在单个时间点测量的终生效应[23]。与非 IV 方法一样,要使这一模型有效,必须假定暴露和介导因素之间的时间关系已被正确指定,这些关系在整个生命过程中不会改变,并且暴露和介导因素已在相关时间点进行了测量。不过,由于 MR 中用作暴露和介导因子 IV 的遗传变异代表终生效应,因此可以采用横断面数据收集方法。在不考虑时变效应的情况下,可将 MR 中介分析的直接效应视为终生暴露中一个单位的变化所产生的效应,而中介因素的变化并不能解释这种效应。

Using simulations, Labrecque and Swanson have explored bias in MVMR and two-step MR due to time varying effects of exposures and mediators []. Where there are bidirectional relationships between an exposure and mediator at different timepoints, estimates of the total, direct and indirect effects can be biased. One key advantage to using MR is that evidence of reverse causality or causal bidirectional associations between the measured exposure, mediator and outcome can be tested. Where instruments are available for the effect of an exposure at different timepoints, the potential time-varying bidirectional relationships can be explored []. In some unique cases instruments may be available for an exposure at different time points (e.g., childhood and adulthood BMI), allowing for a longitudinal approach to MR mediation analysis to be carried out. However, using these instruments come with additional methodological challenges [].
Labrecque 和 Swanson 通过模拟,探讨了由于暴露和中介效应的时间变化而导致的 MVMR 和两步 MR 的偏差[62]。当暴露因子和中介因子在不同时间点存在双向关系时,对总效应、直接效应和间接效应的估计可能会出现偏差。使用 MR 的一个主要优点是,可以检验测量暴露、中介因子和结果之间的反向因果关系或因果双向关系的证据。如果在不同的时间点都有测量暴露效应的工具,就可以探索潜在的时变双向关系[63]。在某些特殊情况下,可能会有不同时间点的暴露工具(如儿童期和成年期的体重指数),从而可以采用纵向方法进行 MR 中介分析。然而,使用这些工具会带来额外的方法学挑战[ 63]。

As GWAS methods develop and sample sizes increase, the potential opportunities for incorporating time varying effects into MR analyses will likely increase. Future methods developments should focus on methods to incorporate instruments reflecting changes in the exposure and mediator across the life course. Additionally, further research should consider the meaning and interpretation of these lifetime effects, or indeed time varying effects, in the context of the direct and indirect effect.
随着 GWAS 方法的发展和样本量的增加,将时间变化效应纳入 MR 分析的潜在机会可能会增加。未来的方法开发应侧重于纳入反映暴露和中介因子在整个生命过程中变化的工具的方法。此外,进一步的研究应在直接效应和间接效应的背景下考虑这些终生效应或时变效应的意义和解释。

Power 电源

MR studies require very large sample sizes to achieve adequate statistical power. Conditional F-statistics in MVMR are typically weaker than standard F-statistics, and indeed are likely to become weaker with each additional mediator included, further decreasing the power of complex analyses. Therefore, to achieve adequate statistical power, or precision, sample sizes for mediation analysis likely need to be even larger than those needed in a univariable MR analyses.
MR 研究需要非常大的样本量才能获得足够的统计量。MVMR 中的条件 F 统计量通常弱于标准 F 统计量,而且每增加一个中介因子,条件 F 统计量就会变弱,从而进一步降低复杂分析的统计量。因此,要达到足够的统计能力或精确度,中介分析的样本量可能需要比单变量 MR 分析所需的样本量更大。

In the absence of formal power calculators for complex MR scenarios, the power of these analyses can be considered by evaluating the precision of the confidence intervals for all of the total, direct and indirect effects, as well as assessing the conditional instrument strength.
在没有针对复杂 MR 情景的正式功率计算器的情况下,可以通过评估所有总效应、直接效应和间接效应的置信区间精度以及评估条件工具强度来考虑这些分析的功率。

Genetic confounding 遗传干扰

Although assumptions about unmeasured confounding in MR can be relaxed compared with traditional non-IV analyses, confounding can be introduced through population stratification, assortative mating, and dynastic effects []. Here, the confounding is not between the exposure, the mediator and the outcome, but between the genetic instruments for the exposure (or mediator) and the outcome. Adjusting for genetic principal components and other explanatory variables that capture population structure or within family analyses can minimise bias [].
虽然与传统的非遗传分析相比,MR 中关于未测量混杂因素的假设可以放宽,但混杂因素可能会通过人群分层、同卵异形交配和世代效应引入[64]。这里的混杂不是暴露、中介和结果之间的混杂,而是暴露(或中介)的遗传工具和结果之间的混杂。调整遗传主成分和其他能反映人群结构或家族内分析的解释变量可以最大限度地减少偏差[64]。

Mediation analysis with summary sample Mendelian randomisation

Methods applied in this paper can be used with summary data MR. Similar considerations will apply for both individual level MR, as presented here, and summary data MR. Importantly, all sources of summary statistics for the exposure, mediator and outcome should be non-overlapping []. As the mediator is considered an outcome in the exposure-mediator model, sample overlap can introduce bias []. As individual level data is not available in summary data MR, bootstrapping cannot be used to estimate the confidence intervals for the indirect effect or proportion mediated, but the delta method can be used to approximate these confidence intervals if samples are independent []. Analyses will also be restricted to the scale reported by the GWAS used, so consideration will need to be given for binary outcomes where sensitivity analyses to test potential non-collapsibility are limited.
本文中应用的方法可用于汇总数据磁共振。类似的考虑因素也适用于本文提出的个体水平 MR 和汇总数据 MR。重要的是,所有来源的暴露、中介和结果的汇总统计数据都不应重叠[65]。由于在暴露-中介模型中中介因子被视为结果,样本重叠会带来偏差[65]。由于汇总数据 MR 中没有个体水平的数据,因此无法使用引导法估算间接效应或中介比例的置信区间,但如果样本是独立的,则可以使用 delta 法来近似估算这些置信区间[30]。分析也将受限于所使用的 GWAS 报告的规模,因此需要考虑二元结果,在这种情况下,测试潜在非共轭性的敏感性分析是有限的。

Which method and when 哪种方法和何时

Although MR is not biased by many of the untestable causal assumptions in non-IV mediation methods, such as unmeasured confounding, there are instead a set of MR specific causal assumptions (Fig. 2), and careful consideration should be given to which assumptions are most plausible. Additionally, the data available, or research question of interest may not be suitable to test in an MR framework. For example, if the research question is interested in exposures and mediators with time varying effects, or where interactions are present between the exposure and mediator.
虽然 MR 不会受到非IV 中介方法中许多无法检验的因果假设(如无法测量的混杂因素)的影响,但还是有一系列 MR 特定的因果假设(图 2),因此应仔细考虑哪些假设是最合理的。此外,现有数据或感兴趣的研究问题可能不适合在 MR 框架内进行检验。例如,如果研究问题关注的是具有时间变化效应的暴露因子和中介因子,或者暴露因子和中介因子之间存在相互作用。

MR has specific advantages compared with non-IV mediation methods where causal assumptions are required. The causal effect of the exposure on the outcome, the exposure on the mediator and the mediator on the outcome can all be tested. Additionally, bi-directional MR could be used to determine which of two variables is the causal exposure and causal mediator, where this is not known.

Our results demonstrate that both MVMR (akin to the difference in coefficients method) and two-step MR (akin to the product of coefficients method) can estimate the mediating effects for both continuous and binary outcomes, with little evidence of bias. However, caution is required in some instances, for example where total effects are weak. Where all exposures, mediators and outcomes are continuous, MVMR may confer an advantage of power, where the standard deviations for the simulated effects estimated in MVMR were smaller compared with the same effects estimated using two-step MR.
我们的结果表明,MVMR(类似于系数差法)和两步 MR(类似于系数乘积法)都可以估计连续结果和二元结果的中介效应,而且几乎没有偏差的迹象。但是,在某些情况下,例如总效应较弱的情况下,需要谨慎。在所有暴露、中介和结果都是连续的情况下,MVMR 可能具有功率优势,因为 MVMR 估算的模拟效应的标准偏差小于使用两步 MR 估算的相同效应。

If an analysis is interested in estimating the effects of multiple mediators, consideration should be given to the causal question of interest when deciding which method to use to analyse multiple mediators. Where the causal question specifically relates to identifying the combined effects of multiple mediators, MVMR is likely to be the most appropriate method. Where the causal question aims to estimate the effect of multiple mediators individually, and potentially any impact of intervening on a mediator, two-step MR may be most appropriate. However, it is important to note, that as the number of mediators included in an MVMR model increases, the power of the analysis would likely decrease. Additionally, future research should be carried out to determine if including increasing numbers of exposures in an MVMR model further violates any of the MR assumptions.
如果一项分析有兴趣估计多重中介效应,那么在决定使用哪种方法分析多重中介效应时,应 考虑到所关注的因果问题。如果因果问题具体涉及确定多个中介因素的综合效应,那么 MVMR 可能是最合适的方法。如果因果问题旨在估算多个中介因素的单独效应,以及对中介因素进行干预可能产生的任何影响,那么两步式多变量模型可能最合适。不过,需要注意的是,随着 MVMR 模型中中介因子数量的增加,分析的有效性可能会降低。此外,今后还应该开展研究,以确定在 MVMR 模型中包含越来越多的暴露因素是否会进一步违反 MR 假设。

Although we have included a range of simulation scenarios, including both continuous and binary outcomes, this is not an exhaustive range of scenarios and there may be further scenarios where MR methods are biased.
尽管我们包含了一系列模拟情景,其中既有连续结果,也有二元结果,但这并不是一个详尽无遗的情景范围,可能还有更多的情景会导致 MR 方法出现偏差。

The flow chart in Fig. 4 aims to help with the decision-making process, based on practical limitations of MR. However, best practice would always be to triangulate across non-IV and MR approaches, and across multiple data sources wherever possible [].
图 4 中的流程图旨在根据 MR 的实际局限性帮助决策过程。不过,最佳做法始终是在非静脉注射和 MR 方法之间进行三角测量,并尽可能在多个数据源之间进行三角测量[66]。

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Flow chart for analytical processes when carrying out mediation analyses using individual level Mendelian randomisation

Conclusions 结论

MR can be extended to estimate direct effects, indirect effects and proportions mediated. MR estimates are not biased by violations of the often-untestable assumptions of non-IV mediation analysis, including unmeasured confounding and measurement error. MR analysis makes its own strong, but distinct assumptions, especially relating to instrument validity. To estimate mediation using MR, we require large sample sizes and strong instruments.
MR 可以扩展到估算直接效应、间接效应和中介比例。MR 估计值不会因违反非 IV 中介分析通常难以检验的假设(包括未测量的混杂因素和测量误差)而产生偏差。MR 分析有其自身强大但独特的假设,尤其是与工具有效性相关的假设。要使用 MR 估算中介效应,我们需要大样本量和强有力的工具。

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 48532 kb)(47M, docx)
补充文件1 (DOCX 48532 kb) (47M, docx)
Supplementary file2 (DOCX 182 kb)(183K, docx)
补充文件2 (DOCX 182 kb) (183K, docx)

Acknowledgements 致谢

We thank Kate Tilling for reading and commenting on an earlier draft of this manuscript.
感谢凯特-蒂林(Kate Tilling)对本手稿初稿的阅读和评论。

Author contributions 作者供稿

ARC devised the project, analysed and cleaned the data, interpreted results, wrote and revised the manuscript. ES devised the project, generated and analysed simulated data, interpreted results and critically revised the manuscript. GH, RCR, GDS, KT, JH AET, NMD and LDH devised the project, interpreted the results, and critically revised the manuscript. All authors had full access to the data in the study and can take responsibility for the integrity of the data and the accuracy of the data analysis. ARC and LDH are the guarantors. The corresponding author attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted. Quality Control filtering of the UK Biobank data was conducted by R.Mitchell, G.Hemani, T.Dudding, L.Paternoster as described in the published protocol (https://doi.org/10.5523/bris.3074krb6t2frj29yh2b03x3wxj ).

Funding 资金筹措

No funding body has influenced data collection, analysis or its interpretations. This research was conducted using the UK Biobank Resource using application 10953. ARC is funded by the UK Medical Research Council Integrative Epidemiology Unit, University of Bristol (MC_UU_00011/1). All authors work in a unit that receives core funding from the UK Medical Research Council and University of Bristol (MC_UU_00011/1, MC_UU_00011/2, MC_UU_00011/3, MC_UU_00011/7). The Economics and Social Research Council support NMD via a Future Research Leaders grant (ES/N000757/1) and a Norwegian Research Council Grant number 295989. AET and GDS are supported by the National Institute for Health Research (NIHR) Biomedical Research Centre based at University Hospitals Bristol NHS Foundation and the University of Bristol. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR, or the Department of Health. RCR is a de Pass Vice Chancellor’s Research Fellow at the University of Bristol. GH is supported by a Sir Henry Wellcome Postdoctoral Fellowship (209138/Z/17/Z). LDH is funded by a Career Development Award from the UK Medical Research Council (MR/M020894/1). This research has been conducted using the UK Biobank Resource under Application Number 10953.
任何资助机构均未对数据收集、分析或解释施加影响。本研究使用英国生物库资源(UK Biobank Resource),申请号为 10953。ARC 由英国医学研究委员会综合流行病学组、布里斯托尔大学(MC_UU_00011/1)资助。所有作者所在单位均接受英国医学研究委员会和布里斯托尔大学的核心资助(MC_UU_00011/1、MC_UU_00011/2、MC_UU_00011/3、MC_UU_00011/7)。经济与社会研究理事会通过未来研究领袖基金(ES/N000757/1)和挪威研究理事会基金(编号 295989)为 NMD 提供支持。AET和GDS由位于布里斯托尔大学医院NHS基金会和布里斯托尔大学的国家健康研究所(NIHR)生物医学研究中心提供支持。文中观点仅代表作者本人,与国家医疗服务系统、国家健康研究院或卫生部无关。RCR 是布里斯托尔大学 de Pass 副校长研究员。GH 由亨利-惠康爵士博士后奖学金(209138/Z/17/Z)资助。LDH 由英国医学研究委员会的职业发展奖(MR/M020894/1)资助。本研究使用英国生物库资源进行,申请号为 10953。

Data and code availability

All code for simulation analyses, applied analyses and example code is available on GitHub (simulations: https://github.com/eleanorsanderson/MediationMR, applied analyses and example code: https://github.com/alicerosecarter/MediationMR). The cleaned dataset for UK Biobank analyses will be archived with UK Biobank. Please contact access@ukbiobank.ac.uk for further information.
模拟分析、应用分析和示例代码的所有代码均可在 GitHub 上获取(模拟:https://github.com/eleanorsanderson/MediationMR,应用分析和示例代码:https://github.com/alicerosecarter/MediationMR)。用于英国生物库分析的净化数据集将与英国生物库一起存档。详情请联系 access@ukbiobank.ac.uk。

Declarations 声明

Conflict of interest 利益冲突

The author declare that they have no conflict of interest.

Ethical approval 伦理批准

This project was approved by UK Biobank under the study application 10953. No specific ethical approval or patient involvement was sought for this project.
本项目已获得英国生物库批准,研究申请号为 10953。本项目未获得专门的伦理批准,也未要求患者参与。

Footnotes 脚注

Publisher's Note 出版商说明

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References 参考资料

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