Mendelian randomisation for mediation analysis: current methods and challenges for implementation
用于中介分析的孟德尔随机化：当前方法和实施挑战

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 [2, 3]. More recently, a large amount of research has built on and improved mediation methods for better causal inference [4].
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 [5] (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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Fig. 1 图 1

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 [4, 6, 7]. Furthermore, measurement error in either the exposure or mediator can introduce bias [8].
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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Fig. 2 图 2

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 [4, 9].
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 [10–14]. 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 [4, 15]. 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 [4, 9, 16].
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 [1, 17, 18]. 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 [17]. 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) [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。

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。

Unmeasured confounding between the exposure, mediator and outcome
暴露因子、中介因子和结果之间未测量的混杂因素

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.
非独立中介分析中的许多关键因果假设都与所有暴露、中介和结果之间没有未测量混杂的假设有关，包括中介和结果的混杂因素是暴露的后代（中间混杂）。在多变量回归分析中控制混杂因素往往会导致残余混杂，因为通常不可能测量所有的混杂因素，而且测量到的混杂因素往往存在误差。

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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Fig. 3 图 3

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) [6, 32, 33]. Given that MR estimates are unbiased by unmeasured confounding of the exposure-outcome and mediator-outcome relationships [1, 17], 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
二元结果分析

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 [34, 35]. 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 [9]. 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) [4].
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
暴露因子或中介因子的测量误差

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 [8]. 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 [1, 17].
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 [36]. 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 [37–39], and methods are now available for testing for weak instrument bias in MVMR [40].
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 [41, 42]. Methods are available for testing for and assessing for pleiotropy, including in MVMR [40, 43–45]. Indeed, MVMR was developed as a method to account for pleiotropic variants [24, 25, 46].
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) [47].
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。

Binary exposures and/or mediators
二元暴露和/或媒介

Very few binary exposures will be truly binary and are likely a dichotomization of an underlying liability, changing the interpretation of an MR analysis [49]. 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 [49]. 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
暴露与介质之间的相互作用

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 [13, 50, 51]. 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 [52]. 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 [23, 53]. Similarly, where MVMR is used, the effects between the exposure, mediator and outcome should all be homogenous [45]. 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 [45, 54]. 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
暴露或媒介的非线性效应

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 [55, 56], 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
随时间变化的接触或介质

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 [57–59]. In a more complex model, the longitudinal time varying relationships between exposures and mediators can be modelled using structural equation models [60]. 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 [61]. 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 [23]. 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 [62]. 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 [63]. 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 [63].
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。

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。