In recent years there has been rapid advancement in the available methods for effect decomposition through mediation analysis and clarification of the assumptions required for the interpretation of the estimated mediation effects.¹ This is largely due to a mathematical formalisation of mediation analysis through the counterfactual framework for causal inference.

In this issue of Pediatric and Perinatal Epidemiology, Rosenquist and colleagues² apply causal mediation analysis to explore mediating pathways between maternal obesity and childhood asthma, which has a well-established connection.³ They hypothesise that this association may be explained by three possible mediators for which they had available data: (i) gestational weight gain; (ii) preterm birth and (iii) childhood body mass index (BMI). Gestational weight gain was ruled out as a possible mediator based on a ‘causal inference test’ as it failed to show an association with childhood asthma after controlling for maternal BMI.

To assess possible meditation, the authors separate the effect of maternal obesity on childhood asthma into natural direct and natural indirect effects through both preterm birth and childhood BMI. Taking childhood BMI as an example, the natural direct effect is interpreted as the counterfactual contrast in asthma risk between a child born to a parent with and without maternal obesity. This invokes the assumption that the childhood BMI is set to the counterfactual value it would have been in the absence of maternal obesity. The natural indirect effect, on the other hand, is the counterfactual contrast in asthma risk between two individuals born from a parent with maternal obesity, assuming that the first individual's childhood BMI takes its natural value, while the second individual's childhood BMI is set to the value it would have had in the absence of maternal obesity. The authors found that childhood BMI had a moderate mediating effect, while preterm birth was not a mediator.

Their study is strengthened by the large set of variables to adjust for possible confounding, the length of available follow-up (8 years old in many children), the use of a Directed Acyclic Graph (DAG) to illustrate the (general) assumed causal structure and conducting several sensitivity analyses. These analyses included altering the functional form of the mediator (continuous vs binary), altering the length of follow up, and conducting a sequential mediation analysis including both preterm birth and childhood BMI. All of these analyses were in line with the primary findings, offering greater reassurance.

Despite its strengths, however, the study does not adequately consider the potential impact of a confounder of the mediator-outcome that is affected by the exposure in identifying causal effects, a complicated issue in causal mediation analysis. In this commentary, we present several options for addressing this problem, including available methods for analyses with multiple mediators.

The authors state that control for these four types of confounders is necessary for the causal interpretation of the natural direct and natural indirect effects discussed above. They are right insofar as assumptions C1–C3 are concerned. The measurement and inclusion of the set of confounders depicted in C1, C2 and C3 are necessary for the unbiased estimation of the natural direct and natural indirect effects. However, if a confounder of the mediator-outcome affected by the exposure (C4) exists, then irrespective of whether it is included in the analysis, the resulting causal estimates will remain biased.¹ Specifically, if C4 is included in the mediation models, then a portion of the direct effect (maternal BMI ➔ C4 ➔ asthma in Figure 1A) is blocked. Conversely, if C4 is omitted then the natural indirect effect is biased as the path maternal BMI ➔ childhood BMI ➔ C4 ➔ asthma (Figure 1A) remains open. In scenarios where a confounder of the mediator-outcome relationship affected by exposure is present, we offer three potential solutions to the problem.

The first, assuming this confounder is measured, is to consider a different interpretation of the natural direct and indirect effects known as ‘randomised interventional’ natural effects.^{4, 5} These effects differ from the conventional natural direct and natural indirect effects discussed above in that rather than contrasting counterfactual cases with individual values for the exposure (direct effect) or mediator (indirect effect), the contrast is based on random draws from the population distribution of the exposure or mediator. For example, the randomised interventional analogue of the traditional natural direct effect would be the counterfactual contrast in asthma risk between a child born to a parent with and without maternal obesity, assuming the childhood BMI is set to a random value from the distribution of all possible childhood BMIs in children born of parents with maternal obesity. To identify these effects, all such confounders must be included in the mediation models, including the other mediators under study.

Then, in the presence of a childhood BMI/asthma confounder affected by maternal BMI (e.g. preterm birth), using the method outlined in,⁶ we know the direct effect would be overestimated, and the indirect effect underestimated.

The third approach is to conduct an analysis that accommodates multiple (associated) mediators, as C4 in the DAG can be seen as an additional mediator.⁸ For these analyses, the assumptions about the temporal ordering of the mediators are required. For example, in Figure 1B, we provide an example DAG where we have replaced C4 with preterm birth. In their article, Rosenquist et al.⁹ addressed this by conducting a sensitivity analysis using an approach based on inverse probability weighting to measure the joint-mediated effect via both preterm birth and childhood BMI. This approach examines the combined indirect effect through both mediators simultaneously and is a good first step in understanding the combined causal indirect pathway. On the other hand, this does not allow the assessment of the relative contributions of each mediator to the natural indirect effect. Assessing the relative contributions of each mediator is analytically complex, but can permit one to assess, for example, the change in asthma risk if one were unable versus able to alter childhood BMI directly to what it would have been without maternal obesity while allowing preterm birth to take its natural value for a woman with obesity. This is a potentially relevant question as childhood BMI may be more modifiable than preterm birth (either spontaneous or clinician-initiated). An available option to estimate these partial indirect effects is using natural (interventional) effects models, which have been previously demonstrated in analyses in perinatal epidemiology, with R code publicly available.¹⁰

Understanding causal pathways between exposure and outcome is an important task in paediatric and perinatal epidemiology as it allows for the potential development or implementation of interventions along the causal pathway. Rosenquist and colleagues make an important contribution to better understanding the relationship between maternal BMI and asthma risk. Future studies to further determine whether these findings are causal should pay close attention to the required assumptions and give specifications about where each variable used in the analysis is assumed to fit into the causal structure.

As mediation analyses continue to become more widely adopted in applied epidemiology, it remains important for users of these methods to understand underlying assumptions and possible solutions to their violations, and to be explicit about the presumed relationships in their data.

近年来，通过中介分析和澄清解释估计中介效应所需的假设，效应分解的可用方法取得了快速进展。¹这主要是由于通过因果推理的反事实框架对中介分析进行了数学形式化。

在本期《儿科和围产期流行病学》中，Rosenquist 及其同事²应用因果中介分析来探索孕产妇肥胖与儿童哮喘之间的中介途径，两者之间存在着明确的联系。³他们假设这种关联可以通过他们拥有可用数据的三种可能的中介因素来解释：(i) 妊娠体重增加；(ii) 早产和 (iii) 儿童体重指数 (BMI)。根据“因果推理测试”，妊娠体重增加被排除为可能的中介因素，因为在控制母亲体重指数后，妊娠体重增加未能显示与儿童哮喘的关联。

为了评估可能的冥想，作者通过早产和儿童体重指数将母亲肥胖对儿童哮喘的影响分为自然直接影响和自然间接影响。以儿童体重指数为例，自然直接效应被解释为母亲肥胖与母亲肥胖的父母所生的孩子之间哮喘风险的反事实对比。这引发了这样的假设：儿童体重指数被设置为在没有母亲肥胖的情况下的反事实值。另一方面，自然间接效应是母亲肥胖的父母所生的两个个体之间哮喘风险的反事实对比，假设第一个个体的儿童期 BMI 取其自然值，而第二个个体的儿童期 BMI 设置为自然值。在没有母亲肥胖的情况下，它的价值是存在的。作者发现，儿童期 BMI 具有中等中介效应，而早产则不是中介效应。

他们的研究通过大量变量来调整可能的混杂因素、可用随访时间的长度（许多儿童为 8 岁）、使用有向无环图 (DAG) 来说明（一般）假设的因果关系而得到加强。结构并进行多项敏感性分析。这些分析包括改变中介变量的功能形式（连续与二元）、改变随访时间的长度以及进行包括早产和儿童体重指数在内的序贯中介分析。所有这些分析都与主要发现一致，让人更加放心。

然而，尽管该研究有其优点，但在识别因果效应时，并没有充分考虑受暴露影响的中介结果混杂因素的潜在影响，这是因果中介分析中的一个复杂问题。在这篇评论中，我们提出了解决这个问题的几种选择，包括使用多个中介进行分析的可用方法。

作者指出，控制这四种类型的混杂因素对于解释上述自然直接和自然间接影响是必要的。就假设 C1-C3 而言，它们是正确的。C1、C2 和 C3 中描述的混杂因素集的测量和包含对于对自然直接和自然间接影响的无偏估计是必要的。然而，如果受暴露（C4）影响的中介结果存在混杂因素，那么无论是否将其包含在分析中，所得的因果估计仍将存在偏差。¹具体而言，如果 C4 包含在中介模型中，则部分直接效应（图 1A 中的母亲 BMI → C4 → 哮喘）被阻止。相反，如果省略 C4，那么自然的间接效应就会出现偏差，因为母亲 BMI → 儿童 BMI → C4 → 哮喘的路径（图 1A）仍然开放。在存在受暴露影响的中介-结果关系混杂因素的情况下，我们提供了三种可能的问题解决方案。

首先，假设测量了这种混杂因素，则考虑对自然直接和间接效应的不同解释，即“随机干预”自然效应。^{4, 5}这些效应与上面讨论的传统自然直接效应和自然间接效应的不同之处在于，不是将反事实案例与暴露（直接效应）或中介（间接效应）的个体值进行对比，而是基于从暴露或介体的人口分布。例如，传统自然直接效应的随机干预类似物将是母亲肥胖和母亲肥胖的父母所生的孩子之间哮喘风险的反事实对比，假设儿童BMI被设置为来自所有可能分布的随机值。母亲肥胖的父母所生儿童的儿童期体重指数。为了识别这些影响，所有这些混杂因素都必须包含在中介模型中，包括正在研究的其他中介因素。

然后，在存在受母亲 BMI 影响的儿童 BMI/哮喘混杂因素（例如早产）的情况下，使用⁶中概述的方法，我们知道直接影响将被高估，而间接影响将被低估。

第三种方法是进行容纳多个（关联）中介的分析，因为 DAG 中的 C4 可以被视为额外的中介。⁸ 对于这些分析，需要对中介的时间顺序进行假设。例如，在图 1B 中，我们提供了一个示例 DAG，其中我们用早产替换了 C4。罗森奎斯特等人在他们的文章中。⁹通过使用基于逆概率加权的方法进行敏感性分析来解决这个问题，以测量早产和儿童 BMI 的联合介导效应。这种方法同时检查两个介体的组合间接效应，是理解组合因果间接途径的良好第一步。另一方面，这不允许评估每个中介对自然间接效应的相对贡献。评估每个中介因素的相对贡献在分析上是复杂的，但可以允许人们评估，例如，如果一个人无法与能够将儿童体重指数直接改变到没有母亲肥胖的情况，同时允许早产，则可以评估哮喘风险的变化以了解其对于肥胖女性的自然价值。这是一个潜在相关的问题，因为儿童体重指数可能比早产（自发的或临床医生发起的）更容易改变。估计这些部分间接影响的一个可用选择是使用自然（干预）效应模型，该模型先前已在围产期流行病学分析中得到证明，并公开了 R 代码。¹⁰

了解暴露与结果之间的因果路径是儿科和围产期流行病学的一项重要任务，因为它允许沿着因果路径潜在地制定或实施干预措施。Rosenquist 及其同事为更好地了解母亲体重指数与哮喘风险之间的关系做出了重要贡献。进一步确定这些发现是否具有因果关系的未来研究应密切关注所需的假设，并详细说明分析中使用的每个变量被假设适合因果结构的位置。

随着中介分析在应用流行病学中继续得到更广泛的采用，这些方法的用户了解潜在的假设和可能的违规解决方案，并明确数据中的假设关系仍然很重要。