Multiple mediators, causal assumptions and potential caveats

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. Dr. Ananth is supported, in part, by the National Heart, Lung, and Blood Institute (R01-HL150065), and the National Institute of Environmental Health Sciences (R01-ES033190), National Institutes of Health. Mr. Bone is supported by a four-year PhD fellowship from the University of British Columbia (6456). Mr. Bone and Dr. Ananth do not have any conflicts to disclose. JNB conceived of and wrote the first draft of the commentary with review and input from CVA. Jeffrey Bone leads the biostatistics division at BC Children's Hospital Research Institute. He has extensive experience working in women's and children's health in both local and global health settings. His primary area of interest is bridging the gap between methodologists and clinicians to improve the overall quality of medical and epidemiological research. Cande Ananth is a Professor and Chief of the Division of Epidemiology and Biostatistics in the Department of Obstetrics, Gynecology, and Reproductive Sciences at Rutgers Robert Wood Johnson Medical School, NJ. His research portfolio is supported by the National Institutes of Health, and includes studying (i) The causal imprints of how ischaemic placental disease and preterm delivery affect the long-term risks of cardiovascular and stroke-related outcomes along the life course; (ii) The impact of air pollution and weather exposures on ischaemic placental disease; and (iii) Applications of innovative analytic approaches, including causal models and mediation methods, to studies in human reproduction. He serves as the editor-in-chief of Paediatric and Perinatal Epidemiology.

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