The primary importance of the research question: implications for understanding natural versus controlled direct effects

Researchers and health care professionals are usually interested in measuring the effects of potentially harmful exposures or beneficial interventions. Studying the mechanisms of these effects through mediation analyses would improve our understanding of causal paths involved, which will help improve health via (i) new interventions that mitigate the detrimental effects and/or (ii) enhancement of currently effective interventions.1,2 The general objective of the analytical strategy is to estimate ‘direct effects’ independent of the blocked path. The two most common methods calculate the controlled direct effect (CDE) and natural (also known as ‘pure’) direct effect (NDE).3,4 The NDE has been criticized because a cross-world independence assumption (see Supplementary Material, available as Supplementary data at IJE online, for more details) is required to identify them,5,6 although there are some contexts where it is not necessary.7–9 In this opinion piece, we argue that the choice between CDE and NDE should be based on whether it addresses the research question; partial identification of NDE provided through bounds may be more important than point identification of CDE in some contexts. This is the same approach as the spirit of John Tukey’s ‘an approximate answer to the right question is worth far more than a precise answer to the wrong one’. We also illustrate why it is very important to clearly describe what the actual interventions would be, to observe the direct effect (NDE or CDE) in addition to the intervention on the main exposure.7,10 Our conceptual perspective is consistent with more recent work on mediation with natural, separable and path-specific effects.7,9,11–13 We use a simple example to estimate the causal effects of smoking on lung disease (Figure 1A), using only binary variables. Smoking (A) causes inhalation of dangerous chemicals (M), which causes an increased risk of chronic obstructive pulmonary disease (COPD) (Y). Occupation (e.g. firefighters) (C) causes inhalation of harmful chemicals leading to COPD, and there may also be a direct effect of heat-related COPD. Thus, C is a mediator-outcome confounder. Finally, L denotes every other cause of inhalation of harmful chemicals (e.g. air pollution, campfires and so on). The causal diagram in panel A represents the naturally occurring context for the effects of smoking (A) on chronic obstructive pulmonary disease (COPD, Y) acting partially through the mediator (M) of inhaled harmful chemicals. Occupation (C) may also cause inhaled chemicals, as well as COPD. In panel B, the causal diagram represents the context where one is interested in the controlled direct effect (CDE). In this world, investigators fix M to a specific value (e.g. M = 0), which means they apply an intervention (ICDE) that becomes the sole cause of M (deterministic, indicated by a double arrow15), and all other arrows into M are removed. In panel C, the causal diagram represents the context where one is interested in natural direct effect (NDE). In this world, investigators apply an intervention (INDE) that removes the effect of A on M (no arrow from A to M) but leaves all other causes affecting M intact. From Rothman’s sufficient causal set framework, the removal of at least one component cause of each sufficient causal set that includes A (i.e. either A = 0 or A = 1) is sufficient for the INDE Within our ‘intervention framework’, we could estimate the total causal effect of smoking on COPD by randomizing participants to smoke or not to smoke. Although we have strong beliefs that inhaling harmful chemicals is creating most of the damage, we remain quite unsure about other ways smoking might cause COPD. Therefore, we might be very interested in obtaining the causal effect of smoking if we could somehow remove these harmful chemicals (known as the direct effect of smoking independent of the mediator ‘inhaled chemicals’). The idea that removing these chemicals might make smoking less harmful is what eventually led to ‘vaping’, which is smoking without inhalation of many of the known harmful chemicals in smoke. We highlight that direct effects are usually estimated by measuring the mediator in a study that is designed to estimate the total causal effect of the main exposure. However, one could answer these questions directly with a new four-arm randomized controlled trial (RCT) that evaluates the effects of interventions that affect both smoking and the mediator.7 In our example, the direct effect of smoking might be due to heat-related damage. Although we consider smoking as a single intervention for simplicity, it occurs over long periods of time and all our variables can be conceptualized as time-dependent. The CDE in our example is the effect of smoking (A in Figure 1) which is not mediated through an increase in harmful chemical inhalation. Mathematically, CDEM=m refers to the observed effect if everyone was switched from A = 0 to A = 1, while keeping M fixed to the same value m for everyone (e.g. M = 0, one-world). Even though authors usually carefully explain the intervention on the exposure of interest, authors rarely define what they mean when they ‘fix M’ to the same value m for every person.14 In an RCT (we will assume 100% adherence for simplicity), the total causal effect of smoking is obtained with an intervention that leads to smoking (A = 1) in the treatment group, and an intervention that leads to not smoking (A = 0) in the control group. However, hypothetical interventions on M to obtain the CDEM=m (i.e. ICDE) also need to be specified. The ICDE must include a component that eliminates the influence of each of the following causal effects for inhalation of harmful chemicals: (i) smoking, (ii) occupational exposure and (iii) every other cause of inhalation of harmful chemicals. In other words, ICDE must ‘overrule’ the effects of every other variable that normally increases or decreases M (i.e. ICDE is deterministic for M). One possible example to set M = 0 for every person in the population is a complex intervention that includes highly effective filters at the ends of cigarettes, prevention of occupational exposure to harmful chemicals, elimination of air pollution, ban campfires and so on. Alternatively, one ‘non-complex’ intervention could be to implant a device into the trachea that filters all harmful chemicals. Essentially, this means that in the world with the new intervention present, M is no longer a function (i.e. caused by) of A, C or any other variable other than ICDE. Figure 1B illustrates this new world where ICDE is included (the double arrow from ICDE to M indicates deterministic relationship15), and all other arrows into M are removed. Although ICDE does not have to be generally included when drawing causal directed acyclic graphs (DAGs) because it is not a common cause of any two variables,16,17 it helps illustrate under-recognized assumptions in some contexts. Within an intervention framework, investigators ‘fix’ M to a value m with an intervention, and then simply randomize participants to A = 0 or A = 1, to obtain the CDEM=m If there is an interaction between the effects of A and M on Y, CDEM=1 (i.e. setting M = 1, where the intervention is smoking plus an intervention that causes all participants to inhale harmful chemicals) will be, by definition, different from CDEM=0. We can also think about the concepts from a potential outcomes approach or cross-over trial with a complete return to baseline between interventions. Fix M = 0 through the administration of ICDE (harmful chemical inhalation = 0) for every person throughout the experiment: no measurements. Fix A = 0 (no smoking), measure Y. Fix A = 1 (smoking), measure Y. The CDEM=0 is a contrast between the risk of COPD (Y) with smoking (Intervention 3) and risk of COPD without smoking (Intervention 2). There are five important points to emphasize. First, as mentioned above, ‘fixing a variable’ means we assume our theoretical ICDE will be deterministic for the value of M Second, because we assumed A does not cause M in this world (Figure 1B), fixing either A first or M first leads to the same distribution of outcomes, as long as we measure Y after both variables are fixed. Here we assume that the fixed M does not change when A is subsequently intervened. Third, there is an assumption that setting A = 0 does not affect the potential outcome of Y when A = 1, i.e. the participant’s states before Step 2 and before Step 3 are identical ('washout' occurs). Fourth, the difference between the total effect and the CDE cannot in general be interpreted as an indirect effect. If there are no interactions between the effects of A and M on Y in an additive model, however, risk differences for CDEM=1 and CDEM=0 become identical and they are equal to risk differences for NDE to be discussed in the next section.18–20 An analogous discussion applies to the risk ratios in a multiplicative model. Finally, even if A does not cause M, CDEs may differ from the total effect if there is an interaction between the effects of A and M on Y.19–21 The NDE is also the effect that occurs due to smoking which is not mediated through harmful chemical inhalation. However, it differs from the CDE because M is expected to be fixed by an intervention similar to ICDE but at different values for different participants. Mathematically, NDE is the effect that would be observed if everyone was switched from A = 0 to A = 1, while keeping M at the value it would have if A = 0 [noted in potential outcome as M = M(0)]. In this world, we assume the intervention to estimate NDE (INDE) leads to every individual’s value of M being unaffected by their value of A. Therefore, the arrow from A to M is removed but other factors, such as environmental exposure, continue to affect M (Figure 1C). In an RCT, our intervention to smoke (A = 1) or not smoke (A = 0) remains the same as our CDE example. However, to answer the NDE question, we only need to ‘remove’ the causal effect of smoking on inhalation of harmful chemicals; we no longer require the intervention ICDE (which retains M = m irrespective of occupational exposure or other causes on inhaling harmful chemicals). An INDE in this context might to be the addition of a highly effective filter to the ends of cigarettes (removing inhalation of harmful chemicals from smoke). More practically, one might consider vaping as a form of this INDE, even though it is not exactly the same. In any case, like the CDE, authors should specify how to intervene on M. Now that we have described the intervention, the mathematical approach using observed data requires fixing the value of M when A = 1 (one world) to what it would have been had A = 0 (second world).5 This has led some to question the meaningfulness of NDE, and also to the development of ‘interventional natural effects’ that can theoretically be assessed through randomized trials.22–24 From the potential outcomes approach, like the CDE, we require only three interventions for the NDE but in a different order. We again assume that the participant’s states before Step 2 and before Step 3 are identical, as would be the case in a cross-over trial with complete washout, as follows. Fix A = 0 (no smoking), measure M (harmful chemical inhalation) and measure Y (COPD). Fix M = the value after our first intervention (no smoking) for each participant through the administration of INDE: no measurements. Fix A = 1 (smoking), measure Y (COPD). The NDE is a contrast between the risk of COPD with smoking (Intervention 3) and the risk of COPD without smoking (Intervention 1). As with CDE, there is no causal effect of A on M (Figure 1C). Both C and L are parents of M, and C is a common cause of M and Y. Because the investigator can obtain the potential outcomes of Y in this cross-over trial with complete washout, however, one does not have to measure or account for C. Viewed from this perspective, both the CDE and the NDE can be assessed with three interventions and two measurements. Although we focused on the meaning of CDE and NDE, we briefly discuss estimation in the context of causal DAGs based on the more commonly used non-parametric structural equation models used by Pearl. In the Supplementary Material, we describe the context of Robins’ finest fully randomized causally interpreted structural tree graph (FFRCISTG) models. The most common reported difference between identifying the NDE and the CDE is that there is a necessary additional assumption that A is not a cause of a confounder of M-Y to identify NDE. This assumption would be violated if Figure 1A included an additional arrow from A to C. In this case, the confounder C is called a recanting witness because there is a path through C that is part of the direct effect (A → C → Y), and a path through C that is part of the indirect effect (A → C → M → Y).8 If a recanting witness is present, the CDEM=0 (combined effect through paths A → Y and A → C → Y) can be estimated because we are fixing M = 0 and therefore all the arrows going into M are removed. For the NDE, after removing the arrow from A to M, A continues to affect Y through both the direct paths (A → Y and A → C → Y) and the indirect path (A → C → M → Y). Therefore, NDE can only be estimated in very specific contexts.6 We now return to what fixing M means. From the interventionist framework, CDEM=0 does not require the NDE assumption that A has no effect on C. However, it does require the assumption that one is able to remove two or more (depending on L) additional causal effects on M with ICDE compared with INDE. Therefore, both CDE and NDE require their own unique assumptions about the interventions of interest. Estimating both CDE and NDE are often said to require no unobserved confounding of the M-Y relationship.7,25 However, it is sometimes possible to estimate both CDE and NDE in this context.7 Furthermore, in contrast to the common understanding that the absence of a ‘recanting witness’ is a necessary condition to identify NDE, NDE can be estimated if the effect of exposure monotonically affects the confounder, or there is no additive interaction between the mediator and the confounder, even if there is a ‘recanting witness’.8 Without these additional restrictions, alternative methods can still estimate other types of direct and indirect effects of interest even if they do not represent NDE.22 We believe that both CDE and NDE have important strengths and limitations. CDEM=m might be easier to estimate but, from an interventionist perspective, interpreting it correctly requires that one is able to describe all the interventions that are necessary to fix M = m for every participant. However, we should carefully consider whether it is meaningful to fix the amount of inhaled harmful chemicals for every participant from every cause to the same value, 0 or otherwise. The underlying assumption of the intervention associated with CDEM=0 is that one can eliminate harmful chemical inhalation (M) from all sources, which seems daunting in epidemiology and public health. Conversely, the NDE informs on our causal question related to an intervention that only removes harmful chemical inhalation from smoking. Despite our argument above, it may be easier to describe ICDE compared with INDE in some contexts. For example, consider that ingestion of sugar drinks during running improves endurance time26 and we are interested in knowing how much of the effect was mediated by the subsequent changes in insulin. One relatively simple ICDE might be to establish an intravenous line that measures insulin and simultaneously infuses or withdraws insulin from the blood depending on its concentration. This allows us to ‘fix’ insulin without having to control each of the individual factors that can affect insulin secretion or elimination. However, the INDE would require blocking the release of insulin specifically due to sugar absorption from the gut, and still allow insulin to rise or fall for other reasons. Practically, the INDE is a much more difficult intervention in this context. We believe that NDE is also helpful when deciding targets for new interventions. Our motivating example was to remove harmful chemicals from smoking, which was likely considered impossible 20 years ago. However, we may be able to achieve this through vaping of safe chemicals (notwithstanding cases under investigation27). Smoking in the presence of the intervention (i.e. without inhaling harmful chemicals as in vaping) may still have negative effects on COPD independent of M through heat damage. Because the CDE estimates the effect when all harmful chemical inhalation is removed and not just those due to smoking, it is the NDE that addresses our research question and would be considered of greater clinical relevance. Although our objective did not include methods to estimate CDE and NDE, we emphasize that estimating these effects is a theoretical exercise with important challenges.5,6,20 For example, whatever new intervention is developed to remove the effect of A on M is unlikely to be an idealized intervention that has one and only one effect.10 The value of the new intervention will depend on the total causal effect across all paths, some of which may be unknown. The recent number of cases with lung damage of unknown causes from vaping (which may or may not eventually lead to COPD in the future) underscores the importance of not relying solely on estimates from any decomposition analysis, whether it is CDE or NDE. As health researchers, we have to decide which of the different hypothetically beneficial interventions that eliminate particular causal effects should be tested given limited funding opportunities. We believe this requires we create a new causal diagram for each of the interventions. Each causal diagram would incorporate our knowledge about the direct and indirect paths in the presence of the intervention. One then simply chooses to test the intervention that is expected to lead to the greatest impact based on our synthesis of evidence and assumptions. From the intervention perspective, NDE is meaningful if one is interested in developing an intervention that removes a specific cause of M, i.e. all effects of A on M. CDE is meaningful if one is interested in developing an intervention that removes every single cause of M. When NDE and/or CDE are not strictly identifiable from the data, there may be contexts where it is best to (i) estimate bounds for the effect, (ii) consider a potentially biased answer to our research question or (iii) consider that substituting a different research question for the one originally posed provides the most valuable information possible. Supplementary data are available at IJE online. Both authors contributed to the writing of this manuscript. This work was unfunded. None declared.

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