Six‐way decomposition of causal effects: Unifying mediation and mechanistic interaction

Abstract

The sufficient component cause (SCC) model and counterfactual model are two common methods for causal inference, each with their own advantages: the SCC model allows the mechanistic interaction to be detailed, whereas the counterfactual model features a systemic framework for quantifying causal effects. Hence, integrating the SCC and counterfactual models may facilitate the conceptualization of causation. Based on the marginal SCC (mSCC) model, we propose a novel counterfactual mSCC framework that includes the steps of definition, identification, and estimation. We further propose a six‐way effect decomposition for assessing mediation and the mechanistic interaction. The results demonstrate that when all variables are binary, the six‐way decomposition is an extension of four‐way decomposition and that without agonism, the six‐way decomposition is reduced to four‐way decomposition. To illustrate the utility of the proposed decomposition, we apply it to a Taiwanese cohort to examine the mechanism of hepatitis C virus (HCV)‐induced hepatocellular carcinoma (HCC) with liver inflammation measured by alanine aminotransferase (ALT) as a mediator. Among the HCV‐induced HCC cases, 62.27% are not explained by either mediation or interaction in relation to ALT; 9.32% are purely mediated by ALT; 16.53% are caused by the synergistic effect of HCV and ALT; and 9.31% are due to the mediated synergistic effect of HCV and ALT. In summary, we introduce an SCC model framework based on counterfactual theory and detail the required identification assumptions and estimation procedures; we also propose a six‐way effect decomposition to unify mediation and mechanistic interaction analyses.

Marginal Sufficient Component Cause Model

“…Thus, individuals of agonistic interaction (i.e., U = 4) and individuals of synergistic interaction (i.e., U = 3) may undergo the same mechanistic process to induce Y via a sufficient cause 𝑉 1 𝐴𝑀. This is inconsistent with the explanation by Huang et al 22 because their would be irrelevant. 22 (P. 4056) To summarize, if one is willing to accept the counterfactual-based definition of agonism, the visualization of agonism in the marginal sufficient component cause model may be useful in some context.…”

“…c By using the compound potential outcomes (or nested counterfactuals), the total effect of A on Y in the population of interest is given as E[𝑌(1, 𝑀(1))] − E[𝑌(0, 𝑀(0))] on the risk difference scale. As mentioned in section 4.2 of Huang et al, 22 the total effect can be decomposed into natural indirect effect (or total indirect effect) (i.e., E[𝑌(1, 𝑀(1))] − E[𝑌(1, 𝑀(0))]) and natural direct effect (or pure direct effect) (i.e., E[𝑌(1, 𝑀(0))] − E[𝑌(0, 𝑀(0))]). Alternatively, the total effect can also be decomposed into pure indirect effect (i.e., E[𝑌(0, 𝑀(1))] − E[𝑌(0, 𝑀(0))]) and total direct effect (i.e., E[𝑌(1, 𝑀(1))] − E[𝑌(0, 𝑀(1))]).…”

“…To clearly understand the meaning of the marginal sufficient component cause model, it would be useful to consider the link between the counterfactual model and the conventional sufficient cause model. As mentioned in section 2.2 of Huang et al, 22 even under the assumptions of sufficient cause monotonicity, linking sufficient causes to the counterfactual model is challenging because of its non-bijective (or more strictly, surjective but not injective) correspondence. Following Suzuki et al, 19 Table 2 shows the correspondence between potential outcomes, sufficient causes, and marginal sufficient causes under the assumption of sufficient cause positive monotonicity.…”

Strength in causality: discerning causal mechanisms in the sufficient cause model

“…Therefore, if one assumes that individuals can be at risk of, at most, only one sufficient cause, this response type is inevitably excluded. Note that response type 2 has been termed "competing antagonism" [30] or "agonism" [31][32][33][34] in the counterfactual framework. By contrast, under assumption 2, individuals of all the 16 risk status types may exist in the total population.…”

Causes of Outcome Learning: A causal inference-inspired machine learning approach to disentangling common combinations of potential causes of a health outcome

“…In the social sciences, Configurational Comparative Methods deal with sufficient causes (referencing earlier work [45]), of which the most famous is the Qualitative Comparative Analysis, [46] which has also been applied in the public health domain. The CoOL approach has similarities to decomposition approaches of mediated and interactive effects in epidemiology, [48,49] however, work is needed to assess the similarities to the LRP properties in the CoOL approach. A recent approach, Algorithm for Learning Pathway Structures (ALPS), which uses a Monte Carlo scheme to update a pathway structure has shown promise for identifying complex interactions in large epidemiological datasets.…”