A counterfactual approach to bias and effect modification in terms of response types

Exchangeability of measures of association before and after exposure status is flipped: its relationship with confounding in the counterfactual model

BACKGROUND

The counterfactual definition of confounding is often explained in the context of exchangeability between the exposed and unexposed groups. One recent approach is to examine whether the measures of association (e.g., associational risk difference) are exchangeable when exposure status is flipped in the population of interest. We discuss the meaning and utility of this approach, showing their relationships with the concept of confounding in the counterfactual framework.

METHODS

Three hypothetical cohort studies are used, in which the target population is the total population. After providing an overview of the notions of confounding in distribution and in measure, we discuss the approach from the perspective of exchangeability of measures of association (e.g., factual associational risk difference vs. counterfactual associational risk difference).

RESULTS

In general, if the measures of association are non-exchangeable when exposure status is flipped, confounding in distribution is always present, although confounding in measure may or may not be present. Even if the measures of association are exchangeable when exposure status is flipped, there could be confounding both in distribution and in measure. When we use risk difference or risk ratio as a measure of interest and the exposure prevalence in the population is 0.5, testing the exchangeability of measures of association is equivalent to testing the absence of confounding in the corresponding measures.

CONCLUSIONS

The approach based on exchangeability of measures of association essentially does not provide a definition of confounding in the counterfactual framework. Subtly differing notions of confounding should be distinguished carefully.

Marginal Sufficient Component Cause Model: An Emerging Causal Model With Merits?

For decades, the sufficient cause model and the counterfactual model have shaped our understanding of causation in biomedical science, and the link between these two models has enabled us to obtain a deeper understanding of causality. Recently, a new causal model-the marginal sufficient component cause model-was proposed and applied in the context of interaction or mediation. The proponents of this model have emphasized its utility in visualizing the presence of "agonism" (a subtype of mechanistic interaction) in the counterfactual framework, claiming that the concept of agonism has not been clearly defined in causal inference and that agonistic interaction cannot be visualized by the conventional sufficient cause model. In this article, we illustrate that careful scrutiny based on the conventional sufficient cause model yields further insights into the concept of agonism in a more biologic sense. We primarily focus on the following three points: (1) "agonism" defined in the counterfactual model can be visualized as sets of sufficient causes in the conventional sufficient cause model; (2) although the so-called independent competing assumption or no redundancy assumption may seem irrelevant in the marginal sufficient component cause model, researchers do need to assume that potential completion times of relevant marginal sufficient causes differ; and (3) possibly differing potential completion times of marginal sufficient causes cannot be discerned until their hidden mechanistic paths are considered in the conventional sufficient cause model. In this rapidly progressing field of research, decades after its introduction, the sufficient cause model retains its worth.

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

The assessment of causality is fundamental to epidemiology and biomedical sciences. One well-known approach to distinguishing causal from noncausal explanations is the nine Bradford Hill viewpoints. A recent article in this journal revisited the viewpoints to incorporate developments in causal thinking, suggesting that the sufficient cause model is useful in elucidating the theoretical underpinning of the first of the nine viewpoints-strength of association. In this article, we discuss how to discern the causal mechanisms of interest in the sufficient cause model, which pays closer attention to the relationship between the sufficient cause model and the Bradford Hill viewpoints. To this end, we explicate the link between the sufficient cause model and the potential-outcome model, both of which have become the cornerstone of causal thinking in epidemiology and biomedicine. A clearer understanding of the link between the two models provides significant implications for interpretation of the observed risks in the subpopulations defined by exposure and confounder. We also show that the concept of potential completion times of sufficient causes is useful to fully discerning completed sufficient causes, which leads us to pay closer attention to the fourth of the nine Bradford Hill viewpoints-temporality. Decades after its introduction, the sufficient cause model may be vaguely understood and thus implicitly used under unreasonably strict assumptions. To strengthen our assessment in the face of multifactorial causality, it is significant to carefully scrutinize the observed associations in a complementary manner, using the sufficient cause model as well as its relevant causal models.

Causal Diagrams: Pitfalls and Tips

Graphical models are useful tools in causal inference, and causal directed acyclic graphs (DAGs) are used extensively to determine the variables for which it is sufficient to control for confounding to estimate causal effects. We discuss the following ten pitfalls and tips that are easily overlooked when using DAGs: 1) Each node on DAGs corresponds to a random variable and not its realized values; 2) The presence or absence of arrows in DAGs corresponds to the presence or absence of individual causal effect in the population; 3) “Non-manipulable” variables and their arrows should be drawn with care; 4) It is preferable to draw DAGs for the total population, rather than for the exposed or unexposed groups; 5) DAGs are primarily useful to examine the presence of confounding in distribution in the notion of confounding in expectation; 6) Although DAGs provide qualitative differences of causal structures, they cannot describe details of how to adjust for confounding; 7) DAGs can be used to illustrate the consequences of matching and the appropriate handling of matched variables in cohort and case-control studies; 8) When explicitly accounting for temporal order in DAGs, it is necessary to use separate nodes for each timing; 9) In certain cases, DAGs with signed edges can be used in drawing conclusions about the direction of bias; and 10) DAGs can be (and should be) used to describe not only confounding bias but also other forms of bias. We also discuss recent developments of graphical models and their future directions.

Using group data to treat individuals: understanding heterogeneous treatment effects in the age of precision medicine and patient-centred evidence

Although often conflated, determining the best treatment for an individual (the task of a doctor) is fundamentally different from determining the average effect of treatment in a population (the purpose of a trial). In this paper, we review concepts of heterogeneity of treatment effects (HTE) essential in providing the evidence base for precision medicine and patient-centred care, and explore some inherent limitations of using group data (e.g. from a randomized trial) to guide treatment decisions for individuals. We distinguish between person-level HTE (i.e. that individuals experience different effects from a treatment) and group-level HTE (i.e. that subgroups have different average treatment effects), and discuss the reference class problem, engendered by the large number of potentially informative subgroupings of a study population (each of which may lead to applying a different estimated effect to the same patient), and the scale dependence of group-level HTE. We also review the limitations of conventional 'one-variable-at-a-time' subgroup analyses and discuss the potential benefits of using more comprehensive subgrouping schemes that incorporate information on multiple variables, such as those based on predicted outcome risk. Understanding the conceptual underpinnings of HTE is critical for understanding how studies can be designed, analysed, and interpreted to better inform individualized clinical decisions.

A typology of four notions of confounding in epidemiology

Confounding is a major concern in epidemiology. Despite its significance, the different notions of confounding have not been fully appreciated in the literature, leading to confusion of causal concepts in epidemiology. In this article, we aim to highlight the importance of differentiating between the subtly different notions of confounding from the perspective of counterfactual reasoning. By using a simple example, we illustrate the significance of considering the distribution of response types to distinguish causation from association, highlighting that confounding depends not only on the population chosen as the target of inference, but also on the notions of confounding in distribution and confounding in measure. This point has been relatively underappreciated, partly because some literature on the concept of confounding has only used the exposed and unexposed groups as the target populations, while it would be helpful to use the total population as the target population. Moreover, to clarify a further distinction between confounding “in expectation” and “realized” confounding, we illustrate the usefulness of examining the distribution of exposure status in the target population. To grasp the explicit distinction between confounding in expectation and realized confounding, we need to understand the mechanism that generates exposure events, not the product of that mechanism. Finally, we graphically illustrate this point, highlighting the usefulness of directed acyclic graphs in examining the presence of confounding in distribution, in the notion of confounding in expectation.