Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms

Abstract

Directed acyclic graphs (DAGs) play a large role in the modern approach to causal inference. DAGs describe the relationship between measurements taken at various discrete times including the effect of interventions. The causal mechanisms, on the other hand, would naturally be assumed to be a continuous process operating over time in a cause-effect fashion. How does such immediate causation, that is causation occurring over very short time intervals, relate to DAGs constructed from discrete observations? We introduce a time-continuous model and simulate discrete observations in order to judge the relationship between the DAG and the immediate causal model. We find that there is no clear relationship; indeed the Bayesian network described by the DAG may not relate to the causal model. Typically, discrete observations of a process will obscure the conditional dependencies that are represented in the underlying mechanistic model of the process. It is therefore doubtful whether DAGs are always suited to describe causal relationships unless time is explicitly considered in the model. We relate the issues to mechanistic modeling by using the concept of local (in)dependence. An example using data from the Swiss HIV Cohort Study is presented.

Keywords: causal inference; directed acyclic graphs; mechanisms; modeling.

Figure 1.

Illustration of causal connections in mediation analysis in the face of unmeasured confounders (U). The upper panel depicts a setup without repeated measures while the lower panel depicts a setup with the mediator being measured twice. In the upper panel, the direct and indirect cannot be estimated separately while this can be done in the lower panel.

Figure 2.

Illustration of local dependence between HAART treatment, viral load or CD4, and AIDS/death. Full lines indicate direct mechanisms while dashed lines indicate indirect effects operating through other variables. The upper panel shows how the treatment works by influencing (reducing) viral load. The lower panel does the same for CD4 count, also including the issue that start of treatment may depend on CD4 count. HAART: highly active anti-retroviral treatment.

Figure 3.

Example sample paths for 10 persons. Dashed lines correspond to people treated with aspirin and ARU is aspirin reaction units.

Figure 4.

Upper panel: local independence (i.e. immediate causation) graph for the Aspirin Example. Lower panel: corresponding graph when treatment (E), blood platelet aggregation (M), and log hazard (D) are measured sequentially and only once for instance at baseline for E, after 2 years of follow-up for M, and after 5 years for D (i.e. the classical DAG).

Figure 5.

Simulated sample paths for 10 persons from either setup 2 (upper panel) or setup 3 (lower panel). The causal structure is as in the aspirin example, but here the speed at which treatment affect the mediator is progressively slower. Dashed lines correspond to people treated with aspirin and ARU is aspirin reaction units.

Figure 6.

Analysis of increments of CD4 and HEM based on repeated regression analyses with lagged and baseline values of RNA, CD4, and HEM as independent variables. Analyses shown for monthly, yearly, and tri-yearly values from left to right.