Analytic Bounds on Causal Risk Differences in Directed Acyclic Graphs Involving Three Observed Binary Variables.

Area of Science:

• Epidemiology
• Causal Inference
• Biostatistics

Background:

• Estimating causal effects requires accounting for confounding and intermediate variables.
• Directed acyclic graphs (DAGs) model causal relationships but require assumptions.
• Bounds on causal effects are crucial when unmeasured confounding exists.

Purpose of the Study:

• To develop a linear programming approach for bounding the causal risk difference (RD(C)).
• To explore how various constraints narrow the bounds on RD(C) in different causal scenarios.
• To apply these refined bounds to real-world epidemiological data.

Main Methods:

• Utilized linear programming with causal risk difference as the objective function.
• Considered two scenarios: Z as a confounder and Z as an intermediate variable.
• Incorporated constraints from DAGs, monotonicity, and interaction assumptions.

Main Results:

• Derived general bounds for RD(C) as -Pr(Y!=X) <= RD(C) <= Pr(Y=X) in the absence of constraints.
• Demonstrated that incorporating background knowledge significantly narrows these bounds.
• Provided comparative analyses of bound widths across different constraint combinations.

Conclusions:

• Linear programming offers a flexible framework for deriving tighter bounds on causal risk differences.
• The choice of constraints significantly impacts the precision of causal effect estimation.
• The method is applicable to real-world studies for more robust causal inference.