HPG 6104 • Epidemiological Methods I

Causal Inference in Epidemiology

Week 4 Student Companion Guide

The Fundamental Problem of Causal Inference

We can never simultaneously observe the outcome of an individual under both the "exposed" and "unexposed" states at the same moment in time. The missing outcome—the one we cannot observe—is the counterfactual.

The 3 Consistency Assumptions

For the potential outcomes framework to yield valid causal estimates, three core assumptions must hold:

1. Consistency: The observed outcome equals the potential outcome under the exposure actually received.
2. Exchangeability: The exposed and unexposed groups are comparable. Potential outcomes are independent of the exposure assignment given covariates (No unmeasured confounding).
3. Positivity: Every individual has a non-zero probability of receiving either exposure level.

Exchangeability: The Core Assumption

Exchangeability requires that exposed and unexposed groups are comparable with respect to all determinants of the outcome other than the exposure itself.

Marginal Exchangeability

Holds unconditionally across the entire population. This is achieved mechanistically in large, well-conducted Randomized Controlled Trials (RCTs).

Conditional Exchangeability

Holds within strata defined by measured covariates. This is what Observational Studies target by using regression adjustment, stratification, or propensity scores.

CRITICAL: Conditional exchangeability is untestable from observed data alone. You can never prove there is no unmeasured confounding.

Directed Acyclic Graphs (DAGs)

DAGs are non-parametric graphical representations of your causal assumptions. They help identify which variables to adjust for (and which to avoid) using the Backdoor Criterion.

Variable Type	Structure (E=Exposure, O=Outcome)	Analytic Decision
Confounder (Fork)	E ← C → O	CONTROL (Adjust) to block backdoor path.
Collider (Inverted Fork)	E → C ← O	DO NOT CONTROL. Conditioning opens a spurious path (Collider Bias).
Mediator (Chain)	E → M → O	DO NOT CONTROL if estimating Total Effect. (Control only for Direct Effect).

Bradford Hill's Criteria for Causality

These are viewpoints or heuristics, not a strict checklist. Temporality is the only criterion considered logically necessary for causation.

Strength: Large magnitude of effect (High RR/OR).

Consistency: Replicated across studies.

Specificity: One exposure → one disease. (Weakest criterion, rarely met).

Temporality: Cause precedes effect. (Essential).

Gradient: Dose-response relationship.

Plausibility: Biologically sensible mechanism.

Coherence: Fits established science.

Experiment: Removal reduces risk.

Analogy: Similar factors cause similar outcomes.