Four Essential Assumptions for Causal Inference: Exchangeability, Positivity, No Interference, Consistency, and SUTVA

1. Exchangeability (Ignorability)

🔎 What it means:

• After adjusting for the observed covariates X, the treated and untreated groups are comparable. Formally:

📌 Why it's critical:

• Ensures your control group reliably predicts the missing counterfactual outcomes of the treatment group, and vice versa. Without it, your estimates suffer from hidden confounding bias.

🚩 Signs of violation:

• Persistent covariate imbalance even after statistical adjustment.
• Known confounders not collected (e.g., clinical severity influencing treatment choice).

🛠 Solutions in practice:

• Randomization (gold standard to ensure balance).
• Adjust for known confounders via Propensity Scores, Regression, or Doubly Robust Estimators.
• Sensitivity analyses (e.g., E-value) to quantify potential unmeasured confounding.

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2. Positivity (Overlap)

🔎 What it means:

• Every subgroup defined by covariates XXX must have a real chance (>0%) of receiving both treatment options:

0<P(D=1∣X=x)<1

📌 Why it's critical:

• If some patients could never receive the treatment, you cannot estimate causal effects for that subgroup—your analysis becomes invalid.

🚩 Signs of violation:

• Propensity scores clustered at 0 or 1 (no overlap).
• Subpopulations clearly excluded by policy or medical contraindication.

🛠 Solutions in practice:

• Restrict analysis to regions with common support.
• Trimming or weighting to remove problematic cases.
• Redefine target population clearly and explicitly.

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3. No Interference (SUTVA Part 1)

🔎 What it means:

• An individual's potential outcome depends solely on their own treatment status, not the treatment status of other individuals. Formally:

📌 Why it's critical:

• Without it, one individual's outcome spills over to others, making individual causal effects ambiguous.

🚩 Signs of violation:

• Treatment has clear spillover effects (vaccines, peer-influence programs).
• Outcomes for "untreated" patients improve as the proportion treated rises.

🛠 Solutions in practice:

• Use cluster-randomized trials or network-structured designs.
• Adopt methods explicitly modeling interference (partial interference, network models).

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4. Consistency (SUTVA Part 2)

🔎 What it means:

• If a patient received a treatment "A", the observed outcome equals their potential outcome under exactly that treatment:

📌 Why it's critical:

• If "treatment A" is multiple indistinct interventions, potential outcomes no longer match the observed data, compromising your causal conclusions.

🚩 Signs of violation:

• Treatment varies widely (dosage, route, timing) within the study.
• Poor adherence or protocol drift.

🛠 Solutions in practice:

• Precisely define treatments (dose, timing, mode).
• Conduct Per-Protocol analyses or Instrumental Variable approaches.

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Stable Unit Treatment Value Assumption (SUTVA)

Rubin (1980) bundled the last two assumptions into a single essential concept known as SUTVA:

📌 Why SUTVA is critical:

• It guarantees each individual's potential outcomes Y(0),Y(1)Y(0),Y(1)Y(0),Y(1) remain stable and meaningful. Without SUTVA, the basic framework of potential outcomes collapses, making causal interpretation impossible.

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Final Valid Checklist

Use this summarized, practical checklist before concluding causal effects:

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Practical Workflow to Secure Causal Validity:

1. Precisely define your treatment intervention (Consistency).
2. Evaluate and mitigate potential spill-over effects (No Interference).
3. Use DAGs and expert input to identify and measure all confounders (Exchangeability).
4. Confirm overlap and common support for propensity scores or covariates (Positivity).

Checking off these four assumptions ensures your reported "treatment effects" are robust, credible, and causal—not merely statistical associations.