SUTVA (Stable Unit Treatment Value Assumption)

Definition

The potential outcome of one unit is not affected by the treatment assignment of other units, and only a single version exists for each treatment level.

Expressed as a formula:

$$Y_i(W_1, W_2, \ldots, W_n) = Y_i(W_i)$$

The potential outcome of unit $i$ depends only on its own treatment $W_i$.

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The Two Components

1. No Interference

The treatment of one unit does not affect the outcome of another unit:

$$Y_i(W_i, W_{-i}) = Y_i(W_i, W'_{-i}), \quad \forall W_{-i}, W'_{-i}$$

Meaning: independence between units, no spillover effects

Examples:

• ✓ Satisfied: an individual’s drug response is independent of other patients’ drug intake
• ✗ Violated: if a friend gets vaccinated, my probability of infection also changes (herd immunity)

2. Single Version of Treatment

Only one version exists for each treatment level:

$$Y_i(W=w) \text{ is uniquely defined for each } w$$

Examples:

• ✓ Satisfied: drug A 100mg administered in a standardized manner
• ✗ Violated: “drug A” exists in multiple manufacturer versions, at different doses

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Intuitive Understanding

Analogy: Exam Scores

SUTVA Satisfied:

• Student A’s score is independent of how student B prepared
• All students receive the same exam paper

SUTVA Violated:

• Curve-based grading: B’s score affects A’s relative ranking
• Different versions of the exam: some students get easy questions, some get hard ones

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Cases of SUTVA Violation

1. Network/Social Effects (Interference)

Situation	Reason for Violation
Social media advertising	If a friend sees the ad, I am also influenced
Vaccination	Herd immunity effect
Educational program	Peer learning effect
Pricing policy	Competitor response affects my customers

2. Diversity of Treatment Versions (Multiple Versions)

Situation	Reason for Violation
Effect of “exercise”	Type, intensity, and duration of exercise vary
Effect of “education”	Teacher, materials, and methods vary
Effect of “drug”	Dose and timing of administration vary

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Responses to SUTVA Violation

1. When There Is Interference

• Exposure Mapping: Extend as a function of neighbors’ treatments $Y_i(W_i, g(W_{-i}))$ where $g$ is a summary function of the neighbors’ treatments

• Network Causal Inference: Explicitly model the network structure

  • See Network Interference

• Cluster Randomization: Assign treatment at the cluster level

2. When There Are Multiple Versions

• Treatment subdivision: Define each version as a separate treatment
• Treatment standardization: Guarantee a single version via protocol
• Random Versions: If the version is random, the average effect can be estimated

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Relationship with Consistency

When SUTVA is satisfied, Consistency holds:

$$Y = Y(W) \quad \text{when treated with } W$$

That is, the observed outcome equals the potential outcome of the corresponding treatment.

For details: Consistency

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Testability

SUTVA is only partially testable:

Component	Testing Method
No Interference	Network analysis, checking spatiotemporal patterns, randomized design
Single Version	Reviewing the treatment protocol, treatment variation analysis

Diagnostic Questions

1. Can the treatment of one unit affect another unit?
2. Is the treatment well defined? Do multiple versions exist?
3. Are the timing and intensity of the treatment uniform?

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Related Concepts

• Causal Assumptions Overview - Integrated overview of the three core assumptions
• Consistency - A consequence of SUTVA
• Network Interference - Relaxation of SUTVA
• Ignorability - Another core assumption
• Positivity - The third core assumption

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References

• Rubin, D. B. (1980). Discussion of “Randomization analysis of experimental data”
• yaoSurveyCausalInference2021 - Section 2.3
• Cox, D. R. (1958). Planning of Experiments - Original introduction of the concept