ITE (Individual Treatment Effect)

Definition

The treatment effect for individual $i$

$$\text{ITE}_i = Y_i(1) - Y_i(0)$$

• $Y_i(1)$: the potential outcome when individual $i$ receives treatment
• $Y_i(0)$: the potential outcome when individual $i$ does not receive treatment

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Intuitive Understanding

Individual-Level Causal Effect

“How effective is the treatment for this particular person?”

Examples:

• The effect of drug A on patient Alice
• The effect of a tutoring program on student Bob
• The purchase-inducing effect of a coupon on customer Charlie

Counterfactual Question

$$\text{ITE}_i = \underbrace{Y_i(1)}_{\text{outcome under treatment}} - \underbrace{Y_i(0)}_{\text{outcome under no treatment (counterfactual)}}$$

The difference between the two outcomes for the same individual: “when treated vs. when not treated.”

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Fundamental Problem

Unobservable

Because of the Fundamental Problem of Causal Inference, the ITE is directly unobservable:

Individual	$W$ (treatment)	$Y(1)$	$Y(0)$	ITE
Alice	1	observed	?	?
Bob	0	?	observed	?

For a given individual, only one of $Y(1)$ and $Y(0)$ can be observed.

Alternative: Estimating CATE

Instead of the individual ITE, estimate the group-level average:

$$\text{CATE}(x) = E[\text{ITE} \mid X=x] = E[Y(1) - Y(0) \mid X=x]$$

The average effect across individuals sharing the same characteristics $X$.

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ITE vs. Other Estimands

Estimand	Definition	Level
ITE	$Y_i(1) - Y_i(0)$	Individual
CATE	$E[Y(1) - Y(0) \mid X]$	Conditional group
ATE	$E[Y(1) - Y(0)]$	Entire population
ATT	$E[Y(1) - Y(0) \mid W=1]$	Treated group

Relationships

$$\text{CATE}(x) = E[\text{ITE}_i \mid X_i = x]$$ $$\text{ATE} = E[\text{ITE}_i] = E_X[\text{CATE}(X)]$$

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Attempts to Estimate the ITE

1. Approximation via CATE

$$\hat{\text{ITE}}_i \approx \hat{\tau}(X_i)$$

Approximate by the average effect across individuals with the same $X$.

Limitation: ignores individual variation

2. Imputation Approach

Treated group ($W_i = 1$):

$$\hat{\text{ITE}}_i = Y_i - \hat{Y}_i(0)$$

Control group ($W_i = 0$):

$$\hat{\text{ITE}}_i = \hat{Y}_i(1) - Y_i$$

Impute the counterfactual outcome with a model.

3. Deep Learning Approach

GANITE and others: attempt to generate individual-level counterfactuals

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Applications

1. Personalized Medicine

• Selecting the optimal treatment per patient
• “For this patient, which treatment, A or B?“

2. Personalized Marketing

• Optimal offers per customer
• “Will a coupon be effective for this customer?“

3. Personalized Recommendation

• Content effects per user
• “Will this content be effective for this user?“

4. Policy Targeting

• Selecting policy recipients
• “For whom is this program effective?”

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Related Concepts

• Treatment Effects Overview - consolidated overview of treatment effects
• CATE - the conditional expectation of the ITE
• HTE - heterogeneous treatment effects
• ATE - the population average of the ITE
• Fundamental Problem of Causal Inference - the unobservability problem
• Meta-learners - approximating the ITE via CATE estimation

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References

• yaoSurveyCausalInference2021 - Section 2.2
• Holland, P. W. (1986). Statistics and Causal Inference
• Rubin, D. B. (1974). Estimating causal effects of treatments