Intention-to-Treat Analysis

Definition

Intention-to-treat (ITT) analysis estimates the causal effect of assignment to treatment — not actual receipt of treatment — thereby preserving the randomization-based validity of an experiment regardless of compliance. Under imperfect compliance (some assigned units do not receive treatment; some unassigned units obtain it), ITT dilutes the underlying treatment effect by including non-compliers in the treated group. It is the numerator of the Wald/instrumental variable (IV) estimator for the local average treatment effect (LATE): $\text{LATE} = \text{ITT}_Y / \text{ITT}_D$ , where $\text{ITT}_Y$ is the reduced-form effect of the instrument on the outcome and $\text{ITT}_D$ is the first-stage effect on treatment take-up (the complier share).

Key Ideas

ITT vs. per-protocol analysis: Per-protocol restricts to units that actually complied with their assignment, reintroducing selection bias. ITT avoids this by analyzing all units as assigned, making it the correct estimand for assessing policy impact when take-up is imperfect.
ITT and the Wald estimator: With binary instrument $Z$ and binary treatment $D$ : $\text{ITT}_Y = E[Y \mid Z=1] - E[Y \mid Z=0]$ $\text{ITT}_D = E[D \mid Z=1] - E[D \mid Z=0] = \Pr(\text{complier})$ $\text{LATE} = \text{ITT}_Y / \text{ITT}_D$
Conservative under imperfect compliance: $|\text{ITT}_Y| \leq |\text{LATE}|$ when compliers respond in a consistent direction, because non-compliers dilute the average. ITT is the appropriate estimate when the question is about assignment policy; LATE is appropriate when the question is about treatment efficacy for takers.
Attenuation direction: ITT underestimates the effect on compliers when non-compliers have a zero effect. IV/LATE recovers the complier average by scaling up the ITT estimate by the inverse of the take-up rate.
RCT context: In randomized controlled trials (RCTs), ITT analysis is the primary pre-specified estimand because it reflects the real-world effect of offering a program, not the effect conditional on participating. The supported employment RCTs in this wiki (Employment Intervention Demonstration Program) report ITT effects.
Quasi-experiment context: In natural experiments, the "instrument" plays the role of random assignment; the first-stage $\text{ITT}_D$ is the compliance rate, and LATE is recovered from the Wald ratio.

How It Works

Partition the population into compliance types per the Angrist, Imbens, and Rubin (AIR) framework: compliers ( $D(0)=0, D(1)=1$ ), never-takers ( $D(0)=D(1)=0$ ), always-takers ( $D(0)=D(1)=1$ ), and defiers ( $D(0)=1, D(1)=0$ ; ruled out by monotonicity). The ITT effect on $Y$ is: $\text{ITT}_Y = \Pr(C) \cdot \text{LATE} + \Pr(AT) \cdot 0 + \Pr(NT) \cdot 0$ under the exclusion restriction (instrument affects outcome only through treatment), giving $\text{ITT}_Y = \Pr(\text{complier}) \cdot \text{LATE}$ and therefore $\text{LATE} = \text{ITT}_Y / \Pr(\text{complier}) = \text{ITT}_Y / \text{ITT}_D$ .

Why It Matters

Program evaluation: Government programs rarely achieve full take-up. An ITT estimate of "offering the program" is often the policy-relevant quantity, even if it understates the impact on participants.
Benchmarking return-to-work interventions: The $3.1\%$ sustained work-exit rate for Disability Insurance (DI)-first awardees (Anand and Ben-Shalom 2016) is effectively an ITT benchmark — what happens to the full cohort of awardees absent targeted intervention.
Connecting RCTs and IV: The Wald formula makes explicit that every IV estimate in a natural experiment is a ratio of ITT effects, connecting the clinical trials tradition of ITT analysis to the econometric IV tradition.

Open Questions

When is ITT preferred to LATE for policy purposes? If the policy instrument is the assignment rule (offering a program), ITT is correct; if the question is about treatment effects for future takers under a different policy, LATE scaled by a different compliance rate may be needed.
Can ITT be estimated with heterogeneous compliance across subgroups without biasing group comparisons?

Sources

Angrist Imbens and Rubin 1996 — Identification of Causal Effects Using Instrumental Variables