Noncompliance and Intent-to-Treat

When people don't follow their assigned treatment in a study, simply comparing those who did vs. didn't can give misleading results. Think of it like a restaurant review: if you only rate the dishes customers actually ordered (instead of what the chef recommended), you might miss whether the chef's recommendations were actually good. Intent-to-Treat analysis preserves randomization by keeping people in their original groups, while Instrumental Variables and LATE help estimate effects for the subset of people who would comply with treatment. Check this: Always ask whether a study reports results by assignment or by actual treatment received.

The Core Problem

Noncompliance breaks the magic of randomization. When participants cross over between groups, the groups become different in ways that can distort results. People who choose to follow a treatment may be healthier, wealthier, or more motivated than those who don't—and those differences, not the treatment itself, might explain better outcomes.

Intent-to-Treat (ITT)

Intent-to-Treat analysis keeps everyone in their original assigned group, regardless of what they actually did. This preserves randomization and gives an unbiased estimate of the effect of being offered treatment. For example, in a study of a new medication, ITT compares everyone assigned to receive the drug against everyone assigned to placebo, even if some people never took their pills. ITT answers the policy-relevant question: "What happens if we offer this treatment broadly?"

The Limitations of ITT

However, ITT mixes two effects: the effect of the treatment itself and the effect of people actually using it. If 80% of participants don't follow the treatment, ITT might show no effect even if the treatment works miracles for those who use it. This is where Instrumental Variables (IV) and Local Average Treatment Effect (LATE) come in.

Instrumental Variables and LATE

Instrumental Variables analysis uses random assignment as a "natural instrument" to isolate causal effects. Random assignment affects treatment uptake but doesn't directly affect outcomes (except through treatment). This lets researchers estimate the effect for compliers—people who would follow treatment if assigned to it but wouldn't otherwise. This is the LATE: the effect for the subpopulation whose treatment status is actually changed by assignment.

Real-World Applications

In education policy, a lottery for charter school admission is an instrument. ITT compares lottery winners vs. losers, answering whether the lottery system improves outcomes overall. IV/LATE estimates the effect for students who would attend charter schools if given the chance but wouldn't otherwise. In medicine, a randomized encouragement to exercise is an instrument for actual exercise behavior, separating the motivational effect of the invitation from the physiological effect of exercise itself.

Noncompliance poses a fundamental challenge to causal inference because it severs the link between random assignment and actual treatment received. The Intent-to-Treat principle preserves the validity of randomization by analyzing participants according to their original assignment, producing unbiased estimates of the effect of treatment offer rather than treatment receipt [1]. When noncompliance is substantial, Instrumental Variables analysis leverages random assignment as an instrument, using the exclusion restriction (assignment affects outcomes only through treatment receipt) and monotonicity (no defiers) assumptions to identify the Local Average Treatment Effect for compliers [2].

• Angrist, Imbens, and Rubin (1996) formalized the LATE framework, showing that IV identifies the average treatment effect for compliers—those who take treatment when assigned to it but not otherwise—under clear assumptions [3].
• Imbens and Rubin (2015) demonstrated that LATE provides more policy-relevant estimates than per-protocol analyses when heterogeneity exists across subpopulations with different compliance behaviors [4].
• Hernán and Robins (2020) caution that ITT effects may be diluted by poor adherence, potentially leading to erroneous conclusions about treatment efficacy when combined with naive non-inferiority margins [5].

Gloss: Compliers are participants who would take the treatment if assigned to receive it but would not if assigned to control. Exclusion restriction means assignment affects outcomes only through its effect on treatment receipt, not through other pathways. Monotonicity assumes there are no "defiers" who would do the opposite of their assignment.

LATE has important limitations. It identifies effects only for compliers, not the entire population—and compliers may be a small or unrepresentative subgroup. If compliers differ systematically from the full population, LATE may not generalize well. The exclusion restriction can be violated if assignment affects outcomes through other channels (e.g., psychological effects of knowing you were "chosen" for treatment). Instrument strength matters too: weak instruments (where assignment barely affects treatment uptake) produce biased estimates. Some situations involve "defiers" (people who do the opposite of their assignment), violating monotonicity, though this is rare in practice. Finally, IV methods cannot estimate effects for "never-takers" or "always-takers"—their treatment status doesn't vary with assignment.