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Intent-to-Treat vs. Treatment-on-the-Treated (Compliance-Adjusted Effects)
When a randomized experiment has imperfect compliance, two distinct causal estimands separate: the Intent-to-Treat (ITT) effect captures the impact of assignment, while the Treatment-on-the-Treated (TOT) effect captures the impact of actually receiving the treatment among takers. Under randomization, ITT is unbiased for the effect of the offer but is attenuated toward zero relative to the effect of exposure as compliance shrinks. TOT can be recovered from ITT by scaling by the compliance rate (Bloom, 1984) or, more generally, by instrumental-variables estimation using assignment as an instrument for realized exposure, which identifies the LATE among compliers under monotonicity (Imbens & Angrist, 1994; Angrist, Imbens & Rubin, 1996). Reporting ITT alone hides the effect of exposure; reporting TOT/IV alone hides what happens at scale when many assigned users do not comply. The distinction is what justifies running an IV on a randomized default rather than just reporting the assignment-level contrast.
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Data Science
Research Paper: Advanced Prompting
Science
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Intent-to-Treat (ITT) Effect
Treatment-on-the-Treated (TOT) Effect
Intent-to-Treat vs. Treatment-on-the-Treated (Compliance-Adjusted Effects)