  In learn-as-you-go (LAGO) adaptive studies, the intervention is a complex
package consisting of multiple components, and is adapted in stages during the
study based on past outcome data. This design formalizes standard practice, and
desires for practice, in public health intervention studies. An effective
intervention package is sought, while minimizing intervention package cost.
When analyzing data from a learn-as-you-go study, the interventions in later
stages depend upon the outcomes in the previous stages, violating standard
statistical theory. We develop methods for estimating the intervention effects
in a LAGO study. We prove consistency and asymptotic normality using a novel
coupling argument, ensuring the validity of the test for the hypothesis of no
overall intervention effect. We develop a confidence set for the optimal
intervention package and confidence bands for the success probabilities under
alternative package compositions. We illustrate our methods in the BetterBirth
Study, which aimed to improve maternal and neonatal outcomes among 157,689
births in Uttar Pradesh, India through a complex, multi-component intervention
package.
