  It is well known that changing the intervention package while a trial is
ongoing does not lead to valid inference using standard statistical methods.
However, it is often necessary to adapt, tailor, or tweak a complex
intervention package in public health implementation trials, especially when
the intervention package does not have the desired effect. This article
presents conditions under which the resulting analyses remain valid even when
the intervention package is adapted while a trial is ongoing. Our results on
such Learn-As-you-GO (LAGO) studies extend the theory of LAGO for binary
outcomes following a logistic regression model (Nevo, Lok and Spiegelman, 2021)
to LAGO for continuous outcomes under flexible conditional mean model. We
derive point and interval estimators of the intervention effects and ensure the
validity of hypothesis tests for an overall intervention effect. We develop a
confidence set for the optimal intervention package, which achieves a
pre-specified mean outcome while minimizing cost, and confidence bands for the
mean outcome under all intervention package compositions. This work will be
useful for the design and analysis of large-scale intervention trials where the
intervention package is adapted, tailored, or tweaked while the trial is
ongoing.
