Learn-As-you-GO (LAGO) trials: optimizing treatments and preventing trial failure through ongoing learning.

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) trials extend the theory of LAGO for binary outcomes following a logistic regression model to LAGO for continuous outcomes under flexible conditional mean models. Because the mathematical methods for binary outcomes do not apply to continuous outcomes, the theory presented in this paper is entirely new. 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.