Adaptive clinical trial designs have gained popularity, allowing for modifications to sample sizes, participant populations, treatment arm selection, and other parameters. However, existing adaptive trial designs do not address changes to the intervention packages themselves, which have a reputation for invalidating statistical inferences. This has motivated the development of Learn-As-you-GO (LAGO), an adaptive clinical trial design that allows for modifications to multicomponent intervention packages over different stages. Centre characteristics might be confounders, predicting both the intervention package implemented and the outcomes in the centres. This work extends LAGO theory by using fixed centre effects to control for confounding by indication through both measured and unmeasured centre-specific characteristics. We show that the fixed centre effects provide reliable control for centre-level confounding even with small numbers of centres, demonstrating the applicability of this LAGO design across various trial settings. We also extend LAGO to allow centres to participate in more than one stage, which is realistic in large-scale implementation trials. Point and interval estimators for the intervention effects are derived. Consistency and asymptotic normality of the intervention effect estimators are established. Moreover, we provide valid hypothesis tests for the overall intervention effect. The optimal intervention package achieving a predetermined outcome mean while minimizing cost is estimated through constrained optimization.

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