Abstract:
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Large-scale intervention studies in public health often have a ``learn-as-you-go'' feature. While the investigators have some knowledge that guides the choice of the intervention package, optimizing the intervention package with respect to cost-efficiency is a primary study goal, along with estimation and inference about the effects of this optimal package on the outcome of interest. In a two-stage "learn-as-you-go" design, the intervention package is adapted at the second stage as a function of the first stage data. We assume that the recommended intervention converges as the number of patients in the first stage grows. Estimation and inference at the end of the study is complex, due to the dependency of the choice of the second stage intervention package on the outcomes at the first stage. We derive the asymptotic properties of the MLE for this design, allowing for center-specific interventions at each stage, using a novel coupling approach. We present simulation studies to verify our results and apply the methods to the BetterBirth Study, an ongoing study covering 172,00 births, that aims to improve quality of care for births at multiple health centers in India.
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