Abstract:
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Personalized decision rule in precision medicine is a `discrete parameter', for which theoretical development of statistical inference is lacking. With the advance of recent technology and data management, the personalized decision rules are usually constructed based on a large number of patients’ characteristics. This high-dimensionality makes the inference on the decision rule even more challenging. Based on the potential outcome framework and confidence distribution (CD) framework, we propose a confidence measure to quantify the estimation uncertainty in a personalized decision with high-dimensional covariates. This measure, with value in [0,1], provides a frequency-based assessment about the decision. It is also shown to match well with the classical assessments of sensitivity and specificity, but without the need to know the true optimal treatment regime. Utility of the development is demonstrated in an adaptive clinical trial.
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