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Abstract:
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Learning an individualized dose rule (IDR) in personalized medicine is a challenging statistical problem. Existing methods for estimating the optimal IDR often suffer from the curse of dimensionality, especially when the IDR is learned nonparametrically using machine learning approaches. The proposed methods exploit that the IDR can be reduced to a nonparametric function which relies only on a few linear combinations of the original covariates, hence leading to a more parsimonious model. To achieve this, we propose two approaches, a direct learning approach that yields the IDR as commonly desired in personalized medicine, and a pseudo-direct learning approach that focuses more on learning the dimension reduction space. Under regularity assumptions, we provide the convergence rate for the semiparametric estimators and Fisher consistency properties for the corresponding value function. For the pseudo-direct learning, we use an orthogonality constrained optimization approach on Stiefel manifold to update the dimension reduction space. For the direct learning, we use an alternative updating scheme the dimension reduction space and the nonparametric optimal dose rule function.
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