A dimension reduction framework for personalized dose finding
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The discovery of individual dose rules (IDRs) in personalized medicine is a challenging statistical problem. Most of existing methods for estimating the optimal IDR will suffer the curse of dimensionality as the dimension of covariates gets higher, especially IDRs are nonlinear. To tackle this problem, we propose a novel dimension reduction framework for estimating the optimal IDR. Underlying this framework, the covariates' information is composited into one or a few linear combinations and these combinations are used to infer the nonlinear IDRs. We propose a Direct-learning and semi-Direct learning approach based on a smooth semiparametric value function, which can be solved by an efficient orthogonality-constraints optimization algorithm. Under minimal regularity assumptions, the asymptotic normality is derived for the obtained dimensionality reduced subspace estimator and also we obtain the consistency and convergence rate of the estimated optimal IDR. The performance of the proposed methods is evaluated by comparing to existing methods via extensive simulation studies and real data analysis.
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