An RKHS approach to estimate individualized treatment rules based on functional predictors

Jun Fan; Fusheng Lv; Lei Shi

doi:10.3934/mfc.2019012

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2019, Volume 2, Issue 2: 169-181. Doi: 10.3934/mfc.2019012

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An RKHS approach to estimate individualized treatment rules based on functional predictors

1.
Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China
2.
School of Mathematical Sciences, Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China

^* Corresponding author: Lei Shi
^* Corresponding author: Lei Shi

Published: July 2019

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Abstract

In recent years there has been massive interest in precision medicine, which aims to tailor treatment plans to the individual characteristics of each patient. This paper studies the estimation of individualized treatment rules (ITR) based on functional predictors such as images or spectra. We consider a reproducing kernel Hilbert space (RKHS) approach to learn the optimal ITR which maximizes the expected clinical outcome. The algorithm can be conveniently implemented although it involves infinite-dimensional functional data. We provide convergence rate for prediction under mild conditions, which is jointly determined by both the covariance kernel and the reproducing kernel.

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Mathematics Subject Classification: Primary: 68T05; Secondary: 62J02.

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