\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

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

  • * Corresponding author: Lei Shi

    * Corresponding author: Lei Shi
Abstract Full Text(HTML) Related Papers Cited by
  • 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.

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

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] T. T. Cai and M. Yuan, Minimax and adaptive prediction for functional linear regression, Journal of the American Statistical Association, 107 (2012), 1201–1216. doi: 10.1080/01621459.2012.716337.
    [2] A. Ciarleglio, E. Petkova, T. Tarpey and R. T. Ogden, Flexible functional regression methods for estimating individualized treatment regimes, 5 (2016), 185–199. doi: 10.1002/sta4.114.
    [3] J. FanT. HuQ. Wu and D. X. Zhou, Consistency analysis of an empirical minimum error entropy algorithm, Applied and Computational Harmonic Analysis, 41 (2016), 164-189.  doi: 10.1016/j.acha.2014.12.005.
    [4] X. GuoJ. Fan and D. X. Zhou, Sparsity and error analysis of empirical feature-based regularization schemes, Journal of Machine Learning Research, 17 (2016), 3058-3091. 
    [5] Z. C. Guo, S. B. Lin and D. X. Zhou, Learning theory of distributed spectral algorithms, Inverse Problems, 33 (2017), 074009, 29pp. doi: 10.1088/1361-6420/aa72b2.
    [6] T. HuJ. FanQ. Wu and D. X. Zhou, Regularization schemes for minimum error entropy principle, Analysis and Applications, 13 (2015), 437-455.  doi: 10.1142/S0219530514500110.
    [7] S. B. Lin, X. Guo and D. X. Zhou, Distributed learning with regularized least squares, Journal of Machine Learning Research, 18 (2017), Paper No. 92, 31 pp.
    [8] I. McKeague and M. Qian, Estimation of treatment policies based on functional predictors, Statistica Sinica, 24 (2014), 1461–1485.
    [9] S. A. Murphy, Optimal dynamic treatment regimes, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65 (2003), 331–366. doi: 10.1111/1467-9868.00389.
    [10] S. A. Murphy, An experimental design for the development of adaptive treatment strategies, Statistics in Medicine, 24 (2005), 1455–1481. doi: 10.1002/sim.2022.
    [11] Z. L. Qi and Y. F. Liu, D-learning to estimate optimal individual treatment rules, Electronic Journal of Statistics, 12 (2018), 3601–3638. doi: 10.1214/18-EJS1480.
    [12] J. O. Ramsay and B. W. Silverman, Applied Functional Data Analysis, Springer, New York, 2002. doi: 10.1007/b98886.
    [13] L. Shi, Distributed Learning with Indefinite Kernels, Analysis and Applications, 2019. doi: 10.1142/S021953051850032X.
    [14] R. Song, W. Wang, D. Zeng and M. R. Kosorok, Penalized q-learning for dynamic treatment regimes, Statistica Sinica, 25 (2015), 901–920.
    [15] M. Yuan and T. T. Cai, A reproducing kernel Hilbert space approach to functional linear regression, The Annals of Statistics, 38 (2010), 3412–3444. doi: 10.1214/09-AOS772.
    [16] T. Zhang, Learning bounds for kernel regression using effective data dimensionality, Neural Computation, 17 (2005), 2077-2098.  doi: 10.1162/0899766054323008.
    [17] Y. Zhao, D. Zeng, A. J. Rush and M. R. Kosorok, Estimating individualized treatment rules using outcome weighted learning, Journal of the American Statistical Association, 107 (2012), 1106–1118. doi: 10.1080/01621459.2012.695674.
  • 加载中
SHARE

Article Metrics

HTML views(941) PDF downloads(335) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return