Statistics and Its Interface

Volume 12 (2019)

Number 3

Optimal treatment assignment of multiple treatments with analysis of variance decomposition

Pages: 355 – 363



Zhilan Lou (School of Data Sciences, Zhejiang University of Finance and Economics; and Key Laboratory of Advanced Theory and Application in Statistics and Data Science, East China Normal University, Shanghai, China)

Jun Shao (School of Statistics, East China Normal University, Shanghai, China)

Menggang Yu (Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wi., U.S.A.)


Personalized medicine to identify individualized treatment assignment rules has received increasing interest. When there are more than two treatments, the outcome weighted learning framework builds an optimal assignment rule via the skill of reproducing kernel Hilbert space. One main challenge is that the interpretation of covariates is difficult since the solution is a black-box classifier. Consequently, we establish a structured optimal treatment assignment rule with the functional analysis of variance decomposition. The method promotes the sparsity of the final solution by using structured kernel function and an $l_1$ penalty term. Meanwhile, we propose an easy-handling iterative procedure to overcome the calculation problem. Convergence of the risk function for resulting estimator is shown in the paper. The finite sample performance of the proposed method is demonstrated by simulation studies and a real data analysis.


personalized medicine, treatment assignment rule, analysis of variance decomposition, structured multi-category support vector machine

This research was partially supported by the First Class Discipline of Zhejiang – A (Zhejiang University of Finance and Economics – Statistics) (for Lou), by the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University), Ministry of Education (for Lou), by a Patient-Centered Outcomes Research Institute (PCORI) Award (ME-1409-21219 for Shao and Yu), by the US National Science Foundation Grant DMS-1612873 (for Shao).

The views in this publication are solely the responsibility of the authors and do not necessarily represent the views of the PCORI, its Board of Governors or Methodology Committee.

Received 6 August 2018

Published 4 June 2019