Li-Xin Zhang
Zhejiang University
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Publication
Featured researches published by Li-Xin Zhang.
Annals of Statistics | 2007
Li-Xin Zhang; Feifang Hu; Siu Hung Cheung; Wai-Sum Chan
Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of response-adaptive designs that include covariates, despite their importance in clinical trials. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted response-adaptive (CARA) designs are very complex to formulate. In this paper, we overcome the technical hurdles and lay out a framework for general CARA designs for the allocation of subjects to K (≥ 2) treatments. The asymptotic properties are studied under certain widely satisfied conditions. The proposed CARA designs can be applied to generalized linear models. Two important special cases, the linear model and the logistic regression model, are considered in detail.
Annals of Statistics | 2009
Feifang Hu; Li-Xin Zhang; Xuming He
Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer-Rao lower bounds on the allocation variances for any allocation proportions, including optimal allocation proportions. The allocation probability functions of proposed procedures are discontinuous. The existing large sample theory for adaptive designs relies on Taylor expansions of the allocation probability functions, which do not apply to nondifferentiable cases. In the present paper, we study stopping times of stochastic processes to establish the asymptotic efficiency results. Furthermore, we demonstrate our proposal through examples, simulations and a discussion on the relationship with earlier works, including Efrons biased coin design.
Acta Mathematica Hungarica | 2000
Li-Xin Zhang
AbstractLet Xk; k ∈ Nd be a random field which is asymptotically negative dependent in a certain sense. Define the partial sum process in the usual way so that
Annals of Statistics | 2011
Li-Xin Zhang; Feifang Hu; Siu Hung Cheung; Wei Sum Chan
Statistics & Probability Letters | 2001
Li-Xin Zhang; Jiwei Wen
W_n \left( t \right) = \sigma _n^{{\text{ - 1}}} \sum\nolimits_{m \leqq n \cdot t} {\left( {X_m - EX_m } \right)} \quad {\text{for}}\quad t \in \left[ {0,1} \right]^d
Applied Mathematics-a Journal of Chinese Universities Series B | 2009
Li-Xin Zhang; Feifang Hu
Science China-mathematics | 2016
Li-Xin Zhang
, where
Stochastic Processes and their Applications | 2001
Li-Xin Zhang
arXiv: Probability | 2015
Li-Xin Zhang
\sigma _n^{\text{2}} = {\text{Var}}\left( {\sum\nolimits_{m \leqq n} {X_m } } \right)
Journal of Multivariate Analysis | 2010
Jia Chen; Degui Li; Li-Xin Zhang