arXiv subjects

Zhang Li-Xin

Publications and source records attributed to Zhang Li-Xin.

3 recordsLinked to original sources

arXiv2026

Efficient Doubly Adaptive Biased Coin Designs for Multiple Treatments

The randomness, efficiency (power and variability), and desirable allocation proportions are important components for evaluating a response-adaptive design in clinical trials and conflicted demands in applications. The aim of this paper is to provide designs dealing with these dilemmas. We first give a general framework for efficient response-adaptive randomization procedures that attain the Cram\'er-Rao lower bounds of the allocation variances for any desired allocation proportions. The general framework is flexible for us to define new families of efficient designs with good properties for both two and multiple-treatment clinical trials. We also prove that, among all response-adaptive randomization procedures with the same limit allocation proportions, the selection biases and entropies as measures of the randomness of the designs have their optimal values. Basing on the theory on efficiency and randomness, we propose a new family of doubly adaptive biased coin designs for multi-treatment clinical trials that can target any allocation proportion and are asymptotically best in terms both the randomness and efficiency so that their randomness is asymptotic optimal and asymptotic allocation variance attains the Cram\'er-Rao lower bound. Theoretical properties, including the strong consistency, the asymptotic normality, and the functional central limit theorem for both the sample allocation proportions and the estimators of the distribution parameters, are developed by using the technique of Gaussian approximation and Gaussian comparing theorems.

math.ST↗

arXiv2026

Covariate-Adaptive Randomization in Clinical Trials without Inflated Variances

Covariate adaptive randomization (CAR) procedures are extensively used to reduce the likelihood of covariate imbalances occurring in clinical trials. In literatures, a lot of CAR procedures have been proposed so that the specified covariates are balanced well between treatments. However, the variance of the imbalance of the unspecified covariates may be inflated comparing to the one under the simple randomization. The inflation of the variance causes the usual test of treatment effects being not valid and adjusting the test being not an easy work. In this paper, we propose a new kind covariate adaptive randomization procedures to balance covariates between two treatments with a ratio $\rho:(1-\rho)$. Under this kind of CAR procedures, the convergence rate of the imbalance of the specified covariates is $o(n^{1/2})$, and at the same time the asymptotic variance of the imbalance of any unspecified (observed or unobserved) covariates does not exceed the one under the simple randomization. The ``shift problem'' found by Liu, Hu, and Ma (2025) will not appear under the new CAR procedures.

math.ST↗

arXiv2013

Quenched invariance principle for a long-range random walk with unbounded conductances

We consider a random walk on a random graph $(V,E)$, where $V$ is the set of open sites under i.i.d. Bernoulli site percolation on the multi-dimensional integer set $\mathbf{Z}^d$, and the transition probabilities of the walk are generated by i.i.d. random conductances (positive numbers) assigned to the edges in $E$. This random walk in random environments has long range jumps and is reversible. We prove the quenched invariance principle for this walk when the random conductances are unbounded from above but uniformly bounded from zero by taking the corrector approach. To this end, we prove a metric comparison between the graph metric and the Euclidean metric on the graph $(V, E)$, an estimation of a first-passage percolation and an almost surely weighted Poincar{\'{e}} inequality on $(V,E)$, which are used to prove the quenched heat kernel estimations for the random walk.

math.PR↗