arXiv subjects

Feifang Hu

Publications and source records attributed to Feifang Hu.

22 records · Page 2Linked to original sources

arXiv2008

A New Family of Covariate-Adjusted Response Adaptive Designs and their Asymptotic Properties

It is often important to incorporating covariate information in the design of clinical trials. In literature, there are many designs of using stratification and covariate-adaptive randomization to balance on certain known covariate. Recently Zhang, Hu, Cheung and Chan (2007) have proposed a family of covariate-adjusted response-adaptive (CARA) designs and studied their asymptotic properties. However, these CARA designs often have high variabilities. In this paper, we propose a new family of covariate-adjusted response-adaptive (CARA) designs. We show that the new designs have smaller variabilities and therefore more efficient.

stat.ME↗

arXiv2006

Asymptotic Properties of Covariate-Adjusted Adaptive Designs

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 experiments. 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 $K (\geq 2)$ 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.

math.ST↗

arXiv2006

Asymptotic theorems of sequential estimation-adjusted urn models

The Generalized Pólya Urn (GPU) is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential estimation-adjusted urn model (a nonhomogeneous GPU) which has a wide spectrum of applications. Because the proposed urn model depends on sequential estimations of unknown parameters, the derivation of asymptotic properties is mathematically intricate and the corresponding results are unavailable in the literature. We overcome these hurdles and establish the strong consistency and asymptotic normality for both the patient allocation and the estimators of unknown parameters, under some widely satisfied conditions. These properties are important for statistical inferences and they are also useful for the understanding of the urn limiting process. A superior feature of our proposed model is its capability to yield limiting treatment proportions according to any desired allocation target. The applicability of our model is illustrated with a number of examples.

math.PR↗

arXiv2005

Asymptotics in randomized urn models

This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2,...,n-1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition and the patient allocation under general assumptions on random generating matrices which determine how balls are added to the urn. Also we obtain explicit forms of the asymptotic variance-covariance matrices of both the urn composition and the patient allocation. The conditions on the nonhomogeneity of generating matrices are mild and widely satisfied in applications. Several applications are also discussed.

math.PR↗