Annals of Statistics

Asymptotic properties of covariate-adjusted response-adaptive designs

Li-Xin Zhang, Feifang Hu, Siu Hung Cheung, and Wai Sum Chan

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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.

Article information

Ann. Statist., Volume 35, Number 3 (2007), 1166-1182.

First available in Project Euclid: 24 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F15: Strong theorems 62G10: Hypothesis testing
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations

Adaptive designs asymptotic normality clinical trial covariate information generalized linear model logistic regression


Zhang, Li-Xin; Hu, Feifang; Cheung, Siu Hung; Chan, Wai Sum. Asymptotic properties of covariate-adjusted response-adaptive designs. Ann. Statist. 35 (2007), no. 3, 1166--1182. doi:10.1214/009053606000001424.

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