## The Annals of Statistics

### Asymptotic Properties of Adaptive designs for Clinical Trials with delayed Response

#### Abstract

For adaptive clinical trials using a generalized Friedman’s urn design, we derive the limiting distribution of the urn composition under staggered entry and delayed response. The stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient’s response. A very general setup is employed with $K$ treatments and $L$ responses. When $L = K =2$, one example of a generalized Friedman’s urn design is the randomized play-the-winner rule. An application of this rule occurred in a clinical trial of depression, which had staggered entry and delayed response. We show that maximum likelihood estimators from such a trial have the usual asymptotic properties.

#### Article information

Source
Ann. Statist., Volume 30, Number 1 (2002), 122-139.

Dates
First available in Project Euclid: 5 March 2002

https://projecteuclid.org/euclid.aos/1015362187

Digital Object Identifier
doi:10.1214/aos/1015362187

Mathematical Reviews number (MathSciNet)
MR1892658

Zentralblatt MATH identifier
1012.62087

Subjects
Primary: 62G10: Hypothesis testing

#### Citation

Bai, Z.D.; Hu, Feifang; Rosenberger, William F. Asymptotic Properties of Adaptive designs for Clinical Trials with delayed Response. Ann. Statist. 30 (2002), no. 1, 122--139. doi:10.1214/aos/1015362187. https://projecteuclid.org/euclid.aos/1015362187

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• CHARLOTTESVILLE, VIRGINIA 22904-4135 E-MAIL: fh6e@pitman.stat.virginia.edu W. F. ROSENBERGER DEPARTMENT OF MATHEMATICS AND STATISTICS
• UNIVERSITY OF MARYLAND, BALTIMORE COUNTY 1000 HILLTOP CIRCLE
• BALTIMORE, MARYLAND 21250