Statistics and Its Interface

Volume 11 (2018)

Number 1

Optimal responses-adaptive designs based on efficiency, ethic, and cost

Pages: 99 – 107



Chen Feng (School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, U.S.A.)

Feifang Hu (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)


The trade-off between power and ethical concerns has been well discussed by researchers. The total costs, however, has hardly ever been considered in the adaptive design of clinical trials. In this article, we derive the compromised optimal allocations based on costs, ethical concerns, and efficiency for clinical trials with binary and normal responses. The compromised optimal allocations are implemented with a doubly biased coin design (DBCD) based on Hu and Zhang’s allocation function. The properties of the proposed designs are studied both theoretically and numerically. In many cases, the proposed designs are more efficient, economical and ethical than complete randomization (equal allocation) under both binary and normal responses.


asymptotical normality, binary response, clinical trial, doubly adaptive biased coin design (DBCD), normal response, sequential method

The research was partially supported by NSF Awards DMS-1442192 and DMS-1612970, the National Natural Science Foundation of China (No. 11371366).

Received 10 November 2016

Published 23 August 2017