  Clinical trials are complex and usually involve multiple objectives such as
controlling type I error rate, increasing power to detect treatment difference,
assigning more patients to better treatment, and more. In literature, both
response-adaptive randomization (RAR) procedures (by changing randomization
procedure sequentially) and sequential monitoring (by changing analysis
procedure sequentially) have been proposed to achieve these objectives to some
degree. In this paper, we propose to sequentially monitor response-adaptive
randomized clinical trial and study it's properties. We prove that the
sequential test statistics of the new procedure converge to a Brownian motion
in distribution. Further, we show that the sequential test statistics
asymptotically satisfy the canonical joint distribution defined in Jennison and
Turnbull (\citeyearJT00). Therefore, type I error and other objectives can be
achieved theoretically by selecting appropriate boundaries. These results open
a door to sequentially monitor response-adaptive randomized clinical trials in
practice. We can also observe from the simulation studies that, the proposed
procedure brings together the advantages of both techniques, in dealing with
power, total sample size and total failure numbers, while keeps the type I
error. In addition, we illustrate the characteristics of the proposed procedure
by redesigning a well-known clinical trial of maternal-infant HIV transmission.
