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**Sequential monitoring of response-adaptive randomized clinical trials.**
*(English)*
Zbl 1194.62095

Summary: Clinical trials are complex and usually involve multiple objectives such as controlling the type I error rate, increasing power to detect treatment difference, assigning more patients to better treatment, and more. In the 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. We propose to sequentially monitor response-adaptive randomized clinical trials and study their 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 by C. Jennison and B. W. Turnbull [Group sequential methods with applications to clinical trials. FL.: Chapman and Hall (2000; Zbl 0934.62078)]. Therefore, type I errors 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 keeping 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.

### MSC:

62L05 | Sequential statistical design |

60F05 | Central limit and other weak theorems |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

92C50 | Medical applications (general) |

62L10 | Sequential statistical analysis |

### Keywords:

asymptotic properties; Brownian process; response-adaptive randomization; power; sample size; type I error### Citations:

Zbl 0934.62078
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\textit{H. Zhu} and \textit{F. Hu}, Ann. Stat. 38, No. 4, 2218--2241 (2010; Zbl 1194.62095)

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