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Stat Med. 2017 Sep 20;36(21):3302-3314. doi: 10.1002/sim.7338. Epub 2017 Jun 7.

BOP2: Bayesian optimal design for phase II clinical trials with simple and complex endpoints.

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Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, 77030, Texas, U.S.A.


We propose a flexible Bayesian optimal phase II (BOP2) design that is capable of handling simple (e.g., binary) and complicated (e.g., ordinal, nested, and co-primary) endpoints under a unified framework. We use a Dirichlet-multinomial model to accommodate different types of endpoints. At each interim, the go/no-go decision is made by evaluating a set of posterior probabilities of the events of interest, which is optimized to maximize power or minimize the number of patients under the null hypothesis. Unlike other existing Bayesian designs, the BOP2 design explicitly controls the type I error rate, thereby bridging the gap between Bayesian designs and frequentist designs. In addition, the stopping boundary of the BOP2 design can be enumerated prior to the onset of the trial. These features make the BOP2 design accessible to a wide range of users and regulatory agencies and particularly easy to implement in practice. Simulation studies show that the BOP2 design has favorable operating characteristics with higher power and lower risk of incorrectly terminating the trial than some existing Bayesian phase II designs. The software to implement the BOP2 design is freely available at


Bayesian adaptive design; co-primary endpoints; early stopping; immunotherapy; ordinal endpoint

[Indexed for MEDLINE]

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