## Bayesian Analysis

### Control of Type I Error Rates in Bayesian Sequential Designs

#### Abstract

Bayesian approaches to phase II clinical trial designs are usually based on the posterior distribution of the parameter of interest and calibration of certain threshold for decision making. If the posterior probability is computed and assessed in a sequential manner, the design may involve the problem of multiplicity, which, however, is often a neglected aspect in Bayesian trial designs. To effectively maintain the overall type I error rate, we propose solutions to the problem of multiplicity for Bayesian sequential designs and, in particular, the determination of the cutoff boundaries for the posterior probabilities. We present both theoretical and numerical methods for finding the optimal posterior probability boundaries with $\alpha$-spending functions that mimic those of the frequentist group sequential designs. The theoretical approach is based on the asymptotic properties of the posterior probability, which establishes a connection between the Bayesian trial design and the frequentist group sequential method. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. We apply least-square fitting to find the $\alpha$-spending function closest to the target. We discuss the application of our method to single-arm and double-arm cases with binary and normal endpoints, respectively, and provide a real trial example for each case.

#### Article information

Source
Bayesian Anal., Volume 14, Number 2 (2019), 399-425.

Dates
First available in Project Euclid: 23 June 2018

https://projecteuclid.org/euclid.ba/1529719226

Digital Object Identifier
doi:10.1214/18-BA1109

Mathematical Reviews number (MathSciNet)
MR3934091

Zentralblatt MATH identifier
07045436

#### Citation

Shi, Haolun; Yin, Guosheng. Control of Type I Error Rates in Bayesian Sequential Designs. Bayesian Anal. 14 (2019), no. 2, 399--425. doi:10.1214/18-BA1109. https://projecteuclid.org/euclid.ba/1529719226

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