Bayesian Analysis

Control of Type I Error Rates in Bayesian Sequential Designs

Haolun Shi and Guosheng Yin

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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 α-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 α-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., Advance publication (2018), 27 pages.

Dates
First available in Project Euclid: 23 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ba/1529719226

Digital Object Identifier
doi:10.1214/18-BA1109

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62P10: Applications to biology and medical sciences

Keywords
Bayesian design group sequential method multiple testing phase II clinical trial posterior probability type I error rate

Rights
Creative Commons Attribution 4.0 International License.

Citation

Shi, Haolun; Yin, Guosheng. Control of Type I Error Rates in Bayesian Sequential Designs. Bayesian Anal., advance publication, 23 June 2018. doi:10.1214/18-BA1109. https://projecteuclid.org/euclid.ba/1529719226


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