Design and analysis of Bayesian adaptive crossover trials for evaluating contact lens safety and efficacy

Quan Zhang, Youssef Toubouti, Brad Carlin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A crossover study, also referred to as a crossover trial, is a form of longitudinal study. Subjects are randomly assigned to different arms of the study and receive different treatments sequentially. While there are many frequentist methods to analyze data from a crossover study, random effects models for longitudinal data are perhaps most naturally modeled within a Bayesian framework. In this article, we introduce a Bayesian adaptive approach to crossover studies for both efficacy and safety endpoints using Gibbs sampling. Using simulation, we find our approach can detect a true difference between two treatments with a specific false-positive rate that we can readily control via the standard equal-tail posterior credible interval. We then illustrate our Bayesian approaches using real data from Johnson & Johnson Vision Care, Inc. contact lens studies. We then design a variety of Bayesian adaptive predictive probability crossover studies for single and multiple continuous efficacy endpoints, indicate their extension to binary safety endpoints, and investigate their frequentist operating characteristics via simulation. The Bayesian adaptive approach emerges as a crossover trials tool that is useful yet surprisingly overlooked to date, particularly in contact lens development.

Original languageEnglish (US)
Pages (from-to)1216-1236
Number of pages21
JournalStatistical methods in medical research
Issue number3
StatePublished - Jun 1 2017


  • Bayesian inference
  • Markov chain Monte Carlo
  • crossover trial
  • device efficacy
  • device safety


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