Robust exchangeability designs for early phase clinical trials with multiple strata

Pharm Stat. Mar-Apr 2016;15(2):123-34. doi: 10.1002/pst.1730. Epub 2015 Dec 18.


Clinical trials with multiple strata are increasingly used in drug development. They may sometimes be the only option to study a new treatment, for example in small populations and rare diseases. In early phase trials, where data are often sparse, good statistical inference and subsequent decision-making can be challenging. Inferences from simple pooling or stratification are known to be inferior to hierarchical modeling methods, which build on exchangeable strata parameters and allow borrowing information across strata. However, the standard exchangeability (EX) assumption bears the risk of too much shrinkage and excessive borrowing for extreme strata. We propose the exchangeability-nonexchangeability (EXNEX) approach as a robust mixture extension of the standard EX approach. It allows each stratum-specific parameter to be exchangeable with other similar strata parameters or nonexchangeable with any of them. While EXNEX computations can be performed easily with standard Bayesian software, model specifications and prior distributions are more demanding and require a good understanding of the context. Two case studies from phases I and II (with three and four strata) show promising results for EXNEX. Data scenarios reveal tempered degrees of borrowing for extreme strata, and frequentist operating characteristics perform well for estimation (bias, mean-squared error) and testing (less type-I error inflation).

Keywords: Bayesian; between-strata heterogeneity; exchangeability-nonexchangeability; hierarchical model; pooling; shrinkage; stratification.

MeSH terms

  • Clinical Trials, Phase I as Topic / methods
  • Clinical Trials, Phase I as Topic / statistics & numerical data*
  • Clinical Trials, Phase II as Topic / methods
  • Clinical Trials, Phase II as Topic / statistics & numerical data*
  • Data Interpretation, Statistical*
  • Humans
  • Models, Theoretical*
  • Research Design / statistics & numerical data