Bayesian credible sets for the risk difference in binomial data with a fallible classifier and a gold standard

Abstract

We consider two-sample binary data consisting of two independent studies. One study is the main study where individuals are classified using a fallible classifier prone to error; the other study is a validation study where individuals are classified using both the fallible classifier and a gold standard which does not misclassify individuals. For such data, we propose a Bayesian model for making statistical inference for all model parameters and particularly the risk difference. We derive a closed-form algorithm for sampling from the posterior distribution. We then illustrate our algorithm using a real data example and conduct Monte Carlo simulation studies to show that our algorithm performs very well under various scenarios.

Keywords:

• Bayesian credible interval
• binary data
• double sampling
• misclassification
• risk difference

Acknowledgements

The authors would like to acknowledge the assistance of the Biostatistics Shared Resource at the Harold C. Simmons Cancer Center, which is supported in part by an NCI Cancer Center Support Grant, 1P30 CA142543-01. In addition, the authors thank the referees and the associate editor for their thoughtful and constructive comments which have improved the presentation of this article.