Bayesian Simultaneous Credible Intervals for Effect Measures from Multiple Markers

Abstract

Inference from multiple markers is often encountered in biomedical research, especially when comparing treatments. Most common statistical methods rely on hypothesis testing with null hypothesis of no effect for each marker and methods based on closed testing for getting the combined p-value. This article proposes the use of simultaneous credible intervals obtained from the joint posterior distribution of effect measures of multiple markers for combined inference. The advantage of this method is that it finds the actual effect sizes and also allows different types of effect measures for various markers. We used equal tailed intervals and highest posterior density regions for effect measures of multiple markers. Simulation studies were carried out to examine frequentist properties of these simultaneous credible regions. These studies revealed that the inference based on simultaneous intervals can be different than the inference based on individual marker. The method is demonstrated through two case studies: (a) an observational study of wet age-related macular degeneration (wet-AMD); and (b) reanalysis of a randomized controlled trial for treatment of migraine. The wet-AMD observational study was the motivation for the present research.

KEYWORDS:

• Bayesian joint posterior distribution
• Equal tailed credible interval
• Highest posterior density regions
• Simultaneous inference

Disclosure Statement

The authors report that there are no competing interests to declare.

Acknowledgments

We thank Juuso Silvennoinen (University of Helsinki) for the technical help provided during development of R-shiny app. We would like to thank the associate editor and the reviewers for their constructive comments.

Additional information

Funding

The first author acknowledges support by the research mobility grant [number 33137] awarded by the Academy of Finland. The second author’s work was supported by the Finnish Eye Foundation, Helsinki, Finland; the Eye and Tissue Bank Foundation, Helsinki, Finland; Finnish Ophthalmological Society, Helsinki, Finland; the Evald and Hilda Nissi Foundation, Helsinki, Finland. The third author’s work was supported by The HUS research funds, under grant [number Y202011401].