Research article

Bayesian versus frequentist statistical inference for investigating a one-off cancer cluster reported to a health department

Michael D Coory^1,2 , Rachael A Wills² and Adrian G Barnett³

¹  School of Population Health, Mayne Medical School, University of Queensland, Herston, Australia

²  Statistical Analysis Unit, Queensland Department of Health, Brisbane, Australia

³  School of Public Health and Institute of Health and Biomedical Innovation, Queensland University of Technology, Kelvin Grove, Australia

author email corresponding author email

BMC Medical Research Methodology 2009, 9:30doi:10.1186/1471-2288-9-30

Published:	11 May 2009

Abstract

Background

The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods.

Methods

This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution.

Results

Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior.

Conclusion

In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.