Journal
STATISTICAL SCIENCE
Volume 24, Issue 3, Pages 328-342Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/09-STS305
Keywords
Bayesian analysis; bias; confounding; epidemiology; hierarchical prior; identifiability; interval coverage; observational studies
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Funding
- Natural Sciences and Engineering Research Council of Canada
- Canadian Institutes for Health Research [62863]
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We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in clean or textbook contexts. We then turn attention to observational-data situations which are messy, where modeling that acknowledges the limitations of study design and data collection leads to nonidentifiability. We argue, via a series of examples, that Bayesian interval estimation is an attractive way to proceed in this context even for frequentists, because it can be supplied with a diagnostic in the form of a calibration-sensitivity simulation analysis. We illustrate the basis for this approach in a series of theoretical considerations, simulations and an application to a study of silica exposure and lung cancer.
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