Putting background information about relative risks into conjugate prior distributions.

Area of Science:

• Epidemiology
• Biostatistics
• Bayesian statistical modeling

Background:

• Bayesian and empirical Bayes analyses commonly use multivariate normal or conjugate priors for relative risks.
• Specifying conjugate priors from background information on relative risks presents implementation challenges.
• Traditional methods using flattening constants can conflict with the true prior covariance structure of log relative risks.

Purpose of the Study:

• To describe problems in translating background information into conjugate priors for relative risks.
• To propose a solution for deriving conjugate priors consistent with the true prior covariance structure.
• To illustrate the method with a logistic regression analysis of neonatal-death risk.

Main Methods:

• Utilizing a data-augmentation approximation to the true log relative-risk prior.
• Deriving a conjugate prior that is consistent with the true prior covariance structure.
• Implementing a rescaling step to ensure the accuracy of the data-augmentation approximation.

Main Results:

• The proposed data-augmentation approximation method allows for the derivation of conjugate priors that respect the true prior covariance structure.
• A rescaling step is identified as necessary for maintaining the accuracy of this approximation.
• The method is demonstrated to be effective in a logistic regression model for neonatal-death risk.

Conclusions:

• A novel approach using data augmentation provides a more accurate method for specifying conjugate priors in Bayesian epidemiologic analyses.
• This method overcomes the limitations of traditional flattening constants, ensuring better alignment with the underlying data structure.
• Accurate prior specification is crucial for reliable inference in epidemiologic studies, particularly in risk assessment.