Reducing Monte Carlo error in the Bayesian estimation of risk ratios using log-binomial regression models.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Logistic regression is commonly used for binary outcomes in cohort studies.
• It is inappropriate for estimating risk ratios with common outcomes.
• Log-binomial regression is a preferred alternative but presents estimation challenges.

Purpose of the Study:

• To address the difficulties in estimating log-binomial regression coefficients.
• To improve the accuracy of risk ratio estimation using Bayesian methods.
• To reduce Markov chain Monte Carlo (MCMC) errors in posterior inference.

Main Methods:

• A Bayesian approach to log-binomial regression was employed.
• A novel reparameterization based on a Poisson model was introduced.
• A sampling algorithm was developed and coded in R to reduce simulation correlation and improve accuracy.

Main Results:

• Bayesian methods offer a more straightforward approach to log-binomial regression compared to frequentist methods.
• The proposed reparameterization and R-coded algorithm resulted in smaller mean squared errors for risk ratio estimation.
• The new methods demonstrated reduced correlation and improved accuracy in posterior inference approximations.

Conclusions:

• The proposed Bayesian method with a Poisson-based reparameterization and R algorithm enhances the estimation of risk ratios from log-binomial models.
• This approach mitigates issues associated with traditional Bayesian implementations using WinBUGS and MCMC.
• The findings provide a more accurate and reliable statistical tool for epidemiological research involving common binary outcomes.