A Bayesian approach to logistic regression models having measurement error following a mixture distribution

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Logistic regression is widely used for binary outcomes.
• Measurement error in predictor variables can bias parameter estimates.
• Accurate risk assessment requires addressing predictor measurement error.

Purpose of the Study:

• To develop and apply a Bayesian method for logistic regression with measurement error.
• To estimate the risk of breast cancer associated with alcohol consumption, accounting for reporting inaccuracies.
• To compare results with standard logistic regression that ignores measurement error.

Main Methods:

• Bayesian approach averaging true logistic probability over conditional posterior distribution.
• Modeling measurement error with mixture distributions when error form varies with exposure.
• Utilizing data from the Nurses Health Study, including a subsample for measurement error estimation.

Main Results:

• Measurement error estimation revealed discrepancies between true and reported alcohol consumption.
• Some individuals reporting no alcohol consumption were identified as true non-drinkers.
• Risk estimates for alcohol-breast cancer link significantly differed from standard logistic regression results.

Conclusions:

• The proposed Bayesian method effectively adjusts for measurement error in logistic regression.
• Ignoring measurement error can lead to substantially different conclusions about risk factors.
• Accurate estimation of exposure-disease relationships necessitates accounting for data inaccuracies.