Bayesian Method for Improving Logistic Regression Estimates under Group-Based Exposure Assessment with Additive Measurement Errors

ABSTRACT

The group-based exposure assessment has been widely used in occupational epidemiology. When the sample size used to estimate group means is “large”, this leads to negligible attenuation in the estimation of odds ratio. However, the bias is proportional to the between-subject variability and is affected by the difference in true group means. We explore a Bayesian method, which adjusts in a natural way for the extra uncertainty in the outcome model associated with using the predicted values as exposures. We aim to improve the estimate obtained in naïve analysis by exploiting the properties of Berkson type error structure. We consider cases where differences in the proximity of group means and the between-subject variance are both large. The results of the simulations show that our Bayesian measurement error adjustment method that follows group-based exposure assessment improves estimates of odds ratios when the between-subject variance is large and group means are far apart.

KEYWORDS:

• Bayesian
• Monte Carlo Markov Chain
• logistic regression
• group-based exposure assessment
• Berkson type measurement error
• semi-ecological design

Acknowledgments

Igor Burstyn received salary support from the Alberta Heritage Foundation for Medical Research as a Population Health Investigator. This research was supported by a grant from the Canadian Institutes for Health Research. Michele Hamm edited and proofread the manuscript.

Notes

MSE = precision + bias²