Bayesian Approaches to Ordinal Exposures with a Mixture of Berkson and Classical Measurement Error

Background: Exposures are occasionally only available in an aggregated form, such as an average physical exposure for each job title. When quantifying the relationship between an individual level outcome and a group level exposure, the variance estimates are contaminated with Berkson measurement error. If the aggregated exposures come from a separate sample, such as a job exposure matrix, the aggregated exposures will contain additional classical measurement error. While measurement error models exist for continuous and binary exposures, methods are less developed for aggregated ordinal exposures. Purpose: To develop Bayesian measurement error models for aggregated ordinal exposures and compare their performance to logistic regression models which ignore the measurement error. Methods: Several sets of 500 simulated data sets were created with exposures, outcomes, and covariates. These used a sample size of 1,000 and varied the number of groups and the odds ratios used for outcome simulation. Fully and partially Bayesian approaches were developed. The performance of these models based on measures of accuracy, bias, coverage, convergence, and power were compared to a naïve approach, which ignores measurement error, and a model using the simulated individual level exposure values. Results: When there was no relationship between the aggregated exposure and outcome, all models performed reasonably well in bivariate and multiple regression analyses. When there was a modest to strong relationship between exposure and outcome, the Bayesian models dominated the naïve approach across all performance metrics. Discussion: Bayesian approaches yield better model estimates with aggregated ordinal exposure data than a naïve approach.