Mixed Models and Empirical Bayes Estimation for Retrospective Exposure Assessment of Dust Exposures in Canadian Sawmills

Abstract

Data on job histories is commonly available from study subjects and worksites, therefore jobs are often used for assigning exposures in historical epidemiological studies. Exposure estimates are often derived by offering jobs as fixed effects in statistical models. An alternative approach would be to offer job as a random effect to obtain empirical Bayes estimates of exposure. This approach is more efficient since it weights exposure estimates according to the within-job and between-job variability and the number of measurements for each job. We assess three models for predicting historical dust exposures of sawmill workers. Models were developed using 407 inhalable dust measurements collected from 58 jobs in four sawmills. The first model incorporated all variables as fixed effects; the second added a random term to account for correlation within workers; and the third offered random terms for worker, job and mill (hierarchical model). Empirical Bayes estimates were used to calculate job-specific exposures from the hierarchical model. The fixed effects and random worker mixed models performed nearly identically because there was low within-worker correlation (r = 0.26). The Bayesian exposure predictions from the hierarchical model were slightly more correlated with the observed mill-job arithmetic means than those from the models where jobs were fixed effects (0.74 versus 0.70). While we observed no large differences in exposure estimates by treating job as a fixed or random effect, treating job as a random effect allowed for job-specific coefficients to be estimated for every job while borrowing strength in the presence of sparse data by assuming that the job means are normally distributed around the group mean. In addition, empirical Bayes job estimates can be used for a posteriori job grouping. The use of this method for retrospective exposure assessment should continue to be examined.