Bayesian Hierarchical Modelling of Individual Expert Assessments in the Development of a General-Population Job-Exposure Matrix

The CANJEM job-exposure matrix compiles expert evaluations of 31 673 jobs from four populationbased case-control studies conducted in Montreal. For each job, experts had derived indices of intensity, frequency, and probability of exposure to 258 agents. CANJEM summarizes the exposures assigned to jobs into cells defined by occupation/industry, agent, and period. Some cells may, however, be less populated than others, resulting in uncertain estimates. We developed a modelling framework to refine the estimates of sparse cells by drawing on information available in adjacent cells. Bayesian hierarchical logistic and linear models were used to estimate the probability of exposure and the geometric mean (GM) of frequency-weighted intensity (FWI) of cells, respectively. The hierarchy followed the Canadian Classification and Dictionary of Occupations (CCDO) classification structure, allowing for exposure estimates to be provided across occupations (seven-digit code), unit groups (four-digit code), and minor groups (three-digit code). The models were applied to metallic dust, formaldehyde, wood dust, silica, and benzene, and four periods, adjusting for the study from which jobs were evaluated. The models provided estimates of probability and FWI for all cells that pulled the sparsely populated cells towards the average of the higher-level group. In comparisons stratified by cell sample size, shrinkage of the estimates towards the group mean was marked below 5 jobs/cell, moderate from 5 to 9 jobs/cell, and negligible at >= 10 jobs/cell. The modelled probability of three-digit cells were slightly smaller than their descriptive estimates. No systematic trend in between-study differences in exposure emerged. Overall, the modelling framework for FWI appears to be a suitable approach to refine CANJEM estimates. For probability, the models could be improved by methods better adapted to the large number of cells with no exposure.