Bayesian Hierarchical Modelling of Historical Data of the South African Coal Mining Industry for Compliance Testing

Bayesian hierarchical framework for exposure data compliance testing is highly recommended in occupational hygiene. However, it has not been used for coal dust exposure compliance testing in South Africa (SA). The Bayesian analysis incorporates prior information, which increases solid decision making regarding risk management. This study compared the posterior 95th percentile (P95) of the Bayesian non-informative and informative prior from historical data relative to the occupational exposure limit (OEL) and exposure categories, and the South African Mining Industry Code of Practice (SAMI CoP) approach. A total of nine homogenous exposure groups (HEGs) with a combined 243 coal mine workers’ coal dust exposure data were included in this study. Bayesian framework with Markov chain Monte Carlo (MCMC) simulation to draw a full P95 posterior distribution relative to the OEL was used to investigate compliance. We obtained prior information from historical data and employed non-informative prior distribution to generate the posterior findings. The findings were compared to the SAMI CoP. The SAMI CoP 90th percentile (P90) indicated that one HEG was compliant (below the OEL), while none of the HEGs in the Bayesian methods were compliant. The analysis using non-informative prior indicated a higher variability of exposure than the informative prior according to the posterior GSD. The median P95 from the non-informative prior were slightly lower with wider 95% credible intervals (CrI) than the informative prior. All the HEGs in both Bayesian approaches were in exposure category four (poorly controlled), with the posterior probabilities slightly lower in the non-informative uniform prior distribution. All the methods mainly indicated non-compliance from the HEGs. The non-informative prior, however, showed a possible potential of allocating HEGs to a lower exposure category, but with high uncertainty compared to the informative prior distribution from historical data. Bayesian statistics with informative prior derived from historical data should be highly encouraged in coal dust overexposure assessments in South Africa for correct decision making.