Expostats: A Bayesian Toolkit to Aid the Interpretation of Occupational Exposure Measurements

Introduction: Interpretation of exposure measurements has evolved into a framework based on the lognormal distribution. Most available practical tools are based on traditional frequentist statistical procedures that do not satisfactorily account for censored data and are not amenable to simple probabilistic risk statements. Bayesian methods offer promising solutions to these challenges. Such methods have been proposed in the literature but are not widely and freely available to practitioners.

Methods: A set of computer applications were developed aimed at answering typical inferential questions that are important to occupational health practitioners: Is a group of workers compliant with an occupational exposure limit? Are some individuals within this group likely to experience substantially higher exposure than its average member? How does an intervention influence the distribution of exposures? These questions were addressed using Bayesian models, simultaneously accounting for left, right, and interval-censored data with multiple censoring points. The models are estimated using the JAGS Gibbs sampler called through the R statistical package.

Results: The Expostats toolkit is freely available from www.expostats.ca as four tools accessible through a Web application, an offline standalone application or algorithms. The tools include a variety of calculations and graphical outputs useful according to current practices in analysis and interpretation of exposure measurements collected by occupational hygienists. Tool1 and its simplified version Tool1 Express focus on inferences from data from a similarly exposed group. Tool2 evaluates within- and between-worker components of variability, as well as the probability that an individual worker might be overexposed. Tool3 compares exposure data across groups, e.g. evaluates the effect of an intervention. Uncertainty management includes the calculation of credible intervals and produces probabilistic statements about the exposure metrics (e.g. probability that over 5% of exposures are above a limit).

Discussion: Expostats is the first freely available toolkit that leverages the flexibility of Bayesian analysis to perform an extensive list of calculations recommended in several international guidelines on the practice of occupational hygiene.