A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring

Area of Science:

• Occupational health and safety
• Environmental science
• Statistical modeling

Background:

• Direct reading instruments provide real-time exposure measurements but face performance limitations.
• Statistical analysis of exposure time-series data is challenged by autocorrelation, non-stationary series, and left-censoring due to the limit-of-detection (LOD).

Purpose of the Study:

• To propose a Bayesian framework to model workplace factors affecting exposure using real-time data.
• To account for non-stationary autocorrelation and LOD issues in exposure time-series data.
• To estimate summary statistics for tasks and covariates with improved accuracy.

Main Methods:

• A spline-based approach was employed to model non-stationary autocorrelation.
• Left-censoring was handled by integrating over the left tail of the distribution.
• The model was fitted using Markov-Chain Monte Carlo (MCMC) within a Bayesian paradigm, implemented in R using the rjags package.

Main Results:

• The Bayesian model demonstrated lower root mean squared errors and less biased standard deviations compared to frequentist models across varying LOD levels.
• Task means were similar between Bayesian and frequentist models, but standard deviations differed.
• Parameter estimates for covariates showed discrepancies, with Bayesian credible intervals often containing zero where frequentist models indicated significance.

Conclusions:

• The proposed Bayesian model offers a robust approach for analyzing exposure time-series data with non-stationary autocorrelation and LOD.
• It provides less biased estimates and better performance characteristics for task means, standard deviations, quantiles, and covariate parameters.
• This hierarchical modeling framework enhances the analysis of real-time exposure data in occupational settings.