A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data

Area of Science:

• Occupational Hygiene and Exposure Assessment
• Statistical Modeling
• Bayesian Inference

Background:

• Classical statistical methods for exposure data below detection limits are established.
• A comprehensive evaluation of Bayesian approaches for censored exposure data is lacking.
• Accurate analysis of exposure data is crucial for occupational health and safety.

Purpose of the Study:

• To describe a Bayesian framework for analyzing censored exposure data.
• To compare the performance of a Bayesian method with the β-substitution method.
• To evaluate methods for estimating exposure distribution parameters like mean and 95th percentile.

Main Methods:

• A simulation study was conducted using lognormal and mixed lognormal distributions.
• Datasets were generated with varying sample sizes, geometric standard deviations (GSDs), and censoring levels.
• Performance was assessed using relative bias, root mean squared error (rMSE), and coverage of uncertainty intervals.

Main Results:

• Bayesian and β-substitution methods showed comparable bias and rMSE for arithmetic and geometric means.
• The Bayesian method with non-informative priors had higher bias and rMSE for GSD and 95th percentile compared to β-substitution.
• Informative priors improved the Bayesian method's performance, making it more comparable to β-substitution.

Conclusions:

• The Bayesian method provides superior uncertainty estimates and coverage for key exposure parameters.
• Its advantage lies in providing full parameter distributions, aiding decision-making.
• The choice between methods depends on practitioner needs, prior information, and data characteristics; Bayesian methods are recommended with computational resources and prior data.