Calibration confidence regions for asbestos fibers with heteroscedasticity and interlaboratory variability

ABSTRACT

It is well known that asbestos exposure causes mesothelioma and asbestosis. We present statistical methodologies for analyzing airborne asbestos fiber counts measured by transmission electron microscopy. We observed from multiple laboratories that the variability of asbestos measurements increases with the true concentration levels. In order to account for the heteroscedasticity and between-laboratories variation of asbestos fiber counts, we use a two-component mixed model as well as a gamma mixed model. We construct calibration confidence regions for unknown true measurements borrowing strength from multiple laboratories. The performances of our calibration confidence regions and their robustness are studied via simulation. To illustrate our results, we analyze a real data set of amosite asbestos.

KEYWORDS:

• Two-component mixed model
• gamma mixed model
• Wilson–Hilferty approximation
• iteratively rewieghted maximum marginal likelihood
• maximum marginal likelihood

AMS SUBJECT CLASSIFICATION:

• 62F25