Bayesian modelling of biometrologic censored measurements for the determination of Biological Limit Values

Context
Biological Limit Values are often determined from the atmospheric reference values in modelling biological data obtained on a number of exposed subjects based on measurements of atmospheric exposure. However, often a large number of measurements are below the limit of quantification (LOQ).
Generally, models applied to this type of data are so-called mixed linear regression models, with main subject random effect, by which the biological log-transformed data (Y) are modelled as a function of the log-transformed exposure data (X). While standard "tobit"-type models can treat censored data Y, no method is available for X-censored data that are usually simply suppressed.
Method
The aim of this work is to propose and validate a statistical method taking into account exposure measurements under the LOQ, based on a Bayesian approach, modelling simultaneously distributions X and Y.
This method is validated by a simulation study in which between 20 and 50% of the measurements are censored.
We apply this method to a real exposure data set containing 268 measures of urinary chromium (61%
Results
Preliminary but incomplete simulation results do not seem to show a clear advantage of taking into account the censored X-values.

Conclusion
The proposed method allows the use of biological exposure measures below the LOQ that would otherwise have been excluded.