Quantile regression for exposure data with repeated measures in the presence of non-detects.

Background: Exposure data with repeated measures from occupational studies are frequently right-skewed and left-censored. To address right-skewed data, data are generally log-transformed and analyses modeling the geometric mean operate under the assumption the data are log-normally distributed. However, modeling the mean of exposure may lead to bias and loss of efficiency if the transformed data do not follow a known distribution. In addition, left censoring occurs when measurements are below the limit of detection (LOD).

Objective: To present a complete illustration of the entire conditional distribution of an exposure outcome by examining different quantiles, rather than modeling the mean.

Methods: We propose an approach combining the quantile regression model, which does not require any specified error distributions, with the substitution method for skewed data with repeated measurements and non-detects.

Results: In a simulation study and application example, we demonstrate that this method performs well, particularly for highly right-skewed data, as parameter estimates are consistent and have smaller mean squared error relative to existing approaches.

Significance: The proposed approach provides an alternative insight into the conditional distribution of an exposure outcome for repeated measures models.