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

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).

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

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.

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.

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