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

• Published in: Journal of exposure science & environmental epidemiology Vol. 31; no. 6; pp. 1057 - 1066
• Main Authors: Chen, I-Chen, Bertke, Stephen J., Curwin, Brian D.
• Format: Journal Article
• Language: English
• Published: New York Nature Publishing Group US 01.11.2021; Nature Publishing Group
• Subjects: Bias; Computer Simulation; Distribution (Probability theory); Epidemiology; Exposure; Humans; Limit of Detection; Medical research; Medicine; Medicine & Public Health; Medicine, Experimental; Methods; Modelling; Models, Statistical; Normal distribution; Occupational exposure; Occupational health; Occupational health and safety; Parameter estimation; Quantile regression; Quantiles; Regression models; Skewness; Standard deviation; Within-subjects design; United States; Limit of detection; Repeated measures; Occupational exposure; Left censoring; Quantile regression model; Right skewness
• ISSN: 1559-0631; 1559-064X; 1559-064X
• DOI: 10.1038/s41370-021-00345-1

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.