Median regression for longitudinal left-censored biomarker data subject to detection limit

Biomarkers are often measured repeatedly in biomedical studies to help understand the development of the disease, identify the patients at high risk, and guide therapeutic strategies for intervention. One common source of measurement error for biomarkers is left-censoring because the assays used may not be sensitive enough to measure concentrations below a detection limit. Likelihood-based approaches that assume multivariate normal distributions have been proposed to account for the left-censoring problem; however, biomarker data are often highly skewed even after transformation. We propose a median regression model that requires minimal assumptions on the distribution and leads to easier interpretation of results in the data's original scale. We develop estimating procedures that incorporate correlations between serial measurements for left-censored longitudinal data. We conduct simulation studies to evaluate the properties of the proposed estimators and to compare median regression models with mixed models under various specifications of distributions and covariance structures. Finally, we demonstrate our method with a dataset from the Genetic and Inflammatory Markers of Sepsis (GenIMS) study.