Quantile regression for longitudinal biomarker data subject to left censoring and dropouts

Quantile regression is increasingly used in biomarker analysis to handle nonnormal or heteroscedastic data. However, in some biomedical studies, the biomarker data can be censored by detection limits of the bioassay or missing when the subjects drop out from the study. Inappropriate handling of these two issues leads to biased estimation results. We consider the censored quantile regression approach to account for the censoring data and apply the inverse weighting technique to adjust for dropouts. In particular, we develop a weighted estimating equation for censored quantile regression, where an individual's contribution is weighted by the inverse probability of dropout at the given occasion. We conduct simulation studies to evaluate the properties of the proposed estimators and demonstrate our method with a real data set from Genetic and Inflammatory Marker of Sepsis (GenIMS) study.