Multiple imputation and quantile regression methods for biomarker data subject to detection limits

Biomarkers are increasingly used in biomedical studies to better understand the natural history and development of a disease, identify the patients at high-risk and guide the therapeutic strategies for intervention. However, the measurement of these markers is often limited by the sensitivity of the given assay, resulting in data that are censored either at the lower limit or upper limit of detection. Ignoring censoring issue in any analysis may lead to the biased results.;For a regression analysis where multiple censored biomarkers are included as predictors, we develop multiple imputation methods based on Gibbs sampling approach. The simulation study shows that our method significantly reduces the estimation bias as compared to the other simple imputation methods when the correlation between markers is high or the censoring proportion is high.;The likelihood based mean regression for repeatedly measured biomarkers often assume a multivariate normal distribution that may not hold for biomarker data even after transformations. We consider a robust alternative, median regression, for censored longitudinal data. We develop an estimating equation approach that can incorporate the serial correlations between repeated measurements. We conduct simulation studies to evaluate the proposed estimators and compare median regression model with the mixed models under various specifications of distributions and covariance structures.;Missing data is a common problem with longitudinal study. Under the assumptions that the missing pattern is monotonic and the missingness may only depend on the observed data, we propose a weighted estimating equation approach for the censored quantile regression models. The contribution of each individual to the estimating equation is weighted by the inverse probability of dropout at the given occasion. The resultant regression estimators are consistent when the dropout process is correctly specified. The performance of our estimating procedure is evaluated via simulation study.;We illustrate all the proposed methods using the biomarker data of the Genetic and Inflammatory Markers of Sepsis (GenIMS) study. Appropriate handling of censored data in biomarker analysis is of public health importance because it will improve the understanding of the biological mechanisms of the underlying disease and aid in the successful development of future effective treatments.