A multiple imputation method based on weighted quantile regression models for longitudinal censored biomarker data with missing values at early visits

MinJae Lee, Mohammad H. Rahbar, Matthew Brown, Lianne Gensler, Michael Weisman, Laura Diekman, John D. Reveille

In patient-based studies, biomarker data are often subject to left censoring due to the detection limits, or to incomplete sample or data collection. In the context of longitudinal regression analysis, inappropriate handling of these issues could lead to biased parameter estimates. We developed a specific multiple imputation (MI) strategy based on weighted censored quantile regression (CQR) that not only accounts for censoring, but also missing data at early visits when longitudinal biomarker data are modeled as a covariate. We assessed through simulation studies the performances of developed imputation approach by considering various scenarios of covariance structures of longitudinal data and levels of censoring. We also illustrated the application of the proposed method to the Prospective Study of Outcomes in Ankylosing spondylitis (AS) (PSOAS) data to address the issues of censored or missing C-reactive protein (CRP) level at early visits for a group of patients. Our findings from simulation studies indicated that the proposed method performs better than other MI methods by having a higher relative efficiency. We also found that our approach is not sensitive to the choice of covariance structure as compared to other methods that assume normality of biomarker data. The analysis results of PSOAS data from the imputed CRP levels based on our method suggested that higher CRP is significantly associated with radiographic damage, while those from other methods did not result in a significant association. The MI based on weighted CQR offers a more valid statistical approach to evaluate a biomarker of disease in the presence of both issues with censoring and missing data in early visits.