Estimation of C-Index for cox proportional hazards model with censored biomarker covariate subject to limits of detection

Biomarkers play an important role to predict the time to event of interest. To evaluate the prediction performance of biomarkers, Cox proportional hazards model and Harrells C-index have been widely used. However, when some of the biomarker measurements are not fully observed due to detection limits of given instrument, evaluation may become complicated. We estimate the Cox model and concordance probability in the presence of censored biomarker data. Simulation study demonstrates that the proposed method outperforms over the simple ad hoc method. Our approach is especially useful to evaluate discrimination potential of the biomarker regardless of variant detection limits.