DAmcqrnn: An approach to censored monotone composite quantile regression neural network estimation

Abstract

Quantile regression neural network (QRNN) model has recently become popular in solving complex nonlinear problems, but the quantile curves achieved by QRNN model may cross each other, leading to unreliable results. To remedy this defect, monotone composite quantile regression neural network (MCQRNN) model is more attractive with non-crossing quantile predictions. However, few works have been involved in the literature to apply MCQRNN model for censoring issues. Based on the data augmentation algorithm, this study presents an iterative estimation method, which is a three-step alternating process, for censored MCQRNN model. Step 1 imputes the censored data through a data augmentation procedure. Step 2 updates the MCQRNN model with the imputed data. Step 3 makes predictions by the updated MCQRNN model. Simulation studies and real data application demonstrate that our proposed method is not only superior to the available censored methods with respect to quantile loss and C-index, but also yields very close prediction results to those obtained by full uncensored data. Avoiding the quantile crossing problem, the proposed method is more flexible to cope with different types of censoring, overcoming the limitation that the existing censored methods only work for single censoring type with unbelievable predictions caused by the crossing phenomenon.