Data augmentation based estimation for the censored quantile regression neural network model

Quantile regression neural network (QRNN) model has received wide attentions in recent years to explore complex nonlinear problems. However, when the responses yi are subject to censoring (left censoring, right censoring and interval censoring might occur), predictions by using observed data, will lead to unbelievable results. Thus, new method for QRNN model with censored data is appealing. In this paper, we propose an iterative approach based on the data augmentation method for censored QRNN model estimation. Firstly the censored data are imputed through a data augmentation process, then the QRNN model is updated with the imputed data, finally we make predictions through the updated QRNN model. It is worth mentioning that simulation studies and real data illustrations show the superiority of our proposed method. Using the results based on full uncensored data as the benchmark, we compare the estimation efficiency of the proposed method with the existing ones. Our method outperforms others in terms of quantile loss and prediction interval width, yielding prediction results that are much closer to the benchmark. The proposed estimation method for censored QRNN model can be easily adapted to deal with different censoring types including left censoring, right censoring and interval censoring, remedying the defect that existing method is only suitable for right censoring type.