Partial Linear Cox Model with Deep ReLU Networks for Interval-Censored Failure Time Data

The partial linear Cox model for interval-censoring is well-studied under the additive assumption but is still under-investigated without this assumption. In this paper, we propose to use a deep ReLU neural network to estimate the nonparametric components of a partial linear Cox model for interval-censored data. This model not only retains the nice interpretability of the parametric component but also improves the predictive power compared to the partial linear additive Cox model. We derive the convergence rate of the proposed estimator and show that it can break the curse of dimensionality under some certain smoothness assumptions. Based on such rate, the asymptotic normality and the semiparametric efficiency are also established. Intensive simulation studies are carried out to demonstrate the finite sample performance on both estimation and prediction. The proposed estimation procedure is illustrated on a real dataset.