  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.
