Deep learning for regression analysis of interval-censored data

Abstract

This paper discusses regression analysis of interval-censored failure time data, and a new deep learning approach is proposed under the partially linear Cox model. For the analysis, we need to overcome theoretical and computational challenges arising from complex data structure where the partial likelihood function is no longer available. We propose to use a deep neural network and a B-spline function for approximating the nonlinear component and the baseline cumulative hazard function in the model, respectively. The proposed approach is flexible and able to circumvent the curse of dimensionality. At the same time, it facilitates the interpretability of covariate effects. The asymptotic properties of the resulting estimators are established. In particular, the finite-dimensional estimator of covariate effects is asymptotically normal and attains the semiparametric efficiency, while the deep nonparametric estimator achieves the minimax optimal rate of convergence. A simulation study is conducted to assess the finite-sample performance of the proposed approach and indicates that it works well in practical situations. Finally, the proposed method is applied to a set of real data that motivated this study.