Efficient estimation for deep generalized accelerated hazards models with interval-censored data

For the analysis of interval-censored data, we propose a deep generalized accelerated hazards model. This model is designed to facilitate a detailed exploration of the relationship between various risk factors and the hazard associated with failure time. We develop a sieve maximum likelihood estimation procedure that combines deep neural networks and monotonic splines. By employing deep neural networks, we can effectively capture nonparametric effects, enabling a flexible and adaptive modeling approach for complex relationships. Under certain regularity conditions, we derive a nonasymptotic error bound for the resulting estimator and show that the finite-dimensional estimator is asymptotically normal and achieves the semiparametric efficiency. We conduct simulation studies to evaluate the finite-sample performance of the proposed approach. Furthermore, the proposed method is applied to the Atherosclerosis Risk in Communities study for practical illustration.