Mixture cure rate model with artificial neural network for interval-censored data

Mixture cure rate models represent a valuable tool to delineate the presence of a cured subgroup in the entire population under study. Among the vast literature, a popular research line is to regress the probability of an individual being cured on covariates through a parametric model, such as the logistic model. However, when the assumed parametric model is mis-specified, one could only attain a biased parameter estimate. In this work, motivated by the robustness and powerful approximation ability of neural networks, we offer a flexible mixture cure rate modeling approach for analyzing interval-censored data, which arise frequently in many scientific fields involving periodic follow-up or cross-sectional screening. In particular, we utilize the artificial neural network to model the cured probability and the proportional hazards model to characterize the latent event time distribution related to uncured individuals. After approximating the cumulative baseline hazard function with monotone splines, we develop a stable expectation-maximization algorithm coupled with a multiple imputation strategy and resilient backpropagation to locate the sieve maximum likelihood estimator. We establish the consistency and convergence rate of the proposed sieve estimator, as well as the asymptotic normality and semiparametric efficiency of the regression parameter estimator. Simulation experiments demonstrate that our proposed method works well and substantially outperforms the comparative methods. We then apply the proposed method to a real-world data set, revealing new findings and a better predictive performance.