Mixture cure rate models with neural network estimated nonparametric components

Survival data including potentially cured subjects are common in clinical studies and mixture cure rate models are often used for analysis. The non-cured probabilities are often predicted by non-parametric, high-dimensional, or even unstructured (e.g. image) predictors, which is a challenging task for traditional nonparametric methods such as spline and local kernel. We propose to use the neural network to model the nonparametric or unstructured predictors’ effect in cure rate models and retain the proportional hazards structure due to its explanatory ability. We estimate the parameters by Expectation–Maximization algorithm. Estimators are showed to be consistent. Simulation studies show good performance in both prediction and estimation. Finally, we analyze Open Access Series of Imaging Studies data to illustrate the practical use of our methods.