Modeling of long-term survival data with unobserved dispersion via neural network

Traditional models in survival analysis assume that every subject will eventually experience the event of interest in the study, such as death or disease recurrence; thus, the survival function is said to be proper. The cure rate model, which was first proposed seven decades ago, accounts for the presence of a fraction of individuals who will never experience the occurrence of the event of interest, referred to as the cure fraction. This cure fraction can be conceptualized as immune or cured subjects in the context of cancer treatment. In the literature, various cure rate models have been widely studied and commonly applied to structured data with a limited number of covariates. Recently, the use of convolutional neural networks, a powerful deep learning technique for image processing, has become increasingly common in the medical field. Medical images, such as histological slides and magnetic resonance images, are directly related to a patient’s prognostic factors. Therefore, it is reasonable to introduce these images as predictors in cure models. In this work, we extend the article by Xie and Yu (Stat Med 40(15):3516–3532, 2021. https://doi.org/10.1002/sim.8980 ), which employed a neural network to model the effect of unstructured predictors in the promotion time cure model setting for cases involving overdispersed data. We refer to our extension as the integrated negative binomial cure rate model, with its parameters estimated through the Expectation–Maximization algorithm.