New paper proves neural net convergence for current-status data

Current-status data arises in survival analysis when the exact event time is unobserved—only an indicator of whether the event occurred before a random examination time is known. This is common in medical and epidemiological follow-up studies. In their new paper (arXiv:2606.10119), Yuan Wu and Tianhui Zhou study a nonparametric neural-network sieve maximum likelihood estimator (NN-SMLE) for the conditional cumulative distribution function (CDF) of the event time. They combine approximation theory for rectified linear unit (ReLU) neural networks with empirical-process arguments to derive an explicit convergence rate under Hölder smoothness assumptions on the true conditional CDF.

This result is significant because it provides the first rigorous theoretical guarantee for using neural networks to estimate conditional distributions from current-status data, a notoriously difficult inverse problem. The convergence rate depends on the smoothness of the underlying function, the number of network parameters, and the sample size. Practically, this validates the use of flexible neural network models in settings like cancer progression or equipment failure where only interval-censored observations are available. The authors also note that the framework can be extended to inference procedures such as confidence bands, paving the way for more reliable AI-driven survival analysis.