Deep Variational Frailty Models for Survival Prediction Under Dependent Censoring

Most survival models assume that censoring is uninformative about event time given observed covariates, an assumption that fails when unobserved factors drive both event and censoring times. Such dependence cannot be identified from right-censored data without structural assumptions. We propose the Deep Variational Frailty Model (DVFM), which jointly models event and censoring times through a shared latent frailty and nonlinear conditional decoders rather than a prespecified copula family. DVFM is trained with a $\beta$-regularized censored-data variational objective and amortized inference. DVFM is neither an assumption-free identification method nor a test for dependent censoring, but a predictive model for settings where shared frailty plausibly explains the dependence. On synthetic and semi-synthetic benchmarks, DVFM matches the strongest dependent-censoring baseline and a Cox-Gamma frailty model on IBS and MAE, and outperforms four frailty-free models that assume independent censoring by 21-35% within a dataset. It also recovers subject-level frailty better than scalar frailty baselines, mainly on censored subjects, whose censoring times other models treat as uninformative. A matched ablation without the latent ($d_z=0$) shows that the latent drives the gains under dependence in synthetic data, while on semi-synthetic data its benefit is dataset-dependent: it lowers IBS on seven of twelve datasets, by 10-25% on four, and raises it by about 8% on two. On real data, where we predict time to death in ALS patients, the latent improves held-out log-likelihood.