What Can Survival Models Recover After Transfer Between Hospitals?

Clinical risk models supporting personalized oncological decisions are survival models: they estimate the probability that a patient experiences the event of interest before a fixed horizon. Their performance often drops when they are transferred to a new center where they were not trained. Domain adaptation and domain generalization are the standard remedies, but previous studies show that a drop can persist. Poor target performance admits two explanations: the target covariates no longer carry outcome-relevant information, or they still do, but the method fails to exploit them. These cases have different implications, yet standard benchmarks report only final target performance, without establishing what is attainable from the target covariates when target labels are available. Survival prediction also requires the model to preserve both the ranking of patients by risk (discrimination, AUROC) and the accuracy of the predicted probabilities (calibration, ECE), and a shift can degrade one while leaving the other intact. We introduce SHIFT-SURV, a controlled benchmark for multi-center survival prediction. Each center $d$ is a parameter tuple $\Theta_d$; latent factors $u_{i,d} = (u^{\mathrm{inv}}, u^{\mathrm{spu}})$ split into an invariant $u^{\mathrm{inv}}$ and a spurious $u^{\mathrm{spu}}$ block, with $u_{i,d} \sim \mathcal{N}(\mu_d, \Sigma_d)$. The relationship between the observed variables and the clinical outcome is the following: $$ x_{i,d} = A_d u_{i,d} + \varepsilon_{i,d} \qquad T_{i,d} \mid u_{i,d}^{\mathrm{inv}} \sim \mathrm{Weibull}(\lambda_{0,d}, \nu_d, \eta_{i,d} = \beta_{0,d} + w_d^{\top} u_{i,d}^{\mathrm{inv}}) \qquad Y_{i,d}^{(\tau)} = \mathbf{1}[T_{i,d} \leq \tau] $$ Only $u^{\mathrm{inv}}$ drives the event time; $u^{\mathrm{spu}}$ becomes predictive only through the center-specific cross-covariance in $\Sigma_d$. The map $A_d$ is the observation process, $(\lambda_{0,d}, \nu_d)$ the absolute event rate, $w_d$ the predictor–outcome relationship. We define and test our generator on a set of shifts, i.e., changes to one of the above-mentioned parameters, namely covariate, measurement, spurious-association, baseline-hazard, label-prior, and concept. We compare adaptation and generalization methods (CORAL, DANN, CDAN, IW-ERM, IRM, GroupDRO) and post-hoc recalibration against ERM and two references: a latent-feature oracle fitted to the true invariant factors and a target-data oracle fitted to the target labels. Their gap is the outcome signal removed by the observation process; the gap between the target-data oracle and ERM is the remaining margin that a method failed to recover. Generator parameters are set so that ERM AUROC and outcome prevalence match the ranges seen across real centers, and gains below 0.02 AUROC are considered to be not relevant. Regarding discrimination, only two of the six regimes leave a recoverable margin large enough for a failure to be a limitation of the method rather than of the transfer. In the other four, ERM already reaches the discrimination that the target covariates support, so failing to improve on it is uninformative. The two informative regimes leave margins of 0.105 AUROC under measurement shift and 0.163 under concept shift; the best method closes less than 2% of either. Across all regimes, the largest mean gain over ERM is +0.003 AUROC ($p = 0.47$, exact sign-flip test); IRM and GroupDRO, trained on three source centers, perform comparably. Calibration behaves differently, improving significantly in three regimes: under label-prior shift, prior adjustment recovers most of the available margin, cutting calibration error from 0.217 to 0.088 against 0.060 for the oracle. The pattern holds on real data: across the six centers of I3LUNG, an immunotherapy cohort of 2075 patients, and on a public breast-cancer registry, no method improves discrimination over ERM, and the best method per target center still leaves an upper 95% limit well below the margin. SHIFT-SURV turns a transfer failure into a measurable question: the two references indicate whether the target covariates still carry the outcome signal, and whether a clinical team should change method or data.