Survival models stop at a risk score: ODDS-DR rewrites outputs as additive log-odds and sweeps a full risk trajectory in two backward passes

A survival model's output becomes a quantity that is continuous in time and additive in log-odds, so the predicted distribution itself decomposes into feature contributions instead of needing a separate explanation step. Distributional regression previously emitted location, scale and shape parameters that vary with the distribution family and do not align with clinical concepts; model-agnostic explainers could attribute post hoc but rely on repeated sampling, are costly and are brittle under nonlinearity. On two real clinical cohorts, ODDS-DR matches or exceeds baselines including DeepSurv, Cox-Time, DeepHit, DSM and CoxNAM: the log-logistic variant reaches a C-index of 0.83 (0.82–0.83) on SUPPORT2, the Gaussian variant 0.66 (0.52–0.82) on the CoA cohort, where the linear Cox model scores 0.68 (0.54–0.81).

Network outputs combine with linear weights into the cumulative log-odds at any prognostic horizon, and the weights depend only on the horizon, so attributions across the whole time axis come from a small set of output neurons. Log-odds map evidence additively onto the real line and put different distribution families on one comparable scale; for Gaussian, logistic and log-logistic families the relation between outputs and log-odds is closed-form and linear. Attribution uses layer-wise relevance propagation, needing one backward pass per output neuron, so two-parameter distributions cover the entire horizon range in two backward passes; on synthetic data the model splits risk into a largely time-invariant baseline and a time-varying term, and assigns higher risk to an undersampled subgroup with no observed events.

The extracted risk markers line up with clinical guidelines and separate short-term from long-term effects. Clinical cohorts rarely have absolute ground-truth markers, so guidelines and established observational studies serve as a proxy reference. Using AUROC over mean absolute attributions of guideline-relevant features, ODDS-DR scores highest on both cohorts; on SUPPORT2 the TISS score and a do-not-resuscitate order drive risk across the whole horizon while a cancer diagnosis grows after 24 months, and in the CoA cohort beta-blocker intake and previous balloon angioplasty point mainly to early reintervention.

The demonstrated scope is two clinical cohorts: the public SUPPORT2 all-cause mortality data and a reintervention cohort of 160 aortic coarctation patients across 218 visits at the Deutsches Herzzentrum der Charité, both split 70/30 into training and validation; synthetic experiments show how risk varies with input and time. The authors explicitly frame the framework as estimating prognostic risk under prevailing care patterns rather than evaluating counterfactual treatment regimes.

The method currently relies on unimodal distribution families with closed-form log-odds expressions, and the authors note that competing events or non-susceptible subgroups would require mixture mechanisms designed in the log-odds domain. The clinical analysis is observational, the CoA cohort is small with high censoring, guidelines are expert consensus rather than exhaustive ground truth, and the early concentration of risk after balloon angioplasty still needs confirmation in other cohorts.