Time-to-event outcomes

A censored follow-up is not a negative label

Many imaging studies ask about time until an event such as death, recurrence, or progression. The outcome is not just an event indicator. For a patient who is still being followed when the observation period ends, the data say that the event time is longer than the observed follow-up. That is right-censoring, not a demonstration that the event will never occur.

The distinction changes both the estimand and the analysis. Coding every patient without an observed event as if the person had an unlimited event-free time, or discarding those patients without a design reason, changes the information in the cohort. A survival analysis must state the event definition, time origin, follow-up rule, censoring status, and population to which the result refers.

Model and metric answer different questions

Kaplan-Meier estimation describes a survival distribution while accounting for right-censored observations under its assumptions. It is a description of the cohort, not an individual forecast. A Cox proportional-hazards model relates covariates to the hazard under a proportional-hazards assumption. The fitted coefficients and hazard ratios are model-dependent quantities, and the assumption must be examined rather than silently treated as true.

The concordance index, or C-index, measures a ranking property for comparable survival pairs. It is analogous to discrimination measures for binary outcomes in that it does not, by itself, establish calibration, clinical utility, or the absolute survival probability for an individual. The estimator and its censoring handling or censoring distribution must be reported, because the number is not self-interpreting. A survival study that reports only a C-index has left those other questions open.

Survival calibration also needs an explicit time horizon and a definition of what is being calibrated. A model can rank patients in a useful order while its estimated event probabilities are systematically displaced. Decision analysis requires the same additional specification as in a binary prediction problem: which action, at which horizon, for which population, and with what costs? For each survival-performance or decision metric, state how censoring enters its estimator. A binary-outcome formula cannot simply be reused without a censoring-specific definition and handling plan.

The honest question is incremental value

An imaging feature is often described as prognostic when it is associated with survival in a model containing only that feature. That result may be compatible with the feature acting as a proxy for information already in the clinical record. When the intended claim is incremental predictive value, the more useful question is:

Does the imaging input add information beyond a prespecified clinical baseline for the stated time-to-event estimand?

One design compares a clinical-only survival model with a model that adds the declared imaging inputs, using the same split, fitted-state, selection, and uncertainty rules. The comparison may involve a change in discrimination, calibration, likelihood-based fit, or decision utility, depending on the claim. A single p-value or an unadjusted C-index difference cannot answer every version of the incremental question.

The baseline is not a nuisance to be removed after the fact. It is a reference comparison for the claim that imaging adds value. If the imaging feature predicts only because it tracks a clinical variable already available at the intended decision point, the result may be predictive in the study without adding actionable information.

A dated case illustrates reportability limits

A dated TRACE-CT M1-08 case, with aggregate provenance in the public project record at the pinned commit, compared survival-model utility with and without synthetic augmentation under one frozen project design. The clinical-predictors-only reference C-index on the untouched real test cohort was 0.789. The synthetic-augmented runs produced C-indices from 0.743 to 0.817 across the recorded seeds, with overlapping intervals and no demonstrated improvement in that bounded comparison. These values are project measurements, not a clinical effect estimate, a general benchmark, or evidence that augmentation improves survival prediction elsewhere.

The same case used a project-specific reportability rule: integrated Brier and survival-calibration summaries were marked not reportable when the evaluation cohort had fewer than 10 events. That threshold belongs to the dated protocol. It is not a general survival-analysis law and must not be turned into a universal minimum-event rule by repeating it in a new study.

The case is useful because it keeps several questions visible at once: whether the outcome was handled as censored, whether a clinical baseline was retained, whether uncertainty was attached to the comparison, whether all seeds were reported, and whether the test cohort stayed untouched. Its negative result is a result for that bounded method comparison, but it does not establish that synthetic data are always harmful or that the clinical baseline is universally adequate.

Survival therefore reinforces the chapter’s central sequence. Define the estimand and units, keep fitted states inside the allowed boundary, compare with the relevant baseline, report metrics that match the outcome, and scope the test setting. The next section turns that sequence into a protocol written before fitting begins.

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