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Survival estimators — Lodestar.Survival

A duration and whether it ended in the event. That pair, one per subject, is what every estimator here takes, and it is the whole of what survival analysis needs to say something a mean cannot.

The problem censoring creates

A subject who leaves the study at month 20 without the event has not survived 20 months — they have survived at least 20 months. Averaging durations throws that away, and dropping the subject throws away more. Right censoring is a subject whose duration is a lower bound, and the three estimators below are the ones that use it rather than discard it.

The Cox proportional hazards model adds covariates: by how much each changes the hazard. Left truncation, interval censoring and the accelerated-failure-time models are each their own lot; nothing here does them.

Which estimator?

flowchart TD
    A["What do you want to read off?"] --> B["the probability of surviving past t"]
    A --> C["the accumulated risk by t"]
    A --> D["whether two groups differ"]
    A --> H["how much a covariate moves the hazard"]
    B --> E["KaplanMeier"]
    C --> F["NelsonAalen"]
    D --> G["LogRank"]
    H --> I["CoxProportionalHazards"]

KaplanMeier and NelsonAalen are two readings of one table, and they share a timeline by construction — the same SurvivalStep[], built once. Where they part is at the end of a sample whose last duration is observed: survival reaches zero and can fall no further, while the hazard keeps the size of that last step.

What all three share

• The pair, as spans. durations and eventObserved, the same length, durations non-negative. Anything else is refused with ArgumentException.
• Ties are the point, not an edge case. A time carrying three events is not three times carrying one, and the two estimators differ on exactly that — see NelsonAalen.Estimate.
• Time zero is a step, with everyone at risk and nothing having happened. It is the shape lifelines' own event table has, and it makes a curve plottable without a special first point.
• Each is a static class with no state, so all three are safe to call from any number of threads at once.
• Each is checked against lifelines 0.30.3, and the corpora are in tests/oracles.

Types

Type	What it is
CoxOptions	The interval level and the iteration budget a Cox fit takes.
CoxProportionalHazards	The Cox model, on Efron's partial likelihood.
CoxSummary	What it returns: the coefficient table, the likelihood-ratio test and the concordance.
KaplanMeier	The survival function, with Greenwood variance and log-log bounds.
KaplanMeierCurve	What it returns: the estimate, its bounds and its steps.
LogRank	The two-sample test comparing two survival curves.
LogRankResult	What it returns: a statistic, a p-value and the degrees of freedom.
NelsonAalen	The cumulative hazard function.
NelsonAalenCurve	What it returns: the accumulated hazard and its steps.
SurvivalStep	One step of either curve: a time, a risk set, and what happened at it.

See also

• Survival analysis — the guide, with a worked trial.
• Python → C# equivalence — the lifelines call each of these replaces.