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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. The parametric fits trade the data's own shape for a smooth one — Weibull, log-normal and the rest — and the accelerated failure time regressions put covariates on that shape, stretching or shrinking time. Both take left censoring, a duration that is an upper bound, interval censoring, an event known to lie between two visits, and delayed entry, a subject watched only from some time on; KaplanMeier.EstimateLeftCensored and BreslowFlemingHarrington take the first and the last respectively, without a model. Turnbull's non-parametric estimate for interval-censored data is not here.

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"]
    A --> J["a smooth curve, past the data too"]
    J --> K["ParametricSurvival"]
    A --> L["how much a covariate stretches time"]
    L --> M["AcceleratedFailureTime"]
    A --> N["how a covariate's effect moves with time"]
    N --> O["AalenAdditive"]

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
AalenAdditive	Aalen's additive hazards model, whose covariate effects move with time.
AalenOptions	The level, the intercept and the two penalties an Aalen fit takes.
AalenSummary	What it returns: the cumulative coefficients, their bounds, the slopes and the predictions.
AcceleratedFailureTime	The Weibull, log-normal and log-logistic regressions on the time axis.
AftModel	Which accelerated failure time regression runs.
AftOptions	The level, the intercept, the ancillary model, the penalty and the robust errors an AFT fit takes.
AftSummary	What it returns: the coefficient table, the likelihood-ratio test and the predictions.
BreslowFlemingHarrington	The survival function as the exponential of minus the Nelson-Aalen hazard.
Concordance	Harrell's concordance index on any predicted scores.
CoxBaseline	One stratum's Breslow baseline of a Cox fit.
CoxOptions	The interval level, the iteration budget, the penalty and the robust variance 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.
CoxTimeTransform	The time scale of the proportional hazards test.
CoxTimeVarying	The Cox model on start-stop intervals.
KaplanMeier	The survival function, with Greenwood variance and log-log bounds.
KaplanMeierCurve	What it returns: the estimate, its bounds and its steps.
LogRank	The log-rank family: two groups or more, weighted, pairwise.
LogRankOptions	The weighting, its exponents and the truncation a test takes.
LogRankResult	What it returns: a statistic, a p-value and the degrees of freedom.
LogRankWeighting	Which member of the family runs.
NelsonAalen	The cumulative hazard function.
NelsonAalenCurve	What it returns: the accumulated hazard and its steps.
PairwiseLogRankResult	One pair of groups from the pairwise test.
ParametricFit	What a parametric fit returns: the parameter table and the fitted curves.
ParametricModel	Which parametric model runs.
ParametricOptions	The level, the iteration budget and the piecewise breakpoints a parametric fit takes.
ParametricSurvival	lifelines' six parametric fitters, right-, left- and interval-censored.
RestrictedMeanResult	The restricted mean survival time and its variance.
SurvivalCurve	What the Breslow-Fleming-Harrington estimator returns: the estimate, its bounds 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.