Survival 0.1.0 estimators - CyrilB1531/lodestar GitHub Wiki

Lodestar.Survival 0.1.0. This page is frozen at that release. Read the current documentation for what main says now. A link to a decision or a migration page follows main, and leaves the archive.

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.

Left truncation, interval censoring, Cox regression 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"]
    B --> E["KaplanMeier"]
    C --> F["NelsonAalen"]
    D --> G["LogRank"]

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
`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.