Survival data

Survival time

= Right-censored
{synonym}

An unobserved <survival time> is <right-censored> when it is known to exceed the last event-free follow-up time. For a potential <survival time> $T$ and potential observation-ending time $C$, record
$$
Y=\min(T,C),\qquad \delta=\mathbf1_{\{T\leq C\}}.
$$
When $\delta=1$, the occurrence was observed at $Y$; when $\delta=0$, only $T>Y=C$ is known. An intact machine at the study's closing date and an event-free subject who stops attending follow-up can both yield <right censoring>, but the reasons for stopping matter for <independent censoring>. A subject <right-censored> at year two has contributed two years to <person-time at risk> and belongs to earlier <risk sets>. Neither recording a failure at year two nor discarding that subject preserves this information.

Under <independent censoring> and separate parameters for the observation mechanism, the part of the <survival likelihood> involving an <absolutely continuous probability distribution> for $T$ is $f(Y)^\delta S(Y)^{1-\delta}$. Thus a <right-censored> observation contributes the <survival function> $S(Y)$, rather than the event <probability density function> $f(Y)$. See https://web.stanford.edu/~lutian/coursepdf/unit2.pdf[Lu Tian's Stanford notes, Section 2.1, equations (2.1)–(2.2)]. The <Kaplan–Meier six-subject cohort> shows exactly how this distinction changes the calculation.


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 Incoming links: Right censoring