Censoring

Builds on Random variable Independence of two random variables

Definition

Let $T$ be a real random variable of interest. An observation of $T$ is censored if it reveals only that $T$ lies in a set, rather than the value of $T$ . The standard types are:

Right censoring: for a censoring time $C$ , one observes $\tilde T = \min(T, C)$ and $\delta = \mathbf{1}\set{T \le C}$ ; when $\delta = 0$ one only learns $T > C$ .
Left censoring: one only learns $T \le c$ for a known $c$ .
Interval censoring: one only learns $L < T \le R$ for known $L < R$ .

Remarks

Right censoring is called independent when $T$ and $C$ are independent; most standard methods of survival analysis assume this or a closely related non-informative censoring condition.

Example: a patient enters a study at month $0$ , the study closes at month $24$ , and the patient has had no relapse by then. With $T$ the relapse time and $C = 24$ , the record is $\tilde T = 24$ , $\delta = 0$ , which says exactly that $T > 24$ .

Non-example: truncation is different. Suppose a study only includes people whose event time exceeds $5$ . Then those with $T \le 5$ never appear in the data, so nothing about them is observed, not even a bound.

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Independence of two random variables concept
Random variable concept
Censoring definition

Tag	`7SWYFFHDBF`
URI	`m2://7SWYFFHDBF`
Kind	definition
Writing	W0 stub
MSC	62N01, 62N02
Defines	Censoring
Uses	Random variable, Independence of two random variables

Censoring

Definition

Remarks

Reading path

Further reading

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