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  "body": "\n## Definition\n\nLet $T$ be a real [[random variable|0PNRKMRC55]] of interest.\nAn observation of $T$ is *censored* if it reveals only that $T$ lies in a set, rather than the value of $T$.\nThe standard types are:\n\n1. *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 $T \u003e C$.\n2. *Left censoring*: one only learns $T \\le c$ for a known $c$.\n3. *Interval censoring*: one only learns $L \u003c T \\le R$ for known $L \u003c R$.\n\n## Remarks\n\nRight censoring is called *independent* when $T$ and $C$ are [[independent|0GBJACNAP6]]; most standard methods of survival analysis assume this or a closely related non-informative censoring condition.\n\nExample: a patient enters a study at month $0$, the study closes at month $24$, and the patient has had no relapse by then.\nWith $T$ the relapse time and $C = 24$, the record is $\\tilde T = 24$, $\\delta = 0$, which says exactly that $T \u003e 24$.\n\nNon-example: truncation is different.\nSuppose a study only includes people whose event time exceeds $5$.\nThen those with $T \\le 5$ never appear in the data, so nothing about them is observed, not even a bound.\n",
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