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  "body": "\n## Definition\n\n*Survival analysis* is the branch of [[statistical inference|JZ2S01BHJJ]] whose data are times to an event.\nIts setting is a nonnegative random variable $T$, the event time, together with observations of $T$ that may be [[censored|MY8ZZP84NP]].\nIts aims are to estimate the [[survival function|QTM1HZM53Q]] $S(t) = P(T \u003e t)$ and the [[hazard function|Y959NKQ3XW]] of $T$.\nIt also compares them between groups and models how they depend on covariates.\n\n## Remarks\n\nThe data of subject $i$ usually take the form $(\\tilde t_i, \\delta_i, x_i)$, where $x_i$ is a vector of covariates.\nHere $\\tilde t_i = \\min(T_i, C_i)$ is the observed time, $C_i$ is a censoring time, and $\\delta_i = 1$ if $T_i \\le C_i$ and $0$ otherwise.\n\nExample: estimating the fraction of light bulbs that still work after $1000$ hours, when the test is stopped at $1500$ hours, is a survival analysis problem.\nThe bulbs still working at $1500$ hours give right-censored times.\n\nNon-example: estimating the mean weight of the bulbs is not survival analysis, since the quantity of interest is not a time to an event.\n",
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