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  "body": "\n## Summary\n\nThe hazard function of a lifetime $T$ gives the instantaneous rate of the event at time $t$.\nThe rate is taken among the subjects that have not had the event yet.\nIt equals the density of $T$ divided by its [[survival function|QTM1HZM53Q]].\nIts integral, the cumulative hazard, determines the survival function through $S(t) = e^{-H(t)}$.\nHazards are the natural scale of many models in [[survival analysis|443ZWDX88P]], such as the [[proportional hazards model|N029V3JX60]].\nIn reliability theory the hazard is called the failure rate.\n\n## Explanations\n\n### L1 human\n\nThe hazard at age $70$ answers: among people alive at $70$, how fast are they dying right now, per year?\nIt is a rate, not a probability, so it can be larger than $1$.\nA machine part that wears out has a hazard that grows with age.\nA part that fails only by pure accident, like a fuse hit by random surges, has a constant hazard; its lifetime is exponential.\nNewborn mortality followed by a long flat period and then ageing gives the well-known bathtub-shaped hazard.\n",
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