{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "XAANCQH8A4"
    }
  ],
  "body": "\n## Summary\n\nA proportional hazards model describes how covariates act on the [[hazard function|Y959NKQ3XW]] of an event time.\nEach covariate multiplies the hazard by a factor that does not change with time.\nIn the Cox model, introduced by David Cox, the hazard is a baseline hazard times $e^{\\beta^T x}$, and the baseline is left completely unspecified.\nThe coefficients $\\beta$ can be estimated by maximising the partial likelihood, which does not involve the baseline hazard.\nIt is the most used regression model of [[survival analysis|443ZWDX88P]].\n\n## Explanations\n\n### L1 human\n\nSuppose smokers have, at every age, twice the risk of a heart attack of non-smokers.\nThe risk itself may rise with age in a complicated way, but the ratio stays $2$.\nA proportional hazards model says exactly this: each factor scales the whole hazard curve up or down by a fixed amount.\nThe doubling corresponds to a coefficient $\\beta = \\log 2$ for the smoking indicator.\nThe method can estimate this ratio without ever estimating the shape of the age curve.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "62N01",
      "62N02",
      "62J12"
    ],
    "name": "Proportional hazards model",
    "same_as": {
      "wikidata": "Q223218",
      "wikipedia": "Proportional hazards model"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Proportional_hazards_model"
      }
    ],
    "tag": "N029V3JX60"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/N029V3JX60/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/N029V3JX60.md",
  "msc": [
    "62N01",
    "62N02",
    "62J12"
  ],
  "name": "Proportional hazards model",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/N02/N029V3JX60.md",
  "status": null,
  "tag": "N029V3JX60",
  "uri": "m2://N029V3JX60",
  "url": "https://tamnd.github.io/math2/wiki/proportional-hazards-model/",
  "writing": {
    "tag": "N029V3JX60",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}