{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Definition\n\n*Causal inference* is the branch of [[statistical inference|JZ2S01BHJJ]] whose targets are causal quantities.\nThese are the values an outcome would take under interventions that set a treatment or exposure to given values.\nIn the [[potential outcomes framework|23ATBZMJHR]], a typical target is the average treatment effect $E[Y(1) - Y(0)]$.\nHere $Y(w)$ is the outcome a unit would have under treatment level $w$.\nA causal quantity is *identified* if, under stated assumptions, it is a function of the distribution of the observed variables.\n\n## Remarks\n\nCausal inference has two steps: identification, which shows that the target is a function of the observed distribution under assumptions, and estimation of that function from data.\n\nExample: in a completely randomised experiment with treatment $W \\in \\set{0, 1}$, randomization makes $W$ independent of $(Y(0), Y(1))$.\nThen $E[Y(1) - Y(0)] = E[Y \\mid W = 1] - E[Y \\mid W = 0]$, so the average treatment effect is identified and estimated by the difference of group means.\n\nNon-example: estimating $E[Y \\mid W = 1] - E[Y \\mid W = 0]$ in observational data, with no assumption linking it to $Y(1)$ and $Y(0)$, is a description of an association, not causal inference.\nIf sicker patients choose the treatment, this difference may even have the opposite sign to the causal effect.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "defines": "V3QJFN5800",
    "kind": "definition",
    "msc": [
      "62D20",
      "62A01"
    ],
    "name": "Causal inference",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Causal_inference"
      }
    ],
    "tag": "FPKRV34TBV",
    "uses": [
      "23ATBZMJHR",
      "JZ2S01BHJJ"
    ]
  },
  "kind": "definition",
  "link": "https://tamnd.github.io/math2/node/FPKRV34TBV/",
  "links": [
    {
      "field": "defines",
      "target": "V3QJFN5800"
    },
    {
      "field": "uses",
      "target": "23ATBZMJHR"
    },
    {
      "field": "uses",
      "target": "JZ2S01BHJJ"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/FPKRV34TBV.md",
  "msc": [
    "62D20",
    "62A01"
  ],
  "name": "Causal inference",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/FPK/FPKRV34TBV.md",
  "status": null,
  "tag": "FPKRV34TBV",
  "uri": "m2://FPKRV34TBV",
  "url": "https://tamnd.github.io/math2/wiki/causal-inference-definition/",
  "writing": {
    "tag": "FPKRV34TBV",
    "kind": "definition",
    "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
      }
    ]
  }
}