A Definition of causal effect (Causal inference: What if, Chapter 1)

38e2af7f8bdad4f2087ab3d42b627e33?s=47 Shuntaro Sato
November 18, 2020

A Definition of causal effect (Causal inference: What if, Chapter 1)

Keywords: 因果推論, Causal effect, Conditional effect(条件付き効果), Causation(因果効果), Effect(効果), Association(関連)

38e2af7f8bdad4f2087ab3d42b627e33?s=128

Shuntaro Sato

November 18, 2020
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  1. Part I Causal inference without models Chapter 1 A DEFINITION

    OF CAUSAL EFFECT Atsushi Mizuno 基本、思考実験
  2. 本⽇の内容

  3. Zeus と Heraの話から 大文字:確率変数 小文字:特定の値 A: an intervention, an exposure,

    or a treatment A (1: treated, 0: untreated) Y (1: death, 0: survival).
  4. Formal definition of a causal effect for an individual 個⼈での因果関係

    potential outcomes or as counterfactual outcomes のとき、Aは個人のアウトカムYに対する因果関係がある ただし、今は は仮定が Deterministicなので 確率変数ではない
  5. Consistency Observed Counterfactrual Zeus was actually treated (A = 1),

    his counterfactual outcome under treatment Y!"# =1 is equal to his observed (actual) outcome Y = 1.
  6. 1.2 Average causal effect 1. 興味のあるアウトカム 2. 比較する介入(action, a=1 or

    0) 3. 反事実の結果 ( Y!"# , Y!"$ ) を持つ比較できる個人 Individual causal effect まぁ、これは難しいので aggregated causal effect 1. 興味のあるアウトカム 2. 比較する介入(action, a=1 or 0) 3. 反事実の結果 ( Y!"# , Y!"$ ) を持つ比較できる集団
  7. Average causal effectの定義 のとき、治療AはアウトカムYに因果関係がある the average causal effect in the

    population is null, we say that the null hypothesis of no average causal effect is true. non-null average causal effect in the population さらに一般化 佐藤先生のスライドのここ
  8. 簡単な注意 • Average causal effectがなくても、個人の効果がないわけでは ない sharp causal null hypothesis

    is true. もし全員 なら
  9. 1.3 Measures of causal effect ここからAverage causal effect ⇒ causal

    effect, null hypothesis of no average effect ⇒ causal null hypothesis i. causal risk difference ii. risk ratio iii. odds ratio Effect measures
  10. 1.4 Random variability では、先ほどの20人を母集団からのサンプルだと考える consistent estimator (一致推定量) of Pr [Y!

    = 1] wiki non-deterministic counterfacturalsは Chapter 10で扱う
  11. 1.5 Causation versus association 実際は = 7/13 the risk of

    death 独立の定義 risk difference risk ratio odds ratio
  12. Independence vs association Association ≠ さらに一般化 参考Average causal effect この不等式が

    【=】 であれば 独立 不等式 ⇒ 因果関係 等式 ⇒因果関係なし
  13. Causation vs Association Conditional probability Unonditional/Marginal probability Association a different

    risk in two disjoint subsets of the population determined by the individuals’ actual treatment value (A = 1 or A = 0) Causation a different risk in the same population under two different treatment values (a = 1 or a = 0).