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

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)

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

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  2. 本⽇の内容

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  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).

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  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

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  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.

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  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

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  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

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  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

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  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

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  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

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  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

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  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

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  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).

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