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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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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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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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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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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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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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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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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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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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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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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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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).