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G-methods for time-varying treatments (Causal inference: What if, Chapter 21-1)

Shuntaro Sato
November 25, 2020

G-methods for time-varying treatments (Causal inference: What if, Chapter 21-1)

Keywords: 因果推論, Time-varying, G-formula, IP weighting, Doubly robust estimation

Shuntaro Sato

November 25, 2020
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  1. ・G-methods for time-fixed treatments
    本日の内容
    ・The g-formula for time-varying treatments
    ・IP weighting for time-varying treatments
    ・A doubly robust estimator for time-varying
    treatments

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  2. ・G-methods for time-fixed treatments
    本日の内容
    ・The g-formula for time-varying treatments
    ・IP weighting for time-varying treatments
    ・A doubly robust estimator for time-varying
    treatments

    View full-size slide

  3. Stratification
    effect measure modification (-)
    effect measure modification (+)
    Mantel-Haenszel method
    別々にオッズ比を報告

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  4. Why model?
    effect measure modification (-)
    effect measure modification (+)
    別々にオッズ比を報告(1つの効果を報告できない)
    g-methods

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  5. g-formula
    A=1を代入
    A=0を代入

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  6. IP weighting
    marginal structural model

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  7. Conditional or Marginal?
    outcome regression
    saturated parametric
    stratification
    g-formula
    IP weighting
    g-estimation
    or
    algebraically equivalent

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  8. Time-varying treatment
    g-methods

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  9. ・G-methods for time-fixed treatments
    本日の内容
    ・The g-formula for time-varying treatments
    ・IP weighting for time-varying treatments
    ・A doubly robust estimator for time-varying
    treatments

    View full-size slide

  10. 前提
    ・本章ではidentifiability conditions(sequential
    exchangeability, positivity, and consistency)のviolationが
    ないものとする。
    ・static treatment strategies (always treat vs. never treat)
    の効果を推定する。

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  11. g-formula (weighted average)
    ・time-fixed treatment (A1
    の反実アウトカム)
    ・time-varying treatment

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  12. g-formula (weighted average)

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  13. g-formula (weighted average)

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  14. g-formula (simulation)
    のシミュレーション

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  15. g-formulaの注意点
    ・DAGに基づいたcovariates L1
    をモデルに含める
    ・static sequential exchangeabilityが成立すればstatic
    treatment strategyの効果はidentify可能

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  16. g-formulaの一般化
    ・static treatment strategy
    ・dynamic treatment strategy
    linear regression logistic regression

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  17. ・G-methods for time-fixed treatments
    本日の内容
    ・The g-formula for time-varying treatments
    ・IP weighting for time-varying treatments
    ・A doubly robust estimator for time-varying
    treatments

    View full-size slide

  18. IP weighting (weights)
    ・nonstabilized IP weights
    ・ stabilized IP weights

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  19. IP weighting (non-stabilized)

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  20. Stabilized weights
    non-stabilized weights: stabilized weights:
    Lと独立であればよい Lと独立であればよい

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  21. IP weighting (stabilized)

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  22. IP weightingの一般化
    ・nonstabilized IP weights
    ・ stabilized IP weights
    logistic regression
    logistic regression
    (misspecifiedでも可)

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  23. Marginal Structural Model
    ・2K > Nのときは推定できない
    ・marginal structural mean model
    stabilized IP weightsを使って推定
    misspecified??

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  24. Effect Measure Modification
    ・baseline variable VによるEMMがある場合、marginal
    structural modelは以下の通り(parametric)
    stabilized IP weightsを使って推定
    Vに入れて良いのはbaseline variableだけ

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  25. ・G-methods for time-fixed treatments
    本日の内容
    ・The g-formula for time-varying treatments
    ・IP weighting for time-varying treatments
    ・A doubly robust estimator for time-varying
    treatments

    View full-size slide

  26. Doubly Robust Estimator
    ・g-formula
    ・ IP weighting

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  27. 1.
    Doubly Robust (time-fixed)
    2.
    3. A=1とA=0でそれぞれ
    を推定
    を推定
    ,
    をLについて標準化

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  28. 1.
    Doubly Robust (time-varying)
    2.
    3.
    を推定
    からパラメータ
    を求める。
    を求めておく
    を推定し、Aの値に応じた を求める。
    これを繰り返して を求める。
    always treat

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