Chapter_23
Introduction
子章节内容
Causal mediation analysis examines pathways through which treatment affects outcomes, extending time-varying treatment frameworks to include mediators. Unlike standard approaches using pure direct/total indirect effects, this chapter's interventionist framework links to empirically verifiable target trials.
技术重点（Technical Points）:
- 核心理论: Mediation analysis decomposes treatment effects into direct and indirect pathways using hypothetical interventions.
- 重要概念:
- Pure direct effect: Effect of treatment if mediator is set to its value under no treatment.
- Total indirect effect: Mediated effect via the mediator.
- 应用场景: Evaluating mechanisms (e.g., how smoking cessation reduces heart attack risk via hypertension).
细节要点（Fine Points）:
- 相关背景: Builds on Part III’s time-varying treatment methods but focuses on causal pathways.
- 辅助信息: Requires no unmeasured common causes of mediator and outcome for identifiability.
23.1 Mediation Analysis Under Attack
子章节内容
A smoking cessation trial illustrates challenges: investigators seek to decompose the effect of quitting smoking (A) on heart attacks (Y) into direct effects and indirect effects mediated by hypertension (M). Pure direct/total indirect effects involve cross-world counterfactuals (e.g., (Y{a=1,M{a=0}})), which are unverifiable experimentally.
技术重点（Technical Points）:
- 关键公式:
- Pure direct effect: $$E[Y{a=1,M{a=0}}] - E[Y{a=0,M{a=0}}]$$
- Total indirect effect: $$E[Y{a=1,M{a=1}}] - E[Y{a=1,M{a=0}}]$$
- Mediation formula: $$\sum_m E[Y \mid A=1, M=m] \cdot P(M=m \mid A=0)$$
- 重要概念: Cross-world quantities (e.g., (Y{a=1,M{a=0}})) require untestable independence assumptions (NPSEM-IE model).
细节要点（Fine Points）:
- 案例分析: In the trial, (E[Y{a=1,M{a=0}}]) is unobservable for continuing smokers.
- 辅助信息: FFRCISTG models avoid unverifiable cross-world assumptions but may not identify effects pointwise.
Technical Point 23.1: Proof of the Mediation Formula
子章节内容
Derives the mediation formula under Figure 23.1’s DAG, assuming cross-world independence (Y^{a=1,m} \perp!!!\perp M^{a=0}). The proof uses probability laws, exchangeability, and consistency.
技术重点（Technical Points）:
- 关键公式:
- 核心理论: Formula validity depends on the NPSEM-IE model, not FFRCISTG.
细节要点（Fine Points）:
- 辅助信息: Cross-world independence is empirically unverifiable.
23.2 A Defense of Mediation Analysis
子章节内容
To justify pure direct effects, investigators reframe (E[Y{a=1,M{a=0}}]) as the effect of nicotine-free cigarettes (O=1, N=0) in a future trial, assuming:
(i) Nicotine (N) affects Y only via M,
(ii) Non-nicotine components (O) do not affect M.
技术重点（Technical Points）:
- 核心理论: Under Figure 23.2’s FFRCISTG, (E[Y^{n=0,o=1}]) equals the mediation formula.
- 重要概念: Separable effects: Effects of treatment components (N and O).
细节要点（Fine Points）:
- 案例分析: Nicotine-free cigarettes’ effect is (E[Y^{n=0,o=1}]) if assumptions hold.
- 相关背景: Assumptions link cross-world quantities to real-world interventions.
Technical Point 23.2: When the Mediation Formula is the g-Formula
子章节内容
Shows that under Figure 23.3’s deterministic relationships (A→N, A→O), the g-formula for (E[Y^{n=0,o=1}]) simplifies to the mediation formula despite positivity violations.
技术重点（Technical Points）:
- 关键公式:
- 核心理论: Deterministic links enable identification without positivity.
细节要点（Fine Points）:
- 辅助信息: Proof uses SWIGs and g-formula properties.
23.3 Empirically Verifiable Mediation
子章节内容
A three-arm trial (standard cigarettes, cessation, nicotine-free cigarettes) tests assumptions (i)–(iii). If (E[Y \mid N=0,O=1]) differs from the mediation formula, assumptions are refuted.
技术重点（Technical Points）:
- 应用场景: Validating separable effects via future randomized trials.
- 重要概念: Assumptions (i) no direct N→Y, (ii) no direct O→M, (iii) no unmeasured M-Y confounders.
细节要点（Fine Points）:
- 案例分析: Associations (e.g., O–M in N=0) refute assumptions.
- 辅助信息: Fine Point 23.1 details falsification methods.
Fine Point 23.1: Empirical Falsification of Separable Effects Assumptions
子章节内容
If N and Y are associated given M and O, either (i) or (iii) is false. An 8-arm trial (intervening on M, N, O) can distinguish these.
细节要点（Fine Points）:
- 辅助信息: Unmeasured confounders may activate only under component interventions.
23.4 An Interventionist Theory of Mediation
子章节内容
Proposes focusing on separable components (e.g., nicotine, non-nicotine) instead of mediators. Requires:
- Decomposing treatment into intervenable components.
- Verifiable assumptions via randomized trials.
技术重点（Technical Points）:
- 核心理论: Separable effects exist even if mediator interventions are undefined.
- 应用场景: Effects of nicotine-free cigarettes without specifying mediator interventions.
细节要点（Fine Points）:
- 相关背景: Extends to survival analysis, competing risks, and interference.
Technical Point 23.3: Path-Specific Effects and the Front Door Formula
子章节内容
Under Figure 23.6, the front door formula identifies path-specific effects (e.g., L→A→Y) using separable components (N, O).
技术重点（Technical Points）:
- 关键公式:
- 核心理论: Deterministic relationships enable identification.
Fine Point 23.2: Separable Effects with a Surrogate Mediator
子章节内容
If M is a surrogate for an unmeasured mediator (H), causal diagrams (Figures 23.4–23.5) help interpret dependencies (e.g., N–Y given M, O).
细节要点（Fine Points）:
- 辅助信息: Independence violations suggest misspecification or faithfulness violations.
总结
本章从批判传统中介分析（依赖不可验证的跨世界反事实）出发，提出了基于可分离效应的干预主义框架。核心创新是将处理分解为可干预的组分（如尼古丁与非尼古丁成分），通过未来随机试验验证假设，并建立中介公式与g公式的等价性。技术要点包括纯直接效应、总间接效应的数学定义及可识别条件，细节要点涵盖吸烟 cessation 试验的案例分析和假设可证伪性设计。