### Chapter 1: A DEFINITION OF CAUSAL EFFECT **技术重点（Technical Points）** - **核心理论**： - 因果效应定义为个体在相同条件下接受不同干预（treatment）时的潜在结果（potential outcomes）差异。若个体在治疗值 \(a=1\) 和 \(a=0\) 下的结果 \(Y^{a=1}\) 与 \(Y^{a=0}\) 不同，则存在个体因果效应： $$Y^{a=1}_i \neq Y^{a=0}_i$$ - 平均因果效应（average causal effect）在群体层面定义：若群体中所有个体接受治疗 \(a=1\) 的期望结果 \(E[Y^{a=1}]\) 与接受 \(a=0\) 的期望结果 \(E[Y^{a=0}]\) 不同，则存在因果效应： $$E[Y^{a=1}] \neq E[Y^{a=0}]$$ - **一致性假设（consistency）**：观测结果 \(Y\) 等于实际接受治疗 \(A\) 对应的反事实结果： $$\text{若 } A_i = a, \text{ 则 } Y^a_i = Y_i$$

### Chapter 10: RANDOM VARIABILITY **Introduction** The chapter begins with a randomized experiment example investigating whether looking up causes others to look up. Despite no systematic biases (confounding, selection, or measurement bias), the small sample size (4 pedestrians) led to chance imbalances (e.g., blindness in the treatment group), diluting the estimated effect. This illustrates that causal inferences can be flawed due to **random variability**, distinct from systematic biases covered in prior chapters.

### Chapter 11: WHY MODEL?

11.1 Data cannot speak for themselves

技术重点（Technical Points）:

• 核心理论: 当处理变量 (A) 是连续或多分类时，特定处理水平（如 (A=90)）可能无观测数据，导致非参数估计器（如样本均值）无法计算。
• 重要概念:
  • 估计量（Estimator）: 用于估计总体参数的函数（如样本均值）。
  • 一致性估计量（Consistent Estimator）: 样本量增大时，估计值收敛于总体参数（如样本均值一致，首个观测值非一致）。
• 应用场景: 处理变量为离散（二分类/多分类）或连续时，估计条件期望 (E[Y|A=a])。

### Chapter 12: IP Weighting and Marginal Structural Models

12.1 The causal question

技术重点 (Technical Points):

• 核心理论: 因果推断的目标是估计吸烟戒烟（处理变量 (A)，1=戒烟，0=未戒烟）对体重增加（结果变量 (Y)，单位kg）的平均因果效应（ACE），定义为反事实均值之差：

  $$E[Y^{a=1}] - E[Y^{a=0}]$$

  其中 (E[Y^{a=1}]) 表示若全部人群戒烟时的平均增重，(E[Y^{a=0}]) 表示若全部人群未戒烟时的平均增重。
• 关键公式: 观测到的关联性差异 (E[Y|A=1] - E[Y|A=0] = 2.5) kg（95% CI: 1.7, 3.4）不等于因果效应，因存在混杂（如年龄、性别等）。
• 重要概念:
  • 混杂变量（Confounders）是既影响处理 (A) 又影响结果 (Y) 的变量（如年龄：戒烟者平均比非戒烟者年长4岁，且年龄独立影响体重）。
  • 需调整的混杂变量 (L)：性别（0:男,1:女）、年龄（岁）、种族（0:白人,1:其他）、教育（5级）、吸烟强度（每日支数）、吸烟年限、日常活动量（3级）、运动量（3级）、基线体重（kg）——共9维变量。
• 应用场景: 使用NHEFS观测数据估计戒烟对体重增加的因果效应，需通过IP加权调整混杂。

### Chapter 13: STANDARDIZATION AND THE PARAMETRIC G-FORMULA **Introduction** This chapter describes standardization as an alternative to IP weighting for estimating the average causal effect of smoking cessation (A) on weight gain (Y) using NHEFS observational data (n=1,629 smokers, 1,566 uncensored). Both methods rely on the same identifiability conditions but differ in modeling assumptions.

### Chapter 14: G-Estimation of Structural Nested Models

14.1 The Causal Question Revisited

• Technical Points:
  • Reiterates the causal effect of smoking cessation ((A)) on weight gain ((Y)) as (E[Y^{a=1,c=0}] - E[Y^{a=0,c=0}]), with censoring indicator (C).
  • Conditional exchangeability assumed given covariates (L): sex, age, race, education, smoking intensity/duration, physical activity, weight.
• Fine Points:
  • Subgroup analysis (e.g., age, sex) can use marginal structural models with product terms or standardization restricted to subsets.
  • With large datasets, strata can be defined by unique combinations of (L) to estimate conditional effects (E[Y^{a=1,c=0}|L] - E[Y^{a=0,c=0}|L]).

### Chapter 15: OUTCOME REGRESSION AND PROPENSITY SCORES **Overview** Outcome regression and propensity score methods are widely used parametric approaches for causal inference but have limited applicability for complex longitudinal data. They are introduced after g-methods (IP weighting, standardization, g-estimation) because conventional implementations cannot handle time-varying treatments.

### Chapter 16: INSTRUMENTAL VARIABLE ESTIMATION

16.1 The three instrumental conditions

技术重点 (Technical Points):

• 核心理论:
  • IV estimation addresses unmeasured confounding by leveraging an instrumental variable (Z) that meets three conditions:
    (i) (Z) is associated with treatment (A) (relevance condition).
    (ii) (Z) affects outcome (Y) only through (A) (exclusion restriction).
    (iii) (Z) and (Y) share no common causes (exchangeability).
  • In randomized trials, (Z) (randomization assignment) is a valid instrument:
    • Condition (i) holds as assignment influences treatment receipt.
    • Condition (ii) holds under double-blind design.
    • Condition (iii) holds due to random assignment.
• 重要概念:
  • Causal instrument: Directly affects treatment (e.g., Figure 16.1).
  • Surrogate instrument: Proxy for an unmeasured causal instrument (U_Z) (e.g., Figures 16.2–16.3).
• 应用场景:
  • Observational studies (e.g., using cigarette price as (Z) for smoking cessation effect on weight).

### Chapter 17: Causal Survival Analysis **逻辑关联**：本章扩展了前几章关于固定时间点因果效应的分析，聚焦于事件发生时间（如死亡时间）的因果推断，引入了生存分析特有的概念（如删失、风险函数）和调整方法。

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17.1 Hazards and risks

技术重点（Technical Points）：

### Chapter 18: VARIABLE SELECTION AND HIGH-DIMENSIONAL DATA *This chapter addresses variable selection challenges in causal inference, contrasting predictive modeling goals with causal objectives. It identifies bias-inducing variables, introduces machine learning solutions for high-dimensional data, and emphasizes domain knowledge for valid causal estimates.*