### Chapter 1: A DEFINITION OF CAUSAL EFFECT

Introduction

The chapter formalizes intuitive causal concepts using mathematical notation. Humans inherently understand causal effects by comparing outcomes under different actions (e.g., "What if I had acted differently?"). The goal is to match this intuition with formal definitions for precise causal inference.

### 章节标题：第10章 随机变异性

10.1 识别与估计

技术重点（Technical Points）：

• 核心理论：因果推断的前九章假设研究人群规模接近无限（识别问题），忽略随机变异性，聚焦混杂、选择和测量偏倚。随机变异性在有限样本中引入额外不确定性。
• 关键公式：
  • 估计量标准误：二项分布标准误为 $\sqrt{\frac{p(1-p)}{n}}$，其中 $p$ 为超人群参数。
  • Wald 95% 置信区间：$\hat{\theta} \pm 1.96 \times \widehat{se}(\hat{\theta})$，其中 $\widehat{se}(\hat{\theta})$ 是估计量的标准误估计值（例如 $\hat{p} = 7/13$ 时，$\widehat{se} = \sqrt{\frac{(7/13)(6/13)}{13}} = 0.138$）。
• 重要概念：
  • 估计目标（Estimand）：超人群中的目标参数（如 $Pr[Y=1|A=a]$）。
  • 估计量（Estimator）：基于样本数据计算估计目标的规则（如样本比例 $\widehat{Pr}[Y=1|A=a]$）。
  • 一致性（Consistency）：当样本量增大时，估计量收敛于估计目标（定义见 Technical Point 10.1）。
• 应用场景：在随机实验中估计超人群的因果效应（如心脏移植对死亡率的影响）。

### Chapter 11: WHY MODEL?

Chapter Introduction

子章节内容
本章介绍第II部分（涉及真实数据分析）与第I部分（概念性分析）的核心差异，强调回归模型（如线性和逻辑模型）在因果推断和预测中的必要性。提供书籍网站链接（含R/SAS/Stata/Python代码），并说明模型的核心作用：弥补数据不足，通过参数化估计补充信息。明确本章目标为对比非参数与参数估计方法，并讨论平滑性（smoothing）和偏差-方差权衡（bias-variance trade-off）。

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

12.1 The Causal Question

技术重点 (Technical Points):

• 核心理论: 估计吸烟戒烟（处理变量 (A)）对体重增加（结果变量 (Y)) 的平均因果效应 (E[Y^{a=1}] - E[Y^{a=0}])。
• 关键公式:
  • 观测关联差异: (E[Y|A=1] - E[Y|A=0] = 2.5)（95% CI: 1.7, 3.4）
  • 因果效应定义: (E[Y^{a=1}] - E[Y^{a=0}])（标准化均值差）
• 重要概念:
  • 混杂因素（如年龄、性别、种族等）需调整，因戒烟组与非戒烟组基线特征不均衡（见表12.1）。
• 应用场景: 使用NHEFS观察性研究数据（1566名吸烟者），调整9个基线协变量（(L)）：性别、年龄、种族、教育、吸烟强度/时长、体力活动、体重。

### Chapter 13: STANDARDIZATION AND THE PARAMETRIC G-FORMULA **Chapter Overview** This chapter introduces standardization as an alternative to IP weighting for estimating the average causal effect of smoking cessation on weight gain using observational data. Both methods rely on the same identifiability conditions but differ in modeling assumptions. The parametric g-formula is presented as a method to handle high-dimensional confounders through modeling and standardization.

### Chapter 14: G-ESTIMATION OF STRUCTURAL NESTED MODELS **Link to Previous Chapters**: This chapter introduces g-estimation as a third method (alongside IP weighting and standardization from Chapters 12–13) to estimate the average causal effect of smoking cessation (\(A\)) on weight gain (\(Y\)) using the NHEFS dataset. G-methods (IP weighting, standardization, g-estimation) are designed for time-varying treatments but are applied here to a time-fixed treatment for pedagogical clarity.

### Chapter 15: OUTCOME REGRESSION AND PROPENSITY SCORES

Introduction
Outcome regression and propensity score methods are widely used parametric approaches for causal inference but are limited to simpler settings. They are unsuitable for time-varying treatments, which require g-methods (IP weighting, standardization, g-estimation). This chapter focuses on conventional methods applicable only to non-longitudinal data.

### Chapter 16: INSTRUMENTAL VARIABLE ESTIMATION **Introduction** - Causal inference methods previously discussed require measuring all confounders, but residual bias persists if unmeasured confounders exist. - Instrumental variable (IV) estimation offers an alternative approach under different assumptions, avoiding the need to measure all confounders.

### Chapter 17: Causal Survival Analysis

Introduction

• Context: Extends causal inference to time-to-event outcomes (e.g., time until death) where events may occur after study end, necessitating specialized methods for administrative censoring.
• Key shift: Previous chapters focused on outcomes at fixed time points; survival analysis handles events occurring at any time during follow-up.
• Administrative censoring: Intrinsic to survival studies (e.g., study end precludes observing all events). Other censoring types (e.g., loss to follow-up, competing events) require adjustment but are deferred to Part III.

### Chapter 18: VARIABLE SELECTION AND HIGH-DIMENSIONAL DATA **Introduction** This chapter addresses variable selection for causal inference, contrasting it with predictive modeling. All causal adjustment methods (stratification, outcome regression, standardization, IP weighting, g-estimation) require a set of adjustment variables \(L\) that ensure conditional exchangeability. The chapter outlines guidelines for selecting \(L\) in causal analyses, emphasizing that criteria differ from predictive modeling due to the risk of introducing bias.