A First Course in Causal Inference (2305.18793v2)

Abstract: I developed the lecture notes based on my ``Causal Inference'' course at the University of California Berkeley over the past seven years. Since half of the students were undergraduates, my lecture notes only required basic knowledge of probability theory, statistical inference, and linear and logistic regressions.

• The paper presents a foundational framework for causal inference using potential outcomes and structured experimental designs.
• The paper demonstrates how randomized trials and stratified methods achieve covariate balance for unbiased causal effect estimation.
• The paper addresses challenges in non-experimental settings by applying techniques to mitigate confounding and selection bias.

An Essay on "A First Course in Causal Inference" by Peng Ding

Peng Ding's book "A First Course in Causal Inference" provides an in-depth exploration into the complexities and methodologies of causal inference, a subfield of statistics and data science focused on understanding the effect of treatments or interventions on outcomes. The book is structured to accommodate different levels of statistical education, reflecting Ding’s extensive experience teaching the subject at UC Berkeley. Over the years, he has developed and refined this subject into a comprehensive course, addressing the needs of both undergraduates and graduates.

Central to Ding’s treatment of causal inference is the potential outcomes framework, initially conceptualized by Jerzy Neyman in the context of randomized experiments and further expanded by Don Rubin. This framework emphasizes the importance of a structured approach to understanding causal relationships, distinguishing between association and genuine causation—a delineation famously encapsulated in the phrase "correlation does not imply causation." The text underscores the necessity of experimental or quasi-experimental designs in estimating causal effects.

Key Concepts and Structure

1. Introduction to Causal Inference: The initial chapters set the stage with a focus on the Yule–Simpson Paradox, illustrating how aggregate data can mislead conclusions about causal relationships, and establishing the foundational necessity of causal inference.
2. Framework and Methodology: The book introduces potential outcomes and discusses the nuances of randomized controlled trials (RCTs), the gold standard for causal inference. Ding expands on different experimental setups such as completely randomized experiments (CREs) and stratified randomization, which include techniques like stratification and post-stratification used to ensure covariate balance across treatment groups.
3. Theoretical Foundations: Significant attention is given to the Neymanian framework which provides tools for repeated sampling inference about average causal effects. This section of the book covers estimation techniques and variance calculations, highlighting the importance of unbiased estimators and conservative variance estimators, especially where treatment effects might be heterogeneous.
4. Challenges in Non-Experimental Settings: Beyond experimental settings, Ding explores the complexities of observational studies where randomization is absent. The book thoroughly examines the concepts of confounding and selection bias, introducing methods such as matching, propensity score analysis, and instrumental variable approaches to mitigate these issues and estimate causal effects accurately.
5. Advanced Topics: Subsequent chapters delve into sophisticated methodologies to address challenges such as overlapping supports (positivity assumption) and unmeasured confounding. Techniques like sensitivity analysis and the E-value are introduced to assess the robustness of causal claims against potential biases from unobserved confounders.
6. Educational Approach: Ding provides detailed recommendations for instructors, emphasizing flexibility in the choice of topics depending on the audience's background. The inclusion of practical data analysis using R ensures that theoretical discussions are firmly grounded in real-world application.

Implications for Research and Future Directions

The implications of Ding’s book for research in fields ranging from biomedical sciences to economics are vast. By equipping researchers with robust analytical tools, the book enhances the reliability of conclusions drawn from complex datasets where causal relationships are not readily apparent. Furthermore, the discussions of limitations and potential biases inherent in non-randomized studies encourage a critical approach and transparency in reporting causal claims.

The future of causal inference, as suggested through the text, lies in the integration of machine learning techniques with traditional statistical methods, pushing the boundaries of what can be inferred from big data while maintaining rigorous standards of evidence. Ding’s work stands as a cornerstone in this evolving landscape, encouraging educators and researchers alike to deepen their understanding of causal mechanisms, ensuring that causal inference continues to mature as a scientific discipline.