Causal Inference in Statistics

Synopsis

CAUSAL INFERENCE IN STATISTICS

A Primer

Causality is central to the understanding and use of data. Without an understanding of cause-effect relationships, we cannot use data to answer questions as basic as "Does this treatment harm or help patients?" But though hundreds of introductory texts are available on statistical methods of data analysis, until now, no beginner-level book has been written about the exploding arsenal of methods that can tease causal information from data.

Causal Inference in Statistics fills that gap. Using simple examples and plain language, the book lays out how to define causal parameters; the assumptions necessary to estimate causal parameters in a variety of situations; how to express those assumptions mathematically; whether those assumptions have testable implications; how to predict the effects of interventions; and how to reason counterfactually. These are the foundational tools that any student of statistics needs to acquire in order to use statistical methods to answer causal questions of interest.

This book is accessible to anyone with an interest in interpreting data, from undergraduates, professors, researchers, or to the interested layperson. Examples are drawn from a wide variety of fields, including medicine, public policy, and law; a brief introduction to probability and statistics is provided for the uninitiated; and each chapter comes with study questions to reinforce the readers understanding.

Summary

Chapter 1: Introduction to Causal Inference

* Summary: Introduces the concept of causality, its importance in research, and common challenges in establishing causal relationships.

* Example: A study examining the impact of a new educational intervention on student test scores. To infer causality, the study needs to control for confounding factors like student background, motivation, and teacher quality.

Chapter 2: Experimental Designs

* Summary: Describes different types of experimental designs, such as randomized controlled trials (RCTs), matched-pairs designs, and before-after designs, and their advantages and disadvantages.

* Example: An RCT that randomly assigns participants to an intervention group or a control group to compare their outcomes.

Chapter 3: Observational Studies

* Summary: Explores observational study designs, including cohort studies, case-control studies, and cross-sectional studies, and discusses their strengths and limitations in inferring causality.

* Example: A cohort study that follows a group of individuals over time to examine the relationship between a certain exposure and a health outcome.

Chapter 4: Propensity Score Matching

* Summary: Introduces the concept of propensity score matching, a statistical technique that aims to mimic the conditions of a randomized experiment by balancing observed characteristics between treatment and control groups.

* Example: Matching patients in a non-randomized study who received different treatments based on their propensity scores to receive each treatment, thus reducing bias.

Chapter 5: Instrumental Variables

* Summary: Discusses instrumental variables, which are variables that are related to the exposure but not directly to the outcome, and can be used to estimate causal effects without the need for randomization.

* Example: Using the distance to a hospital as an instrumental variable for hospital visits, assuming that distance only affects visitation and not patient health directly.

Chapter 6: Regression Discontinuity Design

* Summary: Introduces the regression discontinuity design, a quasi-experimental approach that utilizes a discontinuity in an assignment rule to estimate causal effects when randomization is not feasible.

* Example: Examining the impact of a college placement test cutoff on college enrollment by comparing students who just meet the cutoff to those who just miss it.

Chapter 7: Difference-in-Differences

* Summary: Explains the difference-in-differences (DiD) method, which compares changes in outcomes between a treatment and control group over time to estimate causal effects.

* Example: Evaluating the effectiveness of a new social program by comparing changes in poverty rates between treatment areas and control areas over a period of years.

Chapter 8: Sensitivity Analysis

* Summary: Discusses sensitivity analysis techniques, such as beta regression and bias analysis, that can be used to assess the robustness of causal inference findings to unobserved confounding or model misspecification.

* Example: Performing beta regression to estimate the causal effect of a policy intervention by allowing for unmeasured confounding factors to have a varying degree of influence on the outcome.