Causal Inference in Statistics

We will explore a range of real-world case studies where problems were addressed by creating tools and concepts that have since become central to causal inference. These examples will not only illustrate the significance of causal inference methods but also act as reference points to guide and reinforce understanding throughout the reading.

• 1.1 The Causal Inference Revolution : An Intellectual Landmark
• 1.2 Lord’s Paradox–Decades of Statistical Debates Put To Bed?
• 1.3 To Adjust Or Not To Adjust? .
• 1.4 Why Can’t Pearl and Rubin Agree?
• 1.5 Smoking and Lung Cancer
• 1.6 Further Readings
• 1.7 Exercises

We will introduce the core concepts of the potential outcomes framework, laying out key terminology and notation that will be connected to the examples from Chapter 1. Additionally, we will provide some historical context to show how these ideas evolved, helping the reader appreciate their significance.

• 2.1 Historical Context, Development, and Motivation
• 2.2 Potential Outcomes and Causal Effects
• 2.3 Gaining Strength From A Population
• 2.4 The Treatment Assignment Mechanism–How Experiments Differ From Observations
• 2.5 Average Treatment Effects (ATE)
• 2.6 Modes of Statistical Inference
• 2.7 Exercises
• 2.8 Case-Study
• 2.9 Practice Project – Advanced
• 2.10 Further Readings 
• 2.11 Appendix – Algebraic Manipulations

We will explore the diagrammatic approach developed by Pearl, introducing key terminology and notation that will connect with the examples from Chapter 1. We will cover how to construct causal diagrams, identify common patterns within them, and determine appropriate adjustment sets to identify unconfounded causal effects, using both diagrams and automated tools.

Observational studies are needed when we cannot perform controlled experiments. We will discuss many study designs and methods to uncover causal effects in passively observed data.

One of the major approaches to estimating causal effects in observational data consists in removing confounding, through adjustment on confounding variables. Using Propensity Score adjustment is an alternative method to removing confounding.

Instrumental variables are widely-used in social sciences like economics. We will discuss how this method works and discuss some of its applications.

These methods model a system of variables as a set of structural equations and goes hand-in-hand with the DAG approach discussed earlier in the book. Once a structural equation model is set-up, many causal effects can be estimated, including path coefficients. The latter is known as Path Analysis and is widely used in many disciplines like psychology and biology.

Many causal effects of interest are mediated by a third variable. We will discuss some methods to estimated mediated effects, direct effects, and indirect effects. Effect modification, or interaction, happens when effects changed depending on the level of another variable. These two situations are (mediation and interaction) are often confused, and we will discuss these models and how to use them for analysis. 

Quasi-experimental designs are used when a real-world situation takes place that mimics a controlled experiment. For example, some policies are implemented locally and two nearby areas can be compared, as if the policy was implemented by an experimenter in one area and the second area was left as a control group for the comparison. Quasi-experimental designs we will study are Differences-in-Differences, Regression Discontinuity Designs, and Interrupted Time-Series designs.

Many treatments are not given at a fixed point in time, but rather over a certain period of time. To assess these effects, longitudinal studies are often employed, where measures are taken repeatedly over time. These sorts of time-dependent treatments and time-dependent confounding of effects require more complex models than simple experimental designs do. We will discuss Marginal Structural Models (MSM), time-modified confounding, and more.

Machine Learning (ML) and Artificial Intelligence (AI) have made their way into causal inference, offering powerful and flexible tools and algorithms to estimate causal effects from massive datasets. We will discuss targeted learning, meta-learnings, Double ML, Causal Discovery and more.

Causal Inference is a vast, rapidly-evolving topic that we cannot hope to cover in its entirety in one book. We will discuss some complex cases including causal inference with interference and causal inference with cyclicality, among other topics. We will offer a few concluding words.