Causal Inference in Statistics - A Primer

The book by Judea Pearl and collaborators Madelyn Glymour and Nicholas Jewell, Causal Inference in Statistics: A Primer, provides a concise introduction to a topic of fundamental importance for the enterprise of drawing scientific inferences from data. The book, which weighs in at a trim 125 pages, is written as a supplement to traditional training in statistics and I believe it fills that role admirably. I was very excited when my copy arrived because I am one of those folks who thinks that most statistics texts provide only the technical specs for quantitative science, not the driver’s manual that is needed by researchers who collect and interpret data. After reading it, I think the book is going to be a big hit with both scientists and practicing statisticians. I believe this book will also prove to be useful support for those who teach statistics and data analysis, because the current omission of causal principles in most curricula is an intolerable oversight we must correct.The book starts off by challenging the reader with the intriguing proposition that data, by themselves, lack sufficient information to permit proper causal analysis. What is required for sensible evaluations of data are causal hypotheses. Clever, simple examples are used to show that if we make the wrong scientific assumptions about how a system works, we can derive very incorrect conclusions from our data. This illustration sets the stage for the rest of the book by leaving us wondering, “What additional set of rules would we need in order to draw causal inferences from data?”Chapter 1 does a rather brilliant job of providing the minimum essential set of background information for the task at hand. Basic concepts such as conditional probability and conditional independence are defined, along with essential quantities and relationships, to set the stage for later computations. After a few pages, the book then departs from conventional treatments by presenting the elements of graph theory as an equally-important set of background information. Graphs, specifically probabilistic causal networks, represent one of the key pieces that has been missing from the field of statistics, but that is absolutely essential for representing and evaluating causal hypotheses for analysis. The reader simply needs to get to page 24 to begin to encounter the unique information in this highly readable treatment. As Chapter 1 continues, probability theory and graph theory are married though the combination of the “Structural Causal Model”, which specifies the variables and connecting functions, and the “Graphical Causal Model”, which summaries the causal logic of network relations.In Chapter 2, in only a few pages, the book presents the core “rules” that establish much of the logic for causal analysis within a graph-theoretic framework. Again, the book is truly outstanding in its capacity to distill fundamental ideas to their basics and clearly illustrate with examples. Following this treatment, Chapter 3 then begins to move the reader into a thorough consideration of the interventionist perspective. In essence, causal modeling asks questions about the outcomes of interventions – “What would happen to Y if we were to change X?” Of course sometimes we have information from manipulative experiments, but the greater challenge is to address this question using observational data and causal rules. In this chapter, the rules of engagement are presented. We encounter new mathematical concepts, like the “do” operator and formulae for adjusting for covariates and calculating causal effects. We also encounter rules like the backdoor and front-door criteria. A central feature of causal networks, mediation, is presented and described. Chapter 3 ends by transitioning from general rules that apply to models of all forms to illustrations obtained through reference to linear Gaussian systems. This final set of examples connects the graph-theoretic perspective with more traditional formulations and examples of structural equations. Here more direct comparisons between, for example, regression coefficients and structural coefficients are made. An elegant and crystal clear introduction to instrumental variables ends the chapter and in the process, links the new material presented in this book with yet another historical body of causal modeling literature. It is impressive to see this accomplished in such a compact fashion.Chapter 4 turns to a topic that will be unfamiliar to many as a formal subject – counterfactuals. Simply put, counterfactuals are questions about, “What would have happened to individual i if they had not been exposed to treatment X=1 (if they had not received the drug treatment)?” This seemingly innocent question, as the chapter goes on to reveal, unlocks much additional power derived from the causal modeling system presented in the book. To begin with, counterfactuals lead us necessarily from the population to the individual level, since these are questions about what would have happened to an individual if a different choice or event had happened in the past. Considering the individual level, we begin to realize that all along we have had unique information about individuals that has been ignored via summarization. With counterfactuals, ignoring is no longer appropriate. At the outset, the reader will assume perhaps that the counterfactual question is an impossible question to answer, even with randomized experiments. If individual X(1) is included in the treatment group that received a placebo, how are we to know what might have happened if they had actually received the drug? Surprisingly, a general solution to this problem is offered using the logic of the Structural Causal Model and the fundamental law of counterfactuals. Following a series of illustrations developed for a variety of situations, the chapter ends with a summary of essential information in the form of a computational toolkit for causal analysis. Clearly, this book goes beyond an exposition of ideas to provide the reader with a functional knowledge of causal analysis principles.Throughout, this lucid and concise book explains concepts through the presentation of multiple, simple examples – a strategy that works exceptionally well, making this the most accessible presentation of this material I have read. The reader will be well rewarded for buying and reading this book and I recommend it with enthusiasm for both practicing scientists and students of statistics.

Very good book. Great examples. It really puts to test a lot of conventional wisdom

For a non-statistician interested in causal inference, this books gives an excellent introduction and grounding for tackling more scholarly works such as Peal’s, “Introduction to Causal Inference” or his larger textbook. The writing is what really makes this book, the authors take their academician’s hats off and just simply explain the topic with good use of examples that are easy to follow. With that said, the reader needs to be aware that the writing style does retain some old school academic hallmarks, such as the heavy use of semi-colons between realted independent clauses. This isn’t a criticism, but rather an observation that goes to presentation style. At the moment I am a little more than halfway through the book and it is making thing topic accessiable to me, specifically by not leaving out small details, that to statisticians and mathematicians, may seem obvious or not worth mentioning. This ability to anticipate the students natural question is what makes this book so valuable!I would recommend this book to anyone who has a at least a working knowledge of statistics. I would consider this book for an upper level undergrad course, and certainly one of the books for a graduate course on the topic. If Professor Pearl’s lectures are anything like this book, I would enjoy sitting in on any lecture he gives.

ideally suited for self-study for those with limited time. I loved the numerous exercises and the quality of the explanations. I would have liked if the examples and exercises felt less like “toy examples” and more real world.

I teach R programming to epidemiologists at UC Berkeley. I have appreciated the explosion of data science. However, epidemiologist are not statisticians or computer scientists. Epidemiologists have a central role is understanding causal inference for protecting and promoting health. Graphical causal models (causal graphs) provide a nexus that connects epidemiologists, statisticians, computer scientists to many other fields including machine learning, artificial intelligence, and even to plain old continuous quality improvement and population health improvement. In public health every intervention has a program theory: theory of causation, theory of change, and theory of action. These relationships can be represented with graphical causal models. Causal graphs can be used to capture expert knowledge from community stakeholders. We now have a common visual language to represent causal systems whether if comes from an academic endeavor, quality improvement on the frontlines of practice, or wisdom from community residents. Pearl's book is the first book that makes this world accessible to public health practitioners and epidemiologists like me. I am redesigning my whole course to around causal graphs for epidemiology and Bayesian decision networks for decision analysis. This book is a cause for celebration!

This is a Primer.I am a surgeon. I have a bit of math and coding in my bag as a nerd but nothing on the professional level. I do medical AI research as a faculty but mostly on the nontechnological side.And I had been an ardent disciple of RA Fisher.The gross outlines provided in the Book of Why is pretty much a general map. Anyone who is intrigued beyond that point, yet intimidated to pick up more rigorous tomes of causality would feel welcome with this book.It provides simple enough examples for the layman of math to work out. Althiugh I do recommend to take it slowly. Professor Pearl is very frugal with words and some nuggets of deep wisdom might be missed.