Book review of “Observation and Experiment: An Introduction to Causal Inference” by Paul R. Rosenbaum

Observational Studies 2 (2017) 28-38 Submitted 8/17; Published 8/17 Book review of “Observation and Experiment: An Introduction to Causal Inference” by Paul R. Rosenbaum Dylan S. Small dsmall@wharton.upenn.edu Department of Statistics The Wharton School University of Pennsylvania Philadelphia, PA, U.S.A. The economist Paul Samuelson said, “My belief is that nothing that can be expressed by mathematics cannot be expressed by careful use of literary words.” Paul Rosenbaum brings this perspective to causal inference in his new book Observation and Experiment: An Introduction to Causal Inference (Harvard University Press, 2017). The book is a luminous presentation of concepts and strategies for causal inference with a minimum of technical material. An example of how Rosenbaum explains causal inference in a literary way is his use of a passage from Robert Frost’s poem “The Road Not Taken” to illuminate how causal questions involve comparing potential outcomes under two or more treatments where we can only see one potential outcome: Two roads diverged in a yellow wood, And sorry I could not travel both And be one traveler, long I stood And looked down one as far as I could To where it bent in the undergrowth; (Frost (1916)) “Frost creates the mood attending a decision, one whose full consequences we cannot see or anticipate. ‘Knowing how way leads on to way,’ we will not see the road not taken. So it was for Frost in a yellow wood...so it is for a patient at risk of death in the ProCESS trial [a randomized trial comparing two treatments for septic shock], so it is in every causal question.” In reverse order of its title, Observation and Experiment starts with an account of causal inference from randomized experiments and then moves to observational studies. The randomized experiment is a powerful tool for causal inference – it provides an automatic way to infer the causal effect of a treatment without understanding why different people have different preferences for treatments. It does this by suppressing the role of preferences in choosing treatments – people cede control of their choice to a random coin flip. But in many settings, people refuse to cede control or it would be unethical to try to force them to cede control. We cannot force some people to smoke cigarettes and others not to. “The central problem in an observational study,” Rosenbaum says, “– the problem that defines the distinction between a randomized experiment and an observational study is that treatments are not assigned at random...In the US in 2016, the poor are far more likely than the rich to smoke cigarettes, as the foolish are more likely to smoke than the wise. If c 2017 Dylan S. Small. Book review of “Observation and Experiment” poverty and foolish behavior have consequences for health besides increased smoking, an investigator will need to take care and exert effort to isolate the effects actually caused by smoking.” To make causal inferences from observational data, we must confront that different people have different preferences for treatments. Rosenbaum presents strategies and considerations for confronting this problem. One strategy is to look for circumstances which resemble a randomized experiment in which preferences did not play a major role in determining treatment but instead “a process that is haphazard, senseless, without aim or ambition, equitable, symmetrical” – a natural experiment. Does growing up in a poor neighborhood make a child earn less as an adult? Different parents have different preferences and means for where to live, but in Toronto, there was a haphazard element among families applying for public housing – families on the waiting list were assigned to the next available residence, sending families to public housing projects in varied neighborhoods of the city. Oreopoulus (2003) used the waiting list as a natural experiment to study the effect of growing up in a poor vs. not poor neighborhood on adult earnings. Rosenbaum points out that while it is often assumed that waiting lists resemble randomized experiments and create natural experiments, this needs careful case by case consideration. Similar to the Toronto public housing study, natural experiments have been constructed based on the Gautreaux program which sought to assist black Chicago public housing residents...