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A Review of: “Design of Observational Studies, by P. R. Rosenbaum.”

I should begin by noting that the first time I read the book’s title I thought that it would address the topic of classical epidemiological designs like case-control studies, cohort studies, etc. However, I was wrong. Rosenbaum’s book addresses the crucial topic of designing and analyzing empiric nonrandomized investigations to prove causal relationships between treatments and outcomes. These types of studies, the observational ones, are prone to present two well-known selection biases: overt biases, i.e., differences in outcomes between treatments that may reflect measured pretreatment differences between groups rather than effects of treatments, and hidden biases, i.e., the same situation but with pretreatment differences that were not recorded in the study. To overcome overt biases, applied statisticians usually advocate the use of model-based adjustments, and to overcome hidden biases they usually recommend designing a randomized experiment. However, Rosenbaum’s book addresses these two biases with an alternative approach: propensity score matching for overt biases and sensitivity analysis for hidden biases. Practitioners may think that sensitivity analysis means performing several analyses of the same dataset; however, this is not the Rosenbaum’s approach. The book is divided into four parts. Part I, Beginnings (chapters 1 to 6), covers many of the ideas discussed in the previous book by Rosenbaum (2002) but in a less technical fashion that surely many practitioners will appreciate. Chapter 1 presents some of the issues that arise in observational studies and describes a few studies that will be used in the following chapters as examples. Chapter 2 reviews the logic of causal inference in randomized studies by using distribution-free statistics. Chapter 3 introduces two of the most important concepts in the book: propensity score and sensitivity analysis. The propensity score of a subject is the conditional probability of treatment assignment given his/her observed covariates, and Rosenbaum and Rubin (1983) already showed in their seminal paper how the propensity score is an alternative to model-based adjustments to address overt biases. On the other hand, Rosenbaum’s sensitivity analysis assumes that any pair of subjects with the same pretreatment observed covariates may nonetheless differ in terms of unobserved covariates, so that one subject has an odds of treatment that is up to ≥ 1 times greater than the odds for the other subject. In a randomized experiment, everyone has the same chance of receiving treatment, so = 1. However, in an observational study we cannot exclude that > 1, but, for each fixed > 1, the sensitivity analysis computes bounds on the possible inference values, e.g., p values. For each > 1 one