Causal Inference: What If, by Hernán and Robins, 2020
This soon to be published book on causal inference by Hernán and Robins has been available for free (and still is) in draft form on Hernán’s website as it has been developed. It is my go to resource for learning about causal inference concepts and statistical methods.
The book’s first part begins by introducing the notion of potential outcomes – what outcome each unit or individual would experience under each exposure or treatment level. Causal effects are then defined as contrasts of some function of the population distribution of these potential outcomes under the different levels of exposure/treatment. The fundamental problem of causal inference is that in the real world we can only observe each individual’s outcome under one exposure level, and hence the other potential outcome is unobserved or missing. This raises the question of whether and how we can estimate causal effects from real world observed data. These conditions are explained and defined, following which one can see that these conditions are satisfied in randomised trials. The next step is to see when data from observational studies might satisfy these conditions. The concepts of effect modification and interaction are then introduced. Directed acyclic graphs (DAGs) are then introduced along with a definition of confounding. As part of this, single world intervention graphs (SWIGs) are introduced, which connect DAGs with potential outcomes / counterfactuals.
The second part of the book focuses on different statistical modelling methods for estimating causal effects, starting by explaining why typically parametric or semiparametric models of various kinds are typically needed for estimation. The final part of the book considers more complex settings where the treatment or exposure is time-varying during follow-up.
Technical details that are not essential are placed into separate boxes, which improves the flow for a first reading or for those not necessarily interested in such details. Overall I find the book’s presentation exceptionally clear and well structured. I highly recommend it.