A Bayesian Alternative to Synthetic Control for Comparative Case Studies

This paper proposes a Bayesian alternative to the synthetic control method for comparative case studies with a single or multiple treated units. We adopt a Bayesian posterior predictive approach to Rubin’s causal model, which allows researchers to make inferences about both individual and average treatment effects on treated observations based on the empirical posterior distributions of their counterfactuals. The prediction model we develop is a dynamic multilevel model with a latent factor term to correct biases induced by unit-specific time trends. It also considers heterogeneous and dynamic relationships between covariates and the outcome, thus improving precision of the causal estimates. To reduce model dependency, we adopt a Bayesian shrinkage method for model searching and factor selection. Monte Carlo exercises demonstrate that our method produces more precise causal estimates than existing approaches and achieves correct frequentist coverage rates even when sample sizes are small and rich heterogeneities are present in data. We illustrate the method with two empirical examples from political economy.

Bayesian causal inference: Approaches to estimating the effect of treating hospital type on cancer survival in Sweden using principal stratification

This article discusses the use of Bayesian causal inference, and more specifically the posterior predictive approach of Rubin’s causal model (RCM) and methods of principal stratification, in estimating the effects of ‘treating hospital type’ on cancer survival. Using the Karolinska Institute in Stockholm, Sweden, as a case study, the article investigates which type of hospital (large patient volume vs. small volume) is superior for treating certain serious conditions. The study examines which factors may reasonably be considered ignorable in the context of covariates available, as well as non-compliance complications due to transfers between hospital types for treatment. The article first provides an overview of the general Bayesian approach to causal inference, primarily with ignorable treatment assignment, before introducing the proposed approach and motivating it using simple method-of-moments summary statistics. Finally, the results of simulation using Markov chain Monte Carlo (MCMC) methods are presented.

Internal Validity

Chapter 7 begins with an outline and description of five threats to internal validity common to time series designs: history, maturation, instrumentation, regression, and selection. Given the fundamental role of prediction in the modern scientific method, scientific hypotheses are necessarily causal. After an outline of the evolving definition of “causality” in the social sciences, contemporary Rubin causality or counterfactual causality is introduced. Under the assumption that subjects were randomly assigned to the treatment and control groups, Rubin’s causal model allows one to estimate the unobserved causal parameter from observed data. Control time series are chosen so as to render plausible threats to internal validity implausible. An appropriate control time series may not exist, however, an ideal time series may be possible to construct. Synthetic control group models construct a control time series that optimally recreates the treated unit’s preintervention trend using a combination of untreated donor pool units.

What Would Have Been Is Not What Would Be: Counterfactuals of the Past and Potential Outcomes of the Future

Epidemiology is often described as the basic science of public health. A mainstay of epidemiologic research is to uncover the causes of disease that can serve as the basis for successful public-health interventions (e.g., Institute of Medicine, 1988; Milbank Memorial Fund Commission, 1976). A major obstacle to attaining this goal is that causes can never be seen but only inferred. For this reason, the inferences drawn from our studies must always be interpreted with caution. Considerable progress has been made in the methods required for sound causal inference. Much of this progress is rooted in a full and rich articulation of the logic behind randomized controlled trials (Holland, 1986). From this work, epidemiologists have a much better understanding of barriers to causal inference in observational studies, such as confounding and selection bias, and their tools and concepts are much more refined. The models behind this progress are often referred to as ‘‘counterfactual’’ models. Although researchers may be unfamiliar with them, they are widely (although not universally) accepted in the field. Counterfactual models underlie the methodologies that we all use. Within epidemiology, when people talk about a counterfactual model, they usually mean a potential outcomes model—also known as ‘‘Rubin’s causal model.’’ As laid out by epidemiologists, the potential outcomes model is rooted in the experimental ideas of Cox and Fisher, for which Neyman provided the first mathematical expression. It was popularized by Rubin, who extended it to observational studies, and expanded by Robins to exposures that vary over time (Maldonado & Greenland, 2002; Hernan, 2004; VanderWeele & Hernan, 2006). This rich tradition is responsible for much of the progress we have just noted. Despite this progress in methods of causal inference, a common charge in the epidemiologic literature is that public-health interventions based on the causes we identify in our studies often fail.