A central problem in medical research is how to make inferences about the causal effects of treatments or exposures. In this article, we review fundamental concepts for making such inferences in randomized clinical trials or observational studies. The statistical framework consists of potential outcomes, an assignment mechanism, and probability distributions. Randomization-based and model-based methods of statistical inference are illustrated with a series of extracorporeal membrane oxygenation (ECMO) clinical trials, which are thought-provoking in that each trial used different assignment mechanisms.
