Causal Inference

Basic Principles of Randomized Experiments

Randomized experiments are the gold standard for drawing causal inferences, but drawing such inferences from observational studies is often necessary and requires special care. Here, we use the Rubin causal model (RCM) framework, which begins by defining causal effects using potential outcomes, a formulation originally due to Jerzy Neyman in the context of randomization-based inference in randomized experiments. We use well-accepted statistical principles of design and analysis in experiments to connect to the design and analysis of observational studies.

Randomized controlled trials (RCTs) are commonly used to compare treatments (i.e., interventions). The simplest setting has two groups, with each unit (e.g., person, classroom) having a known probability of assignment into the active treatment or the control treatment, and the units are followed for a predefined period of time to [Page 248]observe outcome variables, generically denoted here by Y. An example would be a posttest score 1 year after randomization.

RCTs ideally have strictly developed protocols specified in advance of implementation. A critical feature of RCTs is that the active versus control treatment is randomly chosen for each unit; thus, in expectation, the treated group and the control group are balanced on measured and unmeasured covariates, where balance here means having the same expected distributions of all covariates. Covariates are variables, like age and baseline pretest scores, thought to be correlated with Y, but that differ from Y because their values are known to be the same for each unit whether the unit was assigned to the treatment or control group; examples include male–female, age, and educational history of parents. Observed covariates are denoted by X.