Average causal effects from nonrandomized studies: a practical guide and simulated example.

In a well-designed experiment, random assignment of participants to treatments makes causal inference straightforward. However, if participants are not randomized (as in observational study, quasi-experiment, or nonequivalent control-group designs), group comparisons may be biased by confounders that influence both the outcome and the alleged cause. Traditional analysis of covariance, which includes confounders as predictors in a regression model, often fails to eliminate this bias. In this article, the authors review Rubin's definition of an average causal effect (ACE) as the average difference between potential outcomes under different treatments. The authors distinguish an ACE and a regression coefficient. The authors review 9 strategies for estimating ACEs on the basis of regression, propensity scores, and doubly robust methods, providing formulas for standard errors not given elsewhere. To illustrate the methods, the authors simulate an observational study to assess the effects of dieting on emotional distress. Drawing repeated samples from a simulated population of adolescent girls, the authors assess each method in terms of bias, efficiency, and interval coverage. Throughout the article, the authors offer insights and practical guidance for researchers who attempt causal inference with observational data.