Propensity score for the analysis of observational data: An introduction and an illustrative example

The principal aim of analysis of any sample of data is to draw causal inferences about the effects of different exposures, such as decisions, actions, medical treatments, or other interventions on relevant outcomes. Data may be the result of several kinds of study designs and approaches, either experimental or observational. In experimental, comparative intervention studies, randomization of patients guarantees that the groups are comparable before the exposure to the treatments and random assignment assures that the choice for a given treatment is not due to the decision by treating physicians and also allows a correct application of statistical tests. In observational studies when randomization is not used for practical or ethical reasons, treatments are decided by physicians (or by patients, or by both) in the context of the best clinical practice and, thus, groups are not comparable and differences in outcomes may reflect either effects caused by the treatment choices or differences in prognosis before treatment. When differences between groups are observed or expected, different kinds of adjustments are used to statistically adjust for the unbalance, using variables describing the condition of patients before treatment. Usually, potential predictive and/or prognostic variables are used together to adjust for confounding by constructing multivariable models. This approach is most of the time able to reduce the effect of confounders or effect modifiers on relevant outcomes, but it makes it difficult for investigators and for final users of the results to assess the adequacy of the approach, the role and impact of each class of variables, and, eventually, the clinical meaning of the results. In 1983, Rosenbaum and Rubin proposed a new method, named Propensity Score, to balance the variables related to the choice of the exposure (treatments) in order to reconstruct a situation similar to random assignment. Since then, there has been an explosion of examples of the use of this approach in the literature. This report introduces the method, uses an empirical example to illustrate its use, and eventually discusses the pros and cons of the method using the authors' experience and some hints extracted from recent commentaries.