Article Estimating Causal Effects from Large Data Sets Using Propensity Scores

The aim of many analyses of large databases is to draw causal inferences about the effects of actions, treatments, or interventions. Examples include the effects of various options available to a physician for treating a particular patient, the relative efficacies of various health care providers, and the consequences of implementing a new national health care policy. A complication of using large databases to achieve such aims is that their data are almost always observational rather than experimental. That is, the data in most large data sets are not based on the results of carefully conducted randomized clinical trials, but rather represent data collected through the observation of systems as they operate in normal practice without any interventions implemented by randomized assignment rules. Such data are relatively inexpensive to obtain, however, and often do represent the spectrum of medical practice better than the settings of randomized experiments. Consequently, it is sensible to try to estimate the effects of treatments from such large data sets, even if only to help design a new randomized experiment or shed light on the generalizability of results from existing randomized experiments. However, standard methods of analysis using available statistical software (such as linear or logistic regression) can be deceptive for these objectives because they provide no warnings about their propriety. Propensity score methods are more reliable tools for addressing such objectives because the assumptions needed to make their answers appropriate are more assessable and transparent to the investigator. Many observational studies based on large databases attempt to estimate the causal effects of some new treatment or exposure relative to a control condition, such as the effect of smoking on mortality. In most such studies, it is necessary to control for naturally occurring systematic differences in background characteristics between the treatment group and the control group, such as age or sex distributions, that would not occur in the context of a randomized experiment. Typically, many background characteristics need to be controlled. Propensity score technology, introduced by Rosenbaum and Rubin [1], addresses this situation by reducing the entire collection of background characteristics to a single composite characteristic that appropriately summarizes the collection. This reduction from many characteristics to one composite characteristic allows the straightforward assessment of whether the treatment and control groups overlap enough with respect to background characteristics to allow a sensible estimation of treatment versus control effects from the data set. Moreover, when such overlap is present, the propensity score approach allows a straightforward estimation of treatment versus control effects that reflects adjustment for differences in all observed background characteristics. Subclassification on One Confounding Variable Before describing the use of propensity scores in the statistical analysis of observational studies with many confounding background characteristics, I begin with an example showing how subclassification adjusts for a single confounding covariate, such as age, in a study of smoking and mortality. I then show how propensity score methods generalize subclassification in the presence of many confounding covariates, such as age, region of the country, and sex. The potential for a large database to suggest causal effects of treatments is indicated i