John W. Robinson, M.D., Ph.D., LLC

Statistics ▪ Analytics ▪ Data Science

Design Suggestion: Match on Estimated Propensity Score in Observational Comparative Effectiveness Studies

In an observational comparative effectiveness study, assignment to treatment group is determined by the choices of patients and providers; choices generally affected by numerous covariates (characteristics of the patient, provider, and treatment context measurable just prior to treatment choice). Importantly, any covariate that is associated with both treatment choice and a study outcome is potentially confounding and will bias estimation of the effect of treatment relative to control on that outcome, unless an appropriate method is used to disentangle the effect of the covariate from the effect of the treatment.

The approach most often used in an attempt to disentangle the effects of covariates from the effect of treatment is regression adjustment, with the observed, potentially confounding covariates included as predictors in the regression model. Unfortunately, this approach assumes that the effects of covariates can be represented equally well by the same fitted model in both treatment and control groups; an assumption unlikely to hold unless the distribution of covariates is quite similar in each group. Thus, for regression adjustment to perform reliably, the distributions of observed covariates must first be balanced between the groups.

In a study with a binary treatment choice, the propensity score is the probability of choosing the treatment over the control given values of observed covariates, and can be estimated for each subject via logistic regression. Constructing treatment and control groups by matching subjects on estimated propensity score is a very effective means of balancing the distributions of observed covariates between the two groups. Furthermore, if all observed, potentially confounding covariates are well-balanced between the groups, regression adjustment is not only more reliable, but usually no longer necessary to reduce confounding. Thus, when groups are matched on estimated propensity score, the treatment effect can generally be estimated using the same methods that would be used had groups been randomly assigned.

Tu JV, Bowen J, Chiu M, et al. Effectiveness and safety of drug-eluting stents in Ontario. N Engl J Med 2007;357(14):1393-402.

Karkouti K, Beattie WS, Dattilo KM, et al. A propensity score case-control comparison of aprotinin and tranexamic acid in high-transfusion-risk cardiac surgery. Transfusion 2006;46:327-38.

Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika 1983;70(1):41-55.

Rubin DB. Using propensity scores to help design observational studies: application to the tobacco litigation. Health Serv Outcomes Res Methodol 2001;2(3-4):169-88.

Rosenbaum PR. Design of Observational Studies. New York: Springer, 2010.