Propensity Scores

Estimating Treatment Effects in Observational Studies

In the context of estimating causal effects in observational studies, the propensity score is the conditional probability that an individual belongs to a specific treatment group (e.g. the treated group or the control group) given a set of observed covariates. Propensity scores are balancing scores, meaning that within subclasses that are homogeneous in the propensity score, the distributions of the covariates are the same for treated and control units (i.e. are “balanced”). This makes it possible to estimate treatment effects, controlling for covariates, by matching or subclassifying on the propensity score since comparisons of individuals with different treatments made within these matched pairs or groups are not confounded by differences in observed co-variate distributions. An unbiased estimate of the average treatment effect is obtained when researchers have controlled for all relevant covariates (the so-called strongly ignorable treatment assignment assumption).

Propensity scores are usually estimated by logistic regression, although other models can be used. Most of the propensity score literature focuses on the binary treatment case (e.g. treated vs. control); however, propensity score methods have been extended more recently to accommodate multiple treatment groups. Propensity scores can be used for stratification, matching, or as a covariate in future analyses.

Adjusting for Nonresponse Bias in Surveys

Propensity scores have been used in survey research to adjust for nonresponse bias. In this case, the propensity score is the probability of being a respondent given observed characteristics. These propensity scores can be used in post-stratification, weighting adjustments, and imputation.

Post-stratification using propensity scores is useful when there are a substantial number of variables available for post-stratification, as there might be in panel surveys where information from a previous wave is available for nonrespondents. In this situation, standard post-stratification methods that form weighting cells by complete cross-classification of all the control variables are not practical, since the number of weighting cells would be very large and could include cells with nonrespondents but few or no respondents. If there are no respondents in a cell, the nonresponse weight adjustment is infinite. An alternative is to estimate the propensity to be a respondent using the available observed variables and then to group these estimated propensities into a reasonable number of weighting classes. This takes advantage of the propensity score's ability to adjust for a large number of covariates simultaneously using only a single scalar summary (the propensity score).

...