In observational studies, investigators have no control over the treatment assignment. The treated and non-treated (that is, control) groups may have large differences on their observed covariates, and these differences can lead to biased estimates of treatment effects. Even traditional covariance analysis adjustments may be inadequate to eliminate this bias. The propensity score, defined as the conditional probability of being treated given the covariates, can be used to balance the covariates in the two groups, and therefore reduce this bias. In order to estimate the propensity score, one must model the distribution of the treatment indicator variable given the observed covariates. Once estimated the propensity score can be used to reduce bias through matching, stratification (subclassification), regression adjustment, or some combination of all three. In this tutorial we discuss the uses of propensity score methods for bias reduction, give references to the literature and illustrate the uses through applied examples.
1998 John Wiley & Sons, Ltd. * This will perform a series of ttests to determine what the initial difference between the * treated and control groups are. Here the variable epidural is the treatment indicator in this * model. proc ttest data"matchset; class epidural; var amladmit cm 1 arom gestage birthwt gender rate chyper phyper height weight momage insprvt momw momb; * This performs a stepwise logistic regression to estimate propensity scores for each subject. * The variable pr is the propensity score The variable epidural is the treatment indicator in * this model. proc logistic data"matchset nosimple; model epidural"amladmit cm 1 arom gestage birthwt gender rate chyper phyper height weight momage insprvt momw momb/selection"stepwise; output out"preds pred"pr; * This takes the propensity score and creates quintiles based on the estimated propensity * score; proc rank groups"5 out"r; ranks rnks; var pr; data a; set r; quintile"rnks#1; * This will show the breakdown of subjects by treatment (here epidural) and propensity score quintile; proc freq; tables quintile*epidural; * This will perform the 2-way anovas to determine whether the propensity score quintiles * removed the initial bias found by the t-tests above. proc glm; class quintile; model amladmit cm 1 arom gestage birthwt gender rate chyper phyper height weight momage insprvt momw momb"quintile epidural quintile*epidural;