The propensity score is a key component of many causal inference procedures. After establishing the basic causal inference framework, we will outline the key methods of construction of propensity score functions, and study their core mathematical properties. We will detail the use of the propensity score in matching, inverse weighting and regression adjustments that allow the unconfounded effect of an exposure or treatment of interest to be estimated consistently.
Using the framework of semiparametric inference, we will contrast the statistical properties of estimators derived using each method. We will investigate issues of model selection for the propensity score, and demonstrate the utility of judicious choice of predictors that enter into the propensity function. This will be illustrated in standard problems and also in the case of high-dimensional predictors. Longitudinal data will also be studied in the causal setting.
Finally, we will develop the Bayesian framework for handling causal inference and investigate how propensity function construction and usage translates to the new setting.
All methods will be illustrated using examples from biostatistics, health research and econometrics. Computation will be performed in R.