It is well known that randomized treatment assignment can dramatically strengthen the force of causal inferences. Unfortunately, there is a wide array of scientific questions where ethical or practical concerns prohibit randomized treatments. It is in this context that nonparametric methods, such as matching and subclassification, are used to help adjust for pretreatment differences between the treatment and control groups. This project will extend the propensity score methods, which are widely used in applied research in order to conduct matching and subclassification with a large number of covariates, to a larger class of problems while maintaining their key advantages. Specifically, the study will (1) develop a generalized propensity score that is designed to handle more general treatment regimes, including categorical, ordinal, continuous, and multivariate treatments and (2) extend the use of propensity score methods to adjust for pretreatment measurements in randomized experiments in order to reduce the post-hoc bias that can be introduced by the choice of adjustment methods in typical data analyses.
Observational studies play a key role in scientific investigation when results from ideal randomized experiments are not available. When practical or ethical concerns prevent randomized exposure to a supposed causal variable, such as smoking or an environmental hazard, scientists must rely on observational studies. Unfortunately, observational studies are difficult to analyze and can be riddled with biases since individuals who happen to be exposed to a supposed causal variable may be quite different from those who are not exposed. The significance of this research lies in an extension of the methods that have proved themselves highly useful in avoiding these biases. The effectiveness of the generalized propensity score methods will be illustrated through three concrete examples from medical and social science research: (1) a study of the effects of summer reading programs on autumn reading scores; (2) an investigation into the effectiveness of a proposed treatment for Fabry disease; and (3) the estimation of the causal effect of exposure to policy proposals on voting behavior. The new methods should have other applications throughout the physical, biological, and social sciences where causal inference is required with more complex causal variables than allowed for with current methods. The project also will extend methods to handle missing data and exploit some advantages of these methods for bias reduction in experimental settings.
