Propensity score stratification methods for continuous treatments.

Continuous treatments propensity scoring remains understudied as the majority of methods are focused on the binary treatment setting. Current propensity score methods for continuous treatments typically rely on weighting in order to produce causal estimates. It has been shown that in some continuous treatment settings, weighting methods can result in worse covariate balance than had no adjustments been made to the data. Furthermore, weighting is not always stable, and resultant estimates may be unreliable due to extreme weights. These issues motivate the current development of novel propensity score stratification techniques to be used with continuous treatments. Specifically, the generalized propensity score cumulative distribution function (GPS-CDF) and the nonparametric GPS-CDF approaches are introduced. Empirical CDFs are used to stratify subjects based on pretreatment confounders in order to produce causal estimates. A detailed simulation study shows superiority of these new stratification methods based on the empirical CDF, when compared with standard weighting techniques. The proposed methods are applied to the "Mexican-American Tobacco use in Children" study to determine the causal relationship between continuous exposure to smoking imagery in movies, and smoking behavior among Mexican-American adolescents. These promising results provide investigators with new options for implementing continuous treatment propensity scoring.