Abstract
Currently, methods for conducting multiple treatment propensity scoring in the presence of high-dimensional covariate spaces that result from "big data" are lacking-the most prominent method relies on inverse probability treatment weighting (IPTW). However, IPTW only utilizes one element of the generalized propensity score (GPS) vector, which can lead to a loss of information and inadequate covariate balance in the presence of multiple treatments. This limitation motivates the development of a novel propensity score method that uses the entire GPS vector to establish a scalar balancing score that, when adjusted for, achieves covariate balance in the presence of potentially high-dimensional covariates. Specifically, the generalized propensity score cumulative distribution function (GPS-CDF) method is introduced. A one-parameter power function fits the CDF of the GPS vector and a resulting scalar balancing score is used for matching and/or stratification. Simulation results show superior performance of the new method compared to IPTW both in achieving covariate balance and estimating average treatment effects in the presence of multiple treatments. The proposed approach is applied to a study derived from electronic medical records to determine the causal relationship between three different vasopressors and mortality in patients with non-traumatic aneurysmal subarachnoid hemorrhage. Results suggest that the GPS-CDF method performs well when applied to large observational studies with multiple treatments that have large covariate spaces.