A0754
Title: Principal stratification with continuous treatments and continuous post-treatment variables
Authors: Joseph Antonelli - University of Florida (United States) [presenting]
Abstract: Principal stratification (PS) is a commonly used approach for understanding the mechanisms through which a treatment affects an outcome. The goal is to extend the PS framework to studies with continuous treatments, which introduces a number of challenges and opportunities in terms of defining causal effects and performing inference. This manuscript provides multiple key methodological contributions: 1) principal causal estimands are introduced for continuous treatments that provide insights into different causal mechanisms, 2) it is shown that nonparametric identification is possible under a principal ignorability assumption but only under a restrictive assumption on the joint distribution of potential mediators, which can be dropped under mild parametric assumptions, 3) nonparametric Bayesian models are utilized for the joint distribution of the potential mediating variables to ensure the approach is robust to model misspecification, and 4) theoretical justification is provided for utilizing an outcome model to identify the joint distribution of the potential mediating variables, and show that this is only possible if a principal ignorability assumption is violated. Lastly, the methodology is applied to a novel study of the relationship between the economy and arrest rates and how this is potentially mediated by police capacity.
