Estimating the causal effect of an intervention on a population typically involves defining parameters in a nonparametric structural equation model (Pearl, 2000, NPSEM) in which the treatment or exposure is deter- ministically assigned in a static or dynamic way. We define a new causal parameter that takes into account the fact that intervention policies can result in stochastically assigned exposures. The statistical parameter that identifies the causal parameter of interest is established. Inverse probability of treatment weighting (IPTW), augmented IPTW (A-IPTW), and targeted maximum likelihood estimators (TMLE) are developed. A simulation study is performed to demonstrate the properties of these estimators, which include the double robustness of the A-IPTW and the TMLE. An application example using physical activity data is presented.
Diaz Munoz, Ivan and van der Laan, Mark J., "Population Intervention Causal Effects Based on Stochastic Interventions" (August 2011). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 289.