Approaches to Efficient Estimation for Targeted Minimum Loss--Based Estimation (TMLE) in Data Structures with Missing Confounders

• Activity Number: 550
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Daniel Brown*+ and Luca Pozzi and Maya Petersen and Mark Van der Laan
• Companies: UC Berkeley and University of California Berkeley and UC Berkeley - Biostatistics and UC Berkeley - Biostatistics
• Keywords: Missing Data ; TMLE ; Doubly-Robust ; Multiple Imputation ; Inverse Weighted ; STAN

Abstract

We consider the problem of efficient estimation of full-data target parameters in data structures in which some of the confounding variables are unmeasured in a portion of the population. We apply a targeting step to update a fit of the missingness mechanism in order to guarantee that the estimator solves the efficient influence curve equation. This is then used as an inverse weight in the application of inverse probability of censoring weighted targeted maximum likelihood estimation (IPCW-TMLE), which allows the generation of doubly-robust and efficient estimators of the full data parameters. The targeting step we describe allows for efficient estimation in the case that the dimension of the always observed variables is large and non-parametric estimation of the missingness mechanism is not possible. We describe several approaches to performing this updating step and compare them to a multiple imputation estimator using the capabilities of a Bayesian Markov Chain Monte Carlo sampler. We perform a simulation study demonstrating the performance of each of the approaches and explore their sensitivity to model misspecification and missingness proportion.