Biomedical Engineering Reference
In-Depth Information
Chapter 8
Targeted Minimum Loss-Based
Estimation of a Causal Eect Using
Interval-Censored Time-
to-Event Data
Marco Carone, Maya Petersen, and Mark J. van der Laan
Division of Biostatistics, University of California, Berkeley, California, USA
8.1
Introduction :::::::::::::::::::::::::::::::::::::::::::::::::::::: 198
8.1.1
Motivation ::::::::::::::::::::::::::::::::::::::::::::::: 198
8.1.2
Overview ::::::::::::::::::::::::::::::::::::::::::::::::: 200
8.2
Formulation of Causal Framework ::::::::::::::::::::::::::::::: 202
8.2.1
Denition of Parameter :::::::::::::::::::::::::::::::::: 202
8.2.2
Identiability :::::::::::::::::::::::::::::::::::::::::::: 205
8.3
Estimation and Inference :::::::::::::::::::::::::::::::::::::::: 206
8.3.1
Overview of Targeted Minimum Loss{Based Estimation
206
8.3.2
Implementation of TMLE ::::::::::::::::::::::::::::::: 210
8.3.2.1
Basic Ingredients ::::::::::::::::::::::::::: 210
8.3.2.2
Description of Algorithm :::::::::::::::::: 211
8.3.3
Asymptotic Results :::::::::::::::::::::::::::::::::::::: 213
8.4
Extension to the Case of Right-Censored Lifetimes ::::::::::::: 215
8.4.1
Causal Framework ::::::::::::::::::::::::::::::::::::::: 215
8.4.2
Estimation and Inference :::::::::::::::::::::::::::::::: 217
197
 
 
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