Van der Laan M.J., Robins J.M. Unified Methods for Censored Longitudinal Data and Causality

NY: Springer, 2003. — 399 p. — (Springer Series in Statistics). — ISBN: 978-1-4419-3055-2.During the last decades, there has been an explosion in computation and information technology. This development comes with an expansion of complex observational studies and clinical trials in a variety of fields such as medicine, biology, epidemiology, sociology, and economics among many others, which involve collection of large amounts of data on subjects or organisms over time. The goal of such studies can be formulated as estimation of a finite dimensional parameter of the population distribution corresponding to the observed time- dependent process. Such estimation problems arise in survival analysis, causal inference and regression analysis. This book provides a fundamental statistical framework for the analysis of complex longitudinal data. It provides the first comprehensive description of optimal estimation techniques based on time-dependent data structures subject to informative censoring and treatment assignment in so called semiparametric models. Semiparametric models are particularly attractive since they allow the presence of large unmodeled nuisance parameters. These techniques include estimation of regression parameters in the familiar (multivariate) generalized linear regression and multiplicative intensity models. They go beyond standard statistical approaches by incorporating all the observed data to allow for informative censoring, to obtain maximal efficiency, and by developing estimators of causal effects. It can be used to teach masters and Ph.D. students in biostatistics and statistics and is suitable for researchers in statistics with a strong interest in the analysis of complex longitudinal data.Motivation, Bibliographic History, and an Overview of the book
Tour through the General Estimation Problem
Example: Causal Effect of Air Pollution on Short-Term Asthma Response
Estimating Functions
Robustness of Estimating Functions
Doubly robust estimation in censored data models
Using Cross-Validation to Select Nuisance Parameter Models
General Methodology
The General Model and Overview
Full Data Estimating Functions
Mapping into Observed Data Estimating Functions
Optimal Mapping into Observed Data Estimating Functions
Guaranteed Improvement Relative to an Initial Estimating Function
Construction of Confidence Intervals
Asymptotics of the One-Step Estimator
The Optimal Index
Estimation of the Optimal Index
Locally Efficient Estimation with Score-Operator Representation
Monotone Censored Data
Data Structure and Model
Examples
Inverse Probability Censoring Weighted (IPCW) Estimators
Optimal Mapping into Estimating Functions
Estimation of Q
Estimation of the Optimal Index
Multivariate failure time regression model
Simulation and data analysis for the nonparametric full data model
Rigorous Analysis of a Bivariate Survival Estimate
Prediction of Survival
Cross-Sectional Data and Right-Censored Data Combined
Model and General Data Structure
Cause Specific Monitoring Schemes
The Optimal Mapping into Observed Data Estimating
Functions
Estimation of the Optimal Index in the MGLM
Example: Current Status Data with Time-Dependent
Covariates
Example: Current Status Data on a Process Until Death
Multivariate Right-Censored Multivariate Data
General Data Structure
Mapping into Observed Data Estimating Functions
Bivariate Right-Censored Failure Time Data
Unified Approach for Causal Inference and Censored Data
General Model and Method of Estimation
Causal Inference with Marginal Structural Models
Nonparametric Information Operator in Causal Inference Models
Double Robustness in Point Treatment MSM
Marginal Structural Model with Right-Censoring
Structural Nested Model with Right-Censoring
Right-Censoring with Missingness
Interval Censored Data