Unified Methods for Censored Longitudinal Data and Causality

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.

1 Introduction. - 1. 1 Motivation, Bibliographic History, and an Overview of the book. - 1. 2 Tour through the General Estimation Problem. - 1. 3 Example: Causal Effect of Air Pollution on Short-Term Asthma Response. - 1. 4 Estimating Functions. - 1. 5 Robustness of Estimating Functions. - 1. 6 Doubly robust estimation in censored data models. - 1. 7 Using Cross-Validation to Select Nuisance Parameter Models. - 2 General Methodology. - 2. 1 The General Model and Overview. - 2. 2 Full Data Estimating Functions. - 2. 3 Mapping into Observed Data Estimating Functions. - 2. 4 Optimal Mapping into Observed Data Estimating Functions. - 2. 5 Guaranteed Improvement Relative to an Initial Estimating Function. - 2. 6 Construction of Confidence Intervals. - 2. 7 Asymptotics of the One-Step Estimator. - 2. 8 The Optimal Index. - 2. 9 Estimation of the Optimal Index. - 2. 10 Locally Efficient Estimation with Score-Operator Representation. - 3 Monotone Censored Data. - 3. 1 Data Structure and Model. - 3. 2 Examples. - 3. 3 Inverse Probability Censoring Weighted (IPCW) Estimators. - 3. 4 Optimal Mapping into Estimating Functions. - 3. 5 Estimation of Q. - 3. 6 Estimation of the Optimal Index. - 3. 7 Multivariate failure time regression model. - 3. 8 Simulation and data analysis for the nonparametric full data model. - 3. 9 Rigorous Analysis of a Bivariate Survival Estimate. - 3. 10 Prediction of Survival. - 4 Cross-Sectional Data and Right-Censored Data Combined. - 4. 1 Model and General Data Structure. - 4. 2 Cause Specific Monitoring Schemes. - 4. 3 The Optimal Mapping into Observed Data Estimating Functions. - 4. 4 Estimation of the Optimal Index in the MGLM. - 4. 5 Example: Current Status Data with Time-Dependent Covariates. - 4. 6 Example: Current Status Data on a Process Until Death. - 5 Multivariate Right-Censored Multivariate Data. - 5. 1 GeneralData Structure. - 5. 2 Mapping into Observed Data Estimating Functions. . - 5. 3 Bivariate Right-Censored Failure Time Data. - 6 Unified Approach for Causal Inference and Censored Data. - 6. 1 General Model and Method of Estimation. - 6. 2 Causal Inference with Marginal Structural Models. - 6. 3 Double Robustness in Point Treatment MSM. - 6. 4 Marginal Structural Model with Right-Censoring. . - 6. 5 Structural Nested Model with Right-Censoring. - 6. 6 Right-Censoring with Missingness. . - 6. 7 Interval Censored Data. - References. - Author index. - Example index.