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Table of Contents
Preface; Contents; Contributors; Part I Overview; 1 Causal Inference: A Statistical Paradigm for Inferring Causality; 1 Introduction; 2 The Counterfactual Outcome Based Causal Paradigm; 2.1 Potential Outcomes; 2.2 Selection Bias in Observational Studies; 2.3 Post-treatment Confounders in Randomized Controlled Studies; 2.4 Mediation for Treatment Effect; 3 Statistical Models for Causal Inference; 3.1 Causal Treatment Effects for Observational Studies; 3.1.1 Case-Control Designs; 3.1.2 Matching and Propensity Score Matching; 3.1.3 Marginal Structural Models.
3.2 Post-treatment Confounders in Randomized Controlled Trials3.2.1 Instrumental Variable Estimate; 3.2.2 Principal Stratification; 3.2.3 Structural Mean Models; 3.3 Mechanisms of Treatment Effects; 3.3.1 Causal Mediation; 3.3.2 Sequential Ignorability and Model Identification; 3.3.3 Models for Causal Mediation Effect; 4 Discussion; References; Part II Propensity Score Method for Causal Inference; 2 Overview of Propensity Score Methods; 1 Introduction; 2 Definition of Propensity Score; 3 Causal Inference Based on Propensity Scores; 3.1 Propensity Score Matching.
3.2 Propensity Score Stratification3.3 Propensity Score Weighting; 3.4 Propensity Score Covariate Adjustment; 4 Example: The Genetic Epidemiology Network of Salt Sensitivity (GenSalt) Study; 4.1 Estimating the Propensity Score; 4.2 Propensity Score Matching; 4.3 Propensity Score Stratification; 4.4 Propensity Score Weighting; 4.5 Propensity Score Covariate Adjustment; 5 Discussion; Appendix: SAS Program Codes; References; 3 Sufficient Covariate, Propensity Variable and Doubly Robust Estimation; 1 Introduction; 2 Framework; 3 Identification of ACE; 3.1 Strongly Sufficient Covariate.
3.2 Specific Causal Effect3.3 Dimension Reduction of Strongly Sufficient Covariate; 4 Propensity Analysis; 4.1 Propensity Score and Propensity Variable; 4.2 Normal Linear Model (Homoscedasticity); 4.2.1 Model Construction; 4.2.2 Precision in Propensity Analysis; 4.2.3 Asymptotic Variance Analysis; 4.2.4 Simulations; 4.3 Normal Linear Model (Heteroscedasticity); 4.3.1 Simulations; 4.4 Propensity Analysis in Logistic Regression; 4.4.1 Model Construction; 4.4.2 Propensity Analysis of Custodial Sanctions Study; 5 Double Robustness; 5.1 Augmented Inverse Probability Weighted Estimator.
5.1.1 Augmented Inverse Probability Weighted Estimator5.2 Parametric Models; 5.2.1 Discussion; 5.3 Precision of ACE0; 090d""0362 ACEACE0; 090d""0362 ACEACE0; 090d""0362 ACEACE0; 090d""0362 ACEAIPW; 5.3.1 Known Propensity Score Model; 5.3.2 Known Response Regression Model; 5.3.3 Discussion; 6 Summary; Appendix: R Code of Simulations and Data Analysis; References; 4 A Robustness Index of Propensity Score Estimation to Uncontrolled Confounders; 1 Introduction; 2 Uncontrolled Confounders in Propensity Score Estimation; 3 Sensitivity and Robustness of Propensity Score Estimation.
3.2 Post-treatment Confounders in Randomized Controlled Trials3.2.1 Instrumental Variable Estimate; 3.2.2 Principal Stratification; 3.2.3 Structural Mean Models; 3.3 Mechanisms of Treatment Effects; 3.3.1 Causal Mediation; 3.3.2 Sequential Ignorability and Model Identification; 3.3.3 Models for Causal Mediation Effect; 4 Discussion; References; Part II Propensity Score Method for Causal Inference; 2 Overview of Propensity Score Methods; 1 Introduction; 2 Definition of Propensity Score; 3 Causal Inference Based on Propensity Scores; 3.1 Propensity Score Matching.
3.2 Propensity Score Stratification3.3 Propensity Score Weighting; 3.4 Propensity Score Covariate Adjustment; 4 Example: The Genetic Epidemiology Network of Salt Sensitivity (GenSalt) Study; 4.1 Estimating the Propensity Score; 4.2 Propensity Score Matching; 4.3 Propensity Score Stratification; 4.4 Propensity Score Weighting; 4.5 Propensity Score Covariate Adjustment; 5 Discussion; Appendix: SAS Program Codes; References; 3 Sufficient Covariate, Propensity Variable and Doubly Robust Estimation; 1 Introduction; 2 Framework; 3 Identification of ACE; 3.1 Strongly Sufficient Covariate.
3.2 Specific Causal Effect3.3 Dimension Reduction of Strongly Sufficient Covariate; 4 Propensity Analysis; 4.1 Propensity Score and Propensity Variable; 4.2 Normal Linear Model (Homoscedasticity); 4.2.1 Model Construction; 4.2.2 Precision in Propensity Analysis; 4.2.3 Asymptotic Variance Analysis; 4.2.4 Simulations; 4.3 Normal Linear Model (Heteroscedasticity); 4.3.1 Simulations; 4.4 Propensity Analysis in Logistic Regression; 4.4.1 Model Construction; 4.4.2 Propensity Analysis of Custodial Sanctions Study; 5 Double Robustness; 5.1 Augmented Inverse Probability Weighted Estimator.
5.1.1 Augmented Inverse Probability Weighted Estimator5.2 Parametric Models; 5.2.1 Discussion; 5.3 Precision of ACE0; 090d""0362 ACEACE0; 090d""0362 ACEACE0; 090d""0362 ACEACE0; 090d""0362 ACEAIPW; 5.3.1 Known Propensity Score Model; 5.3.2 Known Response Regression Model; 5.3.3 Discussion; 6 Summary; Appendix: R Code of Simulations and Data Analysis; References; 4 A Robustness Index of Propensity Score Estimation to Uncontrolled Confounders; 1 Introduction; 2 Uncontrolled Confounders in Propensity Score Estimation; 3 Sensitivity and Robustness of Propensity Score Estimation.