Emerging Topics in Modeling Interval-Censored Survival Data

Preface
Part I: Introduction and Review (Chapters 1 –3)
Part II: Emerging Topics in Methodology (Chapters 4 –9)
Part III: Emerging Topics in Applications (Chapters 10 –15)
Contents
Editors and Contributors
About the Editors
Contributors
Part I Introduction and Review
Overview of Historical Developments in Modeling Interval-Censored Survival Data
1 Emerging Interval-Censored Data
2 Emerging Methods in Analyzing Interval-Censored Data
3 More on Emerging Methods in Analyzing Interval-Censored Data
References
Overview of Recent Advances on the Analysis of Interval-Censored Failure Time Data
1 Introduction
2 Regression Analysis of Univariate Interval-Censored Failure Time Data
2.1 Regression Analysis with Time-Dependent Covariates
2.2 Regression Analysis in the Presence of a Cured Subgroup
2.3 Variable Section for Interval-Censored Data
3 Regression Analysis with Informative Interval Censoring
4 Regression Analysis of Clustered and Multivariate Interval-Censored Data
5 Other Topics on Regression Analysis of Interval-Censored Data
6 Concluding Remarks
References
Predictive Accuracy of Prediction Model for Interval-Censored Data
1 Introduction
2 Time-dependent AUC
2.1 Review of ROC Curve
2.2 ROC for Interval Censored Data
2.3 Simulation
3 Time-Dependent C-index
3.1 Review of C-index
3.2 C-index for Interval Censored Data
3.3 Simulation
4 Brier Score
4.1 Review of Brier Score
4.2 Brier Score for Interval Censored Data
4.3 Simulation
5 Application to Dementia Dataset
6 Concluding Remarks
Appendix: R code
References
Part II Emerging Topics in Methodology
A Practical Guide to Exact Confidence Intervals for a Distribution of Current Status Data Using the Binomial Approach
1 Introduction
2 Current Status Data and Point Estimations
2.1 Current Status Data
2.2 The R package csci: Current Status Confidence Intervals
2.3 Point Estimation for F(t)
3 Valid Binomial Approach Confidence Intervals
3.1 A Structure of the Valid Confidence Interval for F(t)
3.2 A Specific Form of the Functions a(t,n,C) and b(t,n,C)
3.3 Choice of mn
4 The ABA (Approximate Binomial Approach) Confidence Intervals
4.1 The Structure of the ABA Confidence Interval
4.2 Choice of m†n
4.3 Aesthetic Adjustments
5 Simulation Studies
5.1 Simulation 1
5.2 Simulation 2
6 Analyzing the Hepatitis A Data in Bulgaria
7 Conclusion
References
Accelerated Hazards Model and Its Extensions for Interval-Censored Data
1 Why Is Accelerated Hazards Model Needed?
2 Accelerated Hazards Model with Interval-Censored Data
3 Estimation Procedure
3.1 Sieve Semiparametric Maximum Likelihood Estimator
3.2 Implementation
3.3 Choosing the Number of Base Splines
4 Large Sample Properties
5 Simulation Study
6 Example 1: Diabetes Conversion Data
7 Extensions of Accelerated Hazards Model
7.1 Generalized Accelerated Hazards Model
7.2 GAH Mixture Cure Model
8 Sieve Maximum Likelihood Estimation for GAHCure Model
8.1 Sieve Likelihood
8.2 Algorithm
8.3 Simulation Results
9 Example 2: Smoking Cessation Data
References
Maximum Likelihood Estimation of Semiparametric Regression Models with Interval-Censored Data
1 Introduction
2 Cox Model and Right-Censored Data
3 Interval-Censored Data
4 Competing Risks
5 Multivariate Failure Time Data
6 Remarks
References
Use of the INLA Approach for the Analysis of Interval-Censored Data
1 Introduction
2 Approximate Bayesian Inference with INLA
2.1 INLA
2.2 The R-INLA Package
3 Interval Censored Survival Analysis with INLA
3.1 Survival Models as LGMs
3.2 Capabilities and Possibilities for Survival Models in INLA
4 Examples
4.1 Diabetic Nephropathy: Frailty Log-Logistic Model
4.1.1 Frailty Log-Logistic Model as a Latent Gaussian Model
4.1.2 Using R-INLA for Full Bayesian Inference
4.1.3 Results
4.2 Epilepsy Drug Efficacy: Non-linear Joint Model with Competing Risks and Interval Censoring
4.2.1 Non-linear Joint Model with Competing Risks as a Latent Gaussian Model
4.2.2 Results
5 Discussion
Appendix
References
Copula Models and Diagnostics for Multivariate Interval-Censored Data
1 Introduction
2 Notation and Methods
2.1 Copula Model for Multivariate Interval-Censored Data
2.2 Joint Likelihood for Bivariate Interval-Censored Data
2.3 Choice of Marginal Models
3 Parameter Estimation
3.1 Sieve Likelihood with Bernstein Polynomials
4 Goodness-of-Fit Test for Copula Specification
4.1 Hypothesis and Test Statistic
4.2 Estimation of IR Statistic
4.3 Test Procedure
5 Simulation Studies
5.1 Generating Bivariate Interval-Censored Times
5.2 Simulation-I: Parameter Estimation
5.3 Simulation-II: Joint Survival Probability Estimation Performance
5.4 Simulation III: IR Test Performance
6 Real Examples
7 Conclusion
References
Efficient Estimation of the Additive Risks Model for Interval-Censored Data
1 Introduction
2 Statistical Model
2.1 Notations and Setup
2.2 Likelihood
3 Estimation
3.1 MM Algorithm
3.2 Variance Estimation
3.3 Complexity Analysis
4 Simulation Study
5 Application: Breast Cancer Data
6 Implementation: R Package MMIntAdd
7 Conclusions
Appendix
Proof of Theorem 1
References
Part III Emerging Topics in Applications
Modeling and Analysis of Chronic Disease Processes Under Intermittent Observation
1 Introduction
2 Modeling Multistate Disease and Observation Processes
2.1 Multistate Models
2.2 Joint Models for the Disease and Visit Process
3 Partially Specified Models for Marginal Features
4 Cox Models with Markers Under Intermittent Observation
4.1 Joint Marker-Failure Visit Process Models
4.2 Limiting Value of a Cox Model Coefficient Under LOCF
4.3 A Bone Marker and Event-Free Survival
5 Discussion
References
Case-Cohort Studies with Time-Dependent Covariates and Interval-Censored Outcome
1 Introduction
2 Model Specification
2.1 Full Cohort
2.2 Case-Cohort
3 Simulation
4 Hormonal Contraceptive HIV Data
5 Discussion
Supporting Information
References
The BivarIntCensored: An R Package for Nonparametric Inference of Bivariate Interval-Censored Data
1 Introduction
2 Method
2.1 Spline-Based Sieve NPMLE
2.1.1 Notation
2.1.2 Likelihood Function
2.1.3 Spline-Based Sieve NPMLE
2.2 A Nonparametric Association Test
3 Implementation
4 BivarIntCensored Package and Its Illustration
4.1 Main Functions
4.2 Example
5 Conclusions
References
Joint Modeling for Longitudinal and Interval-Censored Survival Data: Application to IMPI Multi-Center HIV/AIDS Clinical Trial
1 Introduction
2 Data and Methods
2.1 Data Structure
2.1.1 Survival Data
2.1.2 Longitudinal Data
2.2 The Joint Model
2.2.1 The Shared Parameter Joint Model
2.2.2 The Joint Models for Interval-Censored Data
3 Data Analysis
3.1 Illustration Using the IMPI Trial Data
3.2 Survival Data Analysis with Time-Dependent Covariates
3.3 Longitudinal Data Analysis: Linear Mixed-Effects Model
3.4 Joint Modeling for Longitudinal CD4 Counts and Interval-Censored Survival Data
4 Discussions
References
Regression Analysis with Interval-Censored Covariates. Application to Liquid Chromatography
1 Introduction
1.1 Interval-Censored Covariates in Regression Models: State of the Art
1.2 Outline
2 Motivating Data
2.1 Notation
2.1.1 Single Compounds
2.1.2 Sum of Compounds
3 Regression Methods Accounting for Limits of Detection and Quantitation
3.1 The GEL Method
3.2 Extension to the Generalized Linear Model
3.2.1 Regression with the Gamma Distribution
3.2.2 Logistic Regression
3.3 Comments on the Inclusion of Exact Observations
3.4 Residuals for Interval-Censored Covariates
3.4.1 Residuals for the Linear Model
3.4.2 Extension of GEL Residuals to the Generalized Linear Model
3.5 Implementation
4 Illustration
4.1 Linear Regression Model to Model log(Glucose)
4.2 Gamma Regression Model to Model Glucose Levels
4.3 Logistic Regression Model for Association with Obesity
5 Discussion
References
Misclassification Simulation Extrapolation Procedure for Interval-Censored Log-Logistic Accelerated Failure Time Model
1 Introduction
2 Methodology
2.1 Interval-Censored (Type II) Survival Data and Log-Logistic AFT Model with Misclassification Matrix
2.2 MC-SIMEX
3 Monte-Carlo Simulation Study
3.1 Simulation Design
3.2 Results of Simulation
4 Real Data Analysis
5 Discussions
References
Index