1st Edition
Cure Models Methods, Applications, and Implementation
Cure Models: Methods, Applications and Implementation is the first book in the last 25 years that provides a comprehensive and systematic introduction to the basics of modern cure models, including estimation, inference, and software. This book is useful for statistical researchers and graduate students, and practitioners in other disciplines to have a thorough review of modern cure model methodology and to seek appropriate cure models in applications. The prerequisites of this book include some basic knowledge of statistical modeling, survival models, and R and SAS for data analysis.
The book features real-world examples from clinical trials and population-based studies and a detailed introduction to R packages, SAS macros, and WinBUGS programs to fit some cure models. The main topics covered include
- the foundation of statistical estimation and inference of cure models for independent and right-censored survival data,
- cure modeling for multivariate, recurrent-event, and competing-risks survival data, and joint modeling with longitudinal data,
- statistical testing for the existence and difference of cure rates and sufficient follow-up,
- new developments in Bayesian cure models,
- applications of cure models in public health research and clinical trials.
1. Introduction
A Brief Review of Cure Models
Time-to-Event Data and Cured Subjects
Survival Models and Cured Models
Aim and Scope of the Book
2. The Parametric Cure Model
Introduction
Parametric Mixture Cure Models
Parametric Incidence Submodel
Parametric Latency Submodel
Parametric PH Latency Submodel
Parametric AFT Latency Submodel
Other Parametric Latency Submodels
Model Estimation
Direct Maximization of Observed Likelihood Function
Estimation via EM Algorithm
Non-Mixture Cure Models
Proportional Hazards Cure Model
Cure Models Based on Tumor Activation Scheme
Cure Models Based on Frailty Models
Cure Models Based on Box-Cox Transformation
Model Assessment
Choosing an Appropriate Parametric Distribution
Mixture vs Non-Mixture Cure Models
Goodness of Fit by Residuals
Software and Applications
R Package gfcure
R Package mixcure
R Package _exsurvcure
SAS Macro PSPMCM
Summary
3. The Semiparametric and Nonparametric Cure Models
Introduction
Semiparametric Mixture Cure Models
Semiparametric PH Latency Submodel
Restrictions on the Upper Tail of the Baseline Distribution
Time-Dependent Covariates in the Latency Submodel
Semiparametric AFT Latency Submodel
Linear Rank Method
M-Estimation Method
Kernel Smoothing Method
Semiparametric AH Latency Submodel
Linear Rank Method
Kernel Smoothing Method
Semiparametric Transformation Latency Submodels
Semiparametric Incidence Submodel
Semiparametric Spline-Based Cure Models
Nonparametric Mixture Cure Models
Nonparametric Incidence Submodels
Kaplan-Meier Estimator
Generalized Kaplan-Meier Estimator
Nonparametric Latency Submodels
Semiparametric Non-Mixture Cure Models
Semiparametric PHC Model
General Non-Mixture Cure Models
Model Assessment
Residuals for Overall Model Fitting
Residuals for Latency Submodels
Assessing Cure Rate Prediction
Concordance Measures for Cure Models
Testing Goodness-of-Fit of Parametric Cure Rate Estimation
Variable Selection
Software and Applications
R Package mixcure
R Package smcure
SAS Macro PSPMCM
R Package Survival
R Package npcure
Summary
4. Cure Models for Multivariate Survival Data and Competing Risks
Introduction
Marginal Cure Models
Marginal Models with Working Independence
Marginal Models with Speci_ed Correlation Structures
Cure Models with Random E_ects
Mixture Cure Models with Frailties
Non-Nixture Cure Model with Frailties
Cure Models for Recurrent Event Data
Cure Models for Competing-Risks Survival Data
Classical Approach
Vertical Approach
Software and Applications
R Package geecure
R Package intcure
Summary
5. Joint Modeling of Longitudinal and Survival Data with a Cure Fraction
Introduction
Longitudinal and Survival Data with a Cured Fraction
Joint Modeling Longitudinal and Survival Data with Shared Random Effects
Modeling Longitudinal Proportional Data in Joint Modeling
Joint Modeling by Including Longitudinal Effects in Cure Model
Applications
Summary
6. Testing the Existence of Cured Subjects and Sufficient Follow-up
Introduction
Tests for Existence of Cured Subjects
Without Covariates
Likelihood Ratio Test
Score Test
With Covariates
Testing for Sufficient Follow-up
Summary
7. Bayesian Cure Model
Introduction
Flexible Cure Model with Latent Activation Schemes
Model Formulation and Inference
Bayesian Cure Model with Negative Binomial Distribution
Application
Bayesian Cure Models with Generalized Modified Weibull Distribution
Model Formulation and Inference
Application
Bayesian Mixture Cure Model with Spatially Correlated Frailties
Spatial Mixture Cure Model
Application
Implementation
Summary
8. Analysis of Population-Based Cancer Survival Data
Introduction
Population-Based Cancer Registry and Survival Data
Parametric Cure Models for Net Survival
Flexible Parametric Survival Model
Flexible Parametric Cure Model
Software Implementations
Testing the Existence of Statistical Cure
Testing Hypothesis of Non-Inferiority of Survival
A Minimum Version of One-Sample Log-Rank Test
Applications
Weibull Mixture Cure Model for Grouped Survival Data
Analysis of Individually-Listed Colorectal Cancer Relative
Survival Data
Testing the Existence of Cure for Colorectal Cancer Patients
Summary
9. Design and Analysis of Cancer Clinical Trials
Introduction
Testing Treatment Effects in the Presence of Cure
Comparison of Log-Rank Type Tests
Sample Size for the Weighted Log-Rank Test under the Proportional Hazards Cure Model
Power and Sample Size in the Presence of Delayed Onset of Treatment Effect and Cure
Some Design Issues in Clinical Trials with Cure
Cure Modeling in Real-Time Prediction
Futility Analysis of Survival Data with Cure
Conditional Power for Mixture Cure Models
Conditional Power for Non-Mixture Cure Models
Application
Sample Size Calculation for Trial Design
Predicting Future Number of Events
Summary
Biography
Yingwei Peng is Professor of Biostatistics in the Departments of Public Health Sciences and Mathematics and Statistics at Queen’s University and a senior Biostatistician at Queen’s Cancer Research Institute. He has been an Associate Editor of Canadian Journal of Statistics since 2010 and provided referee services to all mainstream statistical journals and Canadian federal funding agencies (NSERC and CIHR). He offered short courses on cure models, either by himself or with Jeremy Taylor (University of Michigan, USA), in Joint Statistical Meetings, ENAR Spring Meeting, and Université catholique de Louvain, Belgium, in 2014. Binbing Yu is an Associate Director in the AstraZeneca oncology biometric group. He has extensive experience in the applications of cure models in public health, clinical trials and health economics and made notable contributions to the development and enhancement of cure modeling for the presentation and analysis of cancer survival data for the USA National Cancer Institute.
"The book, written by two well-known experts in the field, deals with cure models, wherein a portion of patients are deemed cured after a long period of follow up. This is a very important topic, both statistically and clinically. Though there are several books covering similar topics, the book clearly distinguishes itself from them in the following aspects:
1. It gives a much more comprehensive and updated treatment to cure models, ranging from parametric models to semi-parametric and nonparametric models, from a single endpoint to multivariate outcomes. Undoubtedly, this gives a solid and informative exposure to statisticians who would want to conduct research in the field.
2. It has been extremely helpful that the authors illustrate all the methods in the book by using the software developed by them. Thus, the book contains actionable knowledge that will benefit practitioners.
3. With a number of interesting datasets included in the book, the authors have nicely embedded the models and techniques with them, another practically appealing point.
As such, I strongly recommend the book and believe it will be useful for both theoreticians as well as practitioners."
(Yi Li, University of Michigan, Ann Arbor)
"I’m very glad that a new book on cure models is in preparation. There is an urgent need for a book on this topic…The book is written from a rather applied perspective, focusing on practical estimation, model validation, applications and software, without going more deeply into more theoretical issues like underlying model assumptions to make cure models identifiable, rigorous mathematical statements and properties, etc… The book is clearly written...Moreover, it is self-comprehensive and pleasant to read. It will definitely become an important reference in the field." (Ingrid Van Keilegom, KU Leuven)
"To the best of my knowledge a book on cure models on its own is not available yet. In view of the state of the art of cure models, a comprehensive book on this topic is very pertinent. It could be used as a textbook for a doctoral course in cure models as well as a reference book for researchers in the field." (Ricardo Cao, A Coruña, CITIC, ITMATI)
"Overall, this book is an admirable compilation of statistical design and methods addressing all phases of oncological drug development. It is primarily targeted at practitioners who will find the illustrative examples utilizing real data helpful. The book presents both Frequentist and Bayesian methods with ample references and useful R libraries, thus allowing readers from many backgrounds to learn about the cure rate model and its application."
Satrajit Roychoudhury, Pfizer USA, Wiley Biometrics, March 2022.