1st Edition

Cure Models Methods, Applications, and Implementation

By Yingwei Peng, Binbing Yu Copyright 2021
    268 Pages
    by Chapman & Hall

    268 Pages
    by Chapman & Hall

    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.