Cure Models : Methods, Applications, and Implementation book cover
1st Edition

Cure Models
Methods, Applications, and Implementation

ISBN 9780367145576
Published March 23, 2021 by Chapman and Hall/CRC
268 Pages

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Book Description

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.

Table of Contents

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


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



3. The Semiparametric and Nonparametric Cure Models


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


R Package Survival

R Package npcure


4. Cure Models for Multivariate Survival Data and Competing Risks


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


5. Joint Modeling of Longitudinal and Survival Data with a Cure Fraction


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



6. Testing the Existence of Cured Subjects and Sufficient Follow-up


Tests for Existence of Cured Subjects

Without Covariates

Likelihood Ratio Test

Score Test

With Covariates

Testing for Sufficient Follow-up


7. Bayesian Cure Model


Flexible Cure Model with Latent Activation Schemes

Model Formulation and Inference

Bayesian Cure Model with Negative Binomial Distribution


Bayesian Cure Models with Generalized Modified Weibull Distribution

Model Formulation and Inference


Bayesian Mixture Cure Model with Spatially Correlated Frailties

Spatial Mixture Cure Model




8. Analysis of Population-Based Cancer Survival Data


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


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


9. Design and Analysis of Cancer Clinical Trials


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


Sample Size Calculation for Trial Design

Predicting Future Number of Events



View More



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.