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.

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.

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

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

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

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

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

Introduction

Tests for Existence of Cured Subjects

Without Covariates

Likelihood Ratio Test

Score Test

With Covariates

Testing for Sufficient Follow-up

Summary…