Mixture Modelling for Medical and Health Sciences provides a direct connection between theoretical developments in mixture modelling and their applications in real world problems. The book describes the development of the most important concepts through comprehensive analyses of real and practical examples taken from real-life research problems in

Dr Angus Ng is a Professor of Biostatistics in the School of Medicine, Griffith University. He was awarded his PhD degree in statistics from the University of Queensland in 1999. Dr Ng is an experienced researcher, with expertise in the fields of biostatistics, statistical modelling, cluster analysis, pattern recognition, machine learning, image analysis, and survival analysis. In these areas, he has more than 100 publications. The focus in the field of statistical modelling has been on the theory and applications of finite mixture models and on estimation via the EM algorithm. In his pioneering work on mixture model-based clustering of longitudinal data, he has elucidated a clear vision for the role of random-effects models to provide a sound theoretical framework for classifying correlated longitudinal data and exploring possible relationships among groups of correlated subjects.

Dr Ng was awarded six ARC grants and has been actively involved in multidisciplinary research projects, NHMRC research projects, as well as consultancy and Government contracts. He is also a researcher with the Centre for Applied Health Economics (CAHE) and is an Associate Editor of the Journal of Statistical Computation and Simulation.

Prof. Kelvin K W Yau is a professor in the department of management sciences at the City University of Hong Kong. His research interests include Generalized Linear Mixed Models, Multivariate Survival Analysis, Finite Mixture Models, Robust Estimation, Statistical Modelling and Zero-Inflated-Poisson Models.

Liming Xiang is a professor of statistics at Nanyang Technological University in Singapore. She got her PhD degree in 2002 from the City University of Hong Kong. She serves as associate editor for Statistics in Medicine, Computational Statistics & Data Analysis and Journal of Statistical Computation and Simulation.

1. Introduction

Why Mixture Modelling is Needed

Example: UCLA Example Data Set

Fundamental Concepts of Finite Mixture Models

Maximum Likelihood Estimation

Spurious Clusters

Determination of the Number of Components

Identifiability of Mixture Distributions

EM Algorithm

Basic Principles of the EM Algorithm

Formulation of Mixture Modelling as Incomplete-Data Problems

Convergence and Initialization of the EM Algorithm

Provision of Standard Errors of Estimates

Applications of Mixture Models in Medical and Health Sciences

Overview of Book

Sample Size Considerations for Mixture Models

Computing Packages for Mixture Models

R Programs

Fortran Programs

2. Mixture of Normal Distributions for Continuous Data

Introduction

E- and M-steps

Diagnostic Procedures

Example: Univariate Normal Mixtures

Example: Multivariate Normal Mixtures

Extensions of the Normal Mixture Model

R Programs for Fitting Mixtures of Normal Distributions

3. Mixture of Gamma Distributions for Continuous Nonnormal Data

Introduction

E- and M-steps

Diagnostic Procedures

Example: Mixture of Gamma Regression Model

Example: Mixture of Gamma Distributions for Clustering Cost Data

Fortran Programs for Fitting Mixtures of Gamma Distributions

4. Mixture of Generalized Linear Models for Count or Categorical Data

Introduction

Poisson Mixture Regression Model

Zero-inflated Poisson Regression Model

Zero-inflated Negative Binomial Regression Models

Example: Pancreas Disorder Length of Stay Data

Score Tests for Zero-inflation in Count Models

Example: Revisit of the Pancreas Disorder LOS Data

Mixture of Generalized Bernoulli Distributions

E- and M-steps

Cluster Analysis in Comorbidity Research

Example: Australian National Health Survey Data

Computing Programs for Fitting Mixture of Generalized Linear Models

5. Mixture Models for Survival Data

Introduction

Application of Mixture Models in Survival Analysis

Mixture Models of Parametric Survival Distributions

The EM Algorithm for Mixtures of Parametric Survival Models

Example: Survival mixture modelling of mortality data

Semi-Parametric Mixture Survival Models

The ECM Algorithm

Example: Survival analysis of competing-risks data

Long-Term Survivor Mixture Models

Example: Long-term survivors mixture model

Diagnostic Procedures

Fortran Programs for Fitting Mixtures of Survival Models

6. Advanced mixture modelling with random-effects components

Why is random effects modelling needed?

Fundamentals for GLMM formulation and derivation

Normally distributed random components and BLUP estimation

Maximum likelihood (ML) estimation

Residual maximum likelihood (REML) estimation

Generalized linear mixed models (GLMM)

Application of GLMM to mixture models with random effects

Poisson mixture models

Zero-inflated Poisson mixture models

Frailty models in survival analysis

Survival mixture models

Long-term survivor models with random effects

7. Advanced Mixture Models for Multilevel or Repeated-measured Data

Introduction

Poisson Mixture Regression Model with Random Effects

Robust Estimation Using Minimum Hellinger Distance

Assessment of Model Adequacy and Influence Diagnostics

Example: Recurrent Urinary Tract Infection Data

Zero-inflated Poisson Mixture Models with Random Effects

Score test for zero-inflation in mixed Poisson models

Example: Revisit of the Recurrent UTI Data

Survival Mixture Models with Random Effects

Example: rhDNase Clinical Trial Data

Long-Term Survivor Mixture Models with Random Effects

Example: Chronic Granulomatous Disease (CGD) Data

Computing Programs for Fitting Multilevel Mixture Models

8. Advanced Mixture Models for Correlated Multivariate Continuous Data

Introduction

Maximum likelihood estimation via the EM algorithm

Clustering of gene-expression data (cross-sectional with repeated measurements)

Inference on differences between classes using cluster specific contrasts of mixed effects

A non-parametric clustering approach for identification of correlated differentially-expressed genes

Example: Cluster analysis of a pancreatic cancer gene expression data set

Clustering of time-course gene-expression data

Inference for gene regulatory interactions

Example: Cluster analysis of a time-course gene expression data set

Clustering of multilevel longitudinal data

EM-based estimation via maximum likelihood

Example: Cluster analysis of a multilevel longitudinal data set

R and Fortran Programs for Fitting Mixtures of Linear Mixed Models

9. Miscellaneous: Handling of Missing Data

Introduction

Mixture model-based clustering of data with missing values

Multiple imputation approach

EM Algorithm

Example: Multivariate nor…