Mixture Modelling for Medical and Health Sciences: 1st Edition (Hardback) book cover

Mixture Modelling for Medical and Health Sciences

1st Edition

By Shu-Kay Ng, Liming Xiang, Kelvin Kai Wing Yau

Chapman and Hall/CRC

296 pages | 40 B/W Illus.

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Hardback: 9781482236750
pub: 2019-05-27
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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 medical and health sciences. This approach represents balance between "theory" and "practice", stimulating readers and enhancing their capacity to apply mixture models in data analysis. Full of reproducible examples using software code and publicly-available data, the book is suitable for graduate-level students, researchers, and practitioners who have a basic grounding in statistics and would like to explore the use of mixture models to analyse their experiments and research data.


  • An in-depth account of the most up-to-date mixture modelling techniques from auser perspective.
  • Extensive real-life examples – from typical daily problems to complex data modelling.
  • Emphasis on the use of a wide variety of component densities for statistical modelling.
  • Coverage of the latest random-effects models in modelling complex correlated data.
  • An accompanying website to provide supplementary materials, including software and detailed programming code, and links to available data sources.
  • Provision of R and Fortran code for readers who want to do analysis of their own data using mixture models.


Shu-Kay Angus Ng is Professor of Biostatistics in the School of Medicine at the Griffith University, Australia. Dr Ng has published extensively on his research interests, which include cluster analysis, pattern recognition, random-effects modelling, and survival analysis.

Liming Xiang is Associate Professor of Statistics in the School of Physical & Mathematical Sciences at the Nanyang Technological University, Singapore. Her research interests include survival analysis, longitudinal/clustered data analysis and mixture models.

Kelvin Kai-wing Yau is Professor of Statistics in the Department of Management Sciences at the City University of Hong Kong. He has been involved in various interdisciplinary research projects, with journal publications in statistics, medical and health science journals on topics such as mixed effects models, survival analysis and statistical modelling in general.

Table of Contents

  1. Introduction
  2. 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

  3. Mixture of Normal Distributions for Continuous Data
  4. 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  

  5. Mixture of Gamma Distributions for Continuous Nonnormal Data
  6. 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

  7. Mixture of Generalized Linear Models for Count or Categorical Data
  8. 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

  9. Mixture Models for Survival Data
  10. 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

  11. Advanced mixture modelling with random-effects components
  12. 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

  13. Advanced Mixture Models for Multilevel or Repeated-measured Data
  14. 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

  15. Advanced Mixture Models for Correlated Multivariate Continuous Data
  16. 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

  17. Miscellaneous: Handling of Missing Data
  18. Introduction

    Mixture model-based clustering of data with missing values

    Multiple imputation approach

    EM Algorithm

    Example: Multivariate normal mixture model

    Missing data in longitudinal studies

    Example: Clustering longitudinal data with missing values


  19. Miscellaneous: Cluster Analysis of "Big Data" Using Mixture Models


Speeding up the EM Algorithm for Multivariate Normal Mixtures

Example: Segmentation of Magnetic Resonance (MR)

Images of the Human Brain

Example: Segmentation of Molecular Pathology Images of Cancer Patients

Mixtures of linear mixed models for clustering big data with a hierarchical structure

Clustering of Multilevel Data from Multiple Sources

Consensus Clustering of Data from Multiple Sources


About the Authors

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 includeGeneralized 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.

About the Series

Chapman & Hall/CRC Biostatistics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General