Sutradhar B.C. Dynamic Mixed Models for Familial Longitudinal Data

Springer – 2011, 512 pages
ISBN: 1441983414, 1441983422This book provides a theoretical foundation for the analysis of discrete data such as count and binary data in the longitudinal setup. Unlike the existing books, this book uses a class of auto-correlation structures to model the longitudinal correlations for the repeated discrete data that accommodates all possible Gaussian type auto-correlation models as special cases including the equi-correlation models.
This new dynamic modelling approach is utilized to develop theoretically sound inference techniques such as the generalized quasi-likelihood (GQL) technique for consistent and efficient estimation of the underlying regression effects involved in the model, whereas the existing ‘working’ correlations based GEE (generalizedestimating equations) approach has serious theoretical limitations both for consistent and efficient estimation, and the existing random effects based correlations approach is not suitable to model the longitudinal correlations. The book has exploited the random effects carefully only to model the correlations of the familial data. Subsequently, this book has modelled the correlations of the longitudinal data collected from the members of a large number of independent families by using the class of auto-correlation structures conditional on the random effects. The book also provides models and inferences for discrete longitudinal data in the adaptive clinical trial set up.The book is mathematically rigorous and provides details for the development of estimation approaches under selected familial and longitudinal models. Further, while the book provides special cares for mathematics behind the correlation models, it also presents theillustrations of the statistical analysis of various real life data. This book will be of interest to the researchers including graduate students in biostatistics and econometrics, among other applied statistics research areas. Brajendra Sutradhar is a University Research Professor at Memorial University in St. John’s, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to thesociety including his special services for society’s annual meetings.I. Introduction
Background of Familial Models
Background of Longitudinal Models.II. Overview of Linear Fixed Models for Longitudinal Data
Estimation of b
Method of Moments (MM)
Ordinary Least Squares (OLS) Method
OLS Versus GLS Estimation Performance
Estimation of b Under Stationary General Autocorrelation Structure
A Class of Autocorrelations
Estimation of b
A Rat Data Example
Alternative Modelling for Time Effects
ExercisesIII. Overview of Linear Mixed Models for Longitudinal Data
Linear Longitudinal Mixed Model
GLS Estimation of b
Moment Estimating Equations for s g and r`
Linear Mixed Models for Rat Data
Linear Dynamic Mixed Models for Balanced Longitudinal Data
Basic Properties of the Dynamic Dependence Mixed Model ()
Estimation of the Parameters of the Dynamic Mixed Model ()
Further Estimation for the Parameters of the Dynamic Mixed Model
GMM/IMM Estimation Approach
GQL Estimation Approach
Asymptotic Efficiency Comparison
ExercisesIV. Familial Models for Count Data
Poisson Mixed Models and Basic Properties
Estimation for Single Random Effect Based Parametric Mixed Models
Exact Likelihood Estimation and Drawbacks
Penalized Quasi-Likelihood Approach
Small Variance Asymptotic Approach: A Likelihood
Approximation (LA)
Hierarchical Likelihood (HL) Approach
Method of Moments (MM)
Generalized Quasi-Likelihood (GQL) Approach
Efficiency Comparison
A Health Care Data Utilization Example
Estimation for Multiple Random Effects Based Parametric Mixed
Models
Random Effects in a Two-Way Factorial Design Setup
One-Way Heteroscedastic Random Effects
Multiple Independent Random Effects
Semiparametric Approach
Computations for μi, li, Si, and Wi
Construction of the Estimating Equation for b When s g Is
Known
Monte Carlo Based Likelihood Estimation
MCEM Approach
MCNR Approach
ExercisesV. Familial Models for Binary Data
Binary Mixed Models and Basic Properties
Computational Formulas for Binary Moments
Estimation for Single Random Effect Based Parametric Mixed Models
Method of Moments (MM)
An Improved Method of Moments (IMM)
Generalized Quasi-Likelihood (GQL) Approach
Maximum Likelihood (ML) Estimation
Asymptotic Efficiency Comparison
COPD Data Analysis: A Numerical Illustration
Binary Mixed Models with Multidimensional Random Effects
Models in Two-Way Factorial Design Setup and Basic
Properties
Estimation of Parameters
Salamander Mating Data Analysis
Semiparametric Approach
GQL Estimation
A Marginal Quasi-Likelihood (MQL) Approach
Asymptotic Efficiency Comparison: An Empirical Study
Monte Carlo Based Likelihood Estimation
ExercisesAppendixVI. Longitudinal Models for Count Data
Marginal Model
Marginal Model Based Estimation of Regression Effects
Correlation Models for Stationary Count Data.
Poisson AR() Model
Poisson MA() Model
Poisson Equicorrelation Model
Inferences for Stationary Correlation Models
Likelihood Approach and Complexity
GQL Approach
GEE Approach and Limitations
Nonstationary Correlation Models
Nonstationary Correlation Models with the Same
Specified Marginal Mean and Variance Functions
Estimation of Parameters
Model Selection
More Nonstationary Correlation Models
Models with Variable Marginal Means and Variances
Estimation of Parameters
Model Selection
Estimation and Model Selection: A Simulation Example
A Data Example: Analyzing Health Care Utilization Count Data
Models for Count Data from Longitudinal Adaptive Clinical Trials
Adaptive Longitudinal Designs
Performance of the SLPW and BRW Designs For Treatment Selection: A Simulation Study
Weighted GQL Estimation for Treatment Effects and
Other Regression Parameters
ExercisesAppendixVII. Longitudinal Models for Binary Data
Marginal Model
Marginal Model Based Estimation for Regression Effects
Some Selected Correlation Models for Longitudinal Binary Data
Bahadur Multivariate Binary Density (MBD) Based Model
Kanter Observation-Driven Dynamic (ODD) Model
A Linear Dynamic Conditional Probability (LDCP) Model
A Numerical Comparison of Range Restrictions for Correlation Index Parameter Under Stationary Binary Models
Low-Order Autocorrelation Models for Stationary Binary Data
Binary AR() Model
Binary MA() Model
Binary Equicorrelation (EQC) Model
Complexity in Likelihood Inferences Under Stationary Binary Correlation Models
GQL Estimation Approach
GEE Approach and Its Limitations for Binary Data
Inferences in Nonstationary Correlation Models for Repeated Binary Data
Nonstationary AR() Correlation Model
Nonstationary MA() Correlation Model
Nonstationary EQC Model
Nonstationary Correlations Based GQL Estimation
Model Selection
SLID Data Example
Introduction to the SLID Data
Analysis of the SLID Data
Application to an Adaptive Clinical Trial Setup
Binary Response Based Adaptive Longitudinal Design
Construction of the Adaptive Design Weights Based
Weighted GQL Estimation
More Nonstationary Binary Correlation Models
Linear Binary Dynamic Regression (LBDR) Model
A Binary Dynamic Logit (BDL) Model
Application of the Binary Dynamic Logit (BDL) Model in an Adaptive Clinical Trial Setup
ExercisesAppendixVIII. Longitudinal Mixed Models for Count Data
A Conditional Serially Correlated Model
Parameter Estimation
Estimation of the Regression Effects b
Estimation of the Random Effects Variance sg:
Estimation of the Longitudinal Correlation Parameter r
A Simulation Study
An Illustration: Analyzing Health Care Utilization Count
Data by Using Longitudinal Fixed and Mixed Models.
A Mean Deflated Conditional Serially Correlated Model
Longitudinal Negative Binomial Fixed Model and Estimation of
Parameters
Inferences in Stationary Negative Binomial Correlation Models
A Data Example: Analyzing Epileptic Count Data by
Using Poisson and Negative Binomial Longitudinal Models
Nonstationary Negative Binomial Correlation Models and
Estimation of Parameters
ExercisesAppendixIX. Longitudinal Mixed Models for Binary Data
A Conditional Serially Correlated Model
Basic Properties of the Model
Parameter Estimation
Binary Dynamic Mixed Logit (BDML) Model
GMM/IMM Estimation
GQL Estimation
Efficiency Comparison: GMM Versus GQL
Fitting the Binary Dynamic Mixed Logit Model to the SLID data
GQL Versus Maximum Likelihood (ML) Estimation for
BDML Model
A Binary Dynamic Mixed Probit (BDMP) Model
GQL Estimation for BDMP Model
GQL Estimation Performance for BDMP Model: A
Simulation Study
ExercisesX. Familial Longitudinal Models for Count Data
An Autocorrelation Class of Familial Longitudinal Models
Marginal Mean and Variance
Nonstationary Autocorrelation Models
Parameter Estimation
Estimation of Parameters Under Conditional AR() Model
Performance of the GQL Approach: A Simulation Study
Analyzing Health Care Utilization Data by Using GLLMM
xviii Contents
Some Remarks on Model Identification
An Exploratory Identification
A Further Improved Identification
ExercisesXI. Familial Longitudinal Models for Binary Data
LDCCP Models
Conditional-Conditional (CC) AR() Model
CC MA() Model
CC EQC Model
Estimation of the AR() Model Parameters
Application to Waterloo Smoking Prevention Data
Family Based BDML Models for Binary Data
FBDML Model and Basic Properties
Quasi-Likelihood Estimation in the Familial Longitudinal Setup
Likelihood Based Estimation
Exercises