Dynamical Biostatistical Models

Dynamical Biostatistical Models presents statistical models and methods for the analysis of longitudinal data. The book focuses on models for analyzing repeated measures of quantitative and qualitative variables and events history, including survival and multistate models. Most of the advanced methods, such as multistate and joint models, can be applied using SAS or R software.

The book describes advanced regression models that include the time dimension, such as mixed-effect models, survival models, multistate models, and joint models for repeated measures and time-to-event data. It also explores the possibility of unifying these models through a stochastic process point of view and introduces the dynamic approach to causal inference.

Drawing on much of their own extensive research, the authors use three main examples throughout the text to illustrate epidemiological questions and methodological issues. Readers will see how each method is applied to real data and how to interpret the results.

Introduction
General presentation of the book
Organization of the book
Notation
Presentation of examples

Classical Biostatistical Models
Inference
Generalities on inference: the concept of model
Likelihood and applications
Other types of likelihoods and estimation methods
Model choice
Optimization algorithms

Survival Analysis
Introduction
Event, origin, and functions of interest
Observation patterns: censoring and truncation
Estimation of the survival function
The proportional hazards model
Accelerated failure time model
Counting processes approach
Additive hazards models
Degradation models

Models for Longitudinal Data
Linear mixed models
Generalized mixed linear models
Non-linear mixed models
Marginal models and generalized estimating equations (GEE)
Incomplete longitudinal data
Modeling strategies

Advanced Biostatistical Models
Extensions of Mixed Models
Mixed models for curvilinear outcomes
Mixed models for multivariate longitudinal data
Latent class mixed models

Advanced Survival Models
Relative survival
Competing risks models
Frailty models
Extension of frailty models
Cure models

Multistate Models
Introduction
Multistate processes
Multistate models: generalities
Observation schemes
Statistical inference for multistate models observed in continuous time
Inference for multistate models from interval-censored data
Complex functions of parameters: individualized hazards, sojourn times
Approach by counting processes
Other approaches

Joint Models for Longitudinal and Time-to-Event Data
Introduction
Models with shared random effects
Latent class joint model
Latent classes versus shared random effects
The joint model as prognostic model
Extension of joint models

The Dynamic Approach to Causality
Introduction
Local independence, direct and indirect influence
Causal influences
The dynamic approach to causal reasoning in ageing studies
Mechanistic models
The issue of dynamic treatment regimes

Daniel Commenges is emeritus research director at INSERM and founder of the Biostatistics Team at the University of Bordeaux. Dr. Commenges has published more than 200 papers and was editor of Biometrics and an associate editor of several other journals. His main research interests focus on statistical models in epidemiology and biology, applications of stochastic processes, statistical inference in dynamical models, and model selection.

Hélène Jacqmin-Gadda is research director at INSERM and head of the Biostatistics Team at the University of Bordeaux. Dr. Jacqmin-Gadda is a member of the International Biometrics Society and was an associate editor of Biometrics. Her research involves methods for analyzing longitudinal data and joint models in areas, including brain aging, HIV, and cancer.