Analysis of Longitudinal Data

, by Diggle, Peter; Heagerty, Patrick; Liang, Kung-Yee; Zeger, Scott

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ISBN: 9780198524847 | 0198524846
Cover: Hardcover
Copyright: 8/29/2002

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The first edition of Analysis for Longitudinal Data has become a classic. Describing the statistical models and methods for the analysis of longitudinal data, it covers both the underlying statistical theory of each method, and its application to a range of examples from the agricultural andbiomedical sciences. The main topics discussed are design issues, exploratory methods of analysis, linear models for continuous data, general linear models for discrete data, and models and methods for handling data and missing values. Under each heading, worked examples are presented in parallelwith the methodological development, and sufficient detail is given to enable the reader to reproduce the author's results using the data-sets as an appendix. This new edition of Analysis for Longitudinal Data provides a thorough and expanded revision of this important text. It includes two newchapters; the first discusses fully parametric models for discrete repeated measures data, and the second explores statistical models for time-dependent predictors.

Introduction

(21)

Longitudinal studies

(2)

Examples

(12)

Notation

(1)

Merits of longitudinal studies

(1)

Approaches to longitudinal data analysis

(3)

Organization of subsequent chapters

(2)

Design considerations

(11)

Introduction

(1)

Bias

(2)

Efficiency

(2)

Sample size calculations

(5)

Continuous responses

(2)

Binary responses

(1)

Further reading

(2)

Exploring longitudinal data

(21)

Introduction

(1)

Graphical presentation of longitudinal data

(7)

Fitting smooth curves to longitudinal data

(5)

Exploring correlation structure

(6)

Exploring association amongst categorical responses

(1)

Further reading

(1)

General linear models for longitudinal data

(27)

Motivation

(1)

The general linear model with correlated errors

(4)

The uniform correlation model

(1)

The exponential correlation model

(1)

Two-stage least-squares estimation and random effects models

(2)

Weighted least-squares estimation

(5)

Maximum likelihood estimation under Gaussian assumptions

(2)

Restricted maximum likelihood estimation

(4)

Robust estimation of standard errors

(11)

Parametric models for covariance structure

(33)

Introduction

(1)

Models

(11)

Pure serial correlation

(5)

Serial correlation plus measurement error

(1)

Random intercept plus serial correlation plus measurement error

(1)

Random effects plus measurement error

(2)

Model-fitting

(6)

Formulation

(1)

Estimation

(2)

Inference

(1)

Diagnostics

(1)

Examples

(11)

Estimation of individual trajectories

110

(3)

Further reading

113

(1)

Analysis of variance methods

114

(12)

Preliminaries

114

(1)

Time-by-time ANOVA

115

(1)

Derived variables

116

(7)

Repeated measures

123

(2)

Conclusions

125

(1)

Generalized linear models for longitudinal data

126

(15)

Marginal models

126

(2)

Random effects models

128

(2)

Transition (Markov) models

130

(1)

Contrasting approaches

131

(6)

Inferences

137

(4)

Marginal models

141

(28)

Introduction

141

(1)

Binary responses

142

(6)

The log-linear model

142

(1)

Log-linear models for marginal means

143

(3)

Generalized estimating equations

146

(2)

Examples

148

(12)

Counted responses

160

(5)

Parametric modelling for count data

160

(2)

Generalized estimating equation approach

162

(3)

Sample size calculations revisited

165

(2)

Further reading

167

(2)

Random effects models

169

(21)

Introduction

169

(2)

Estimation for generalized linear mixed models

171

(4)

Conditional likelihood

171

(1)

Maximum likelihood estimation

172

(3)

Logistic regression for binary responses

175

(9)

Conditional likelihood approach

175

(3)

Random effects models for binary data

178

(2)

Examples of logistic models with Gaussian random effects

180

(4)

Counted responses

184

(5)

Conditional likelihood method

184

(2)

Random effects models for counts

186

(2)

Poisson-Gaussian random effects models

188

(1)

Further reading

189

(1)

Transition models

190

(18)

General

190

(2)

Fitting transition models

192

(2)

Transition models for categorical data

194

(10)

Indonesian children's study example

197

(4)

Ordered categorical data

201

(3)

Log-linear transition models for count data

204

(2)

Further reading

206

(2)

Likelihood-based methods for categorical data

208

(37)

Introduction

208

(1)

Notation and definitions

209

(1)

Generalized linear mixed models

209

(7)

Maximum likelihood algorithms

212

(2)

Bayesian methods

214

(2)

Marginalized models

216

(15)

An example using the Gaussian linear model

218

(2)

Marginalized log-linear models

220

(2)

Marginalized latent variable models

222

(3)

Marginalized transition models

225

(6)

Summary

231

(1)

Examples

231

(12)

Crossover data

231

(3)

Madras schizophrenia data

234

(9)

Summary and further reading

243

(2)

Time-dependent covariates

245

(37)

Introduction

245

(2)

An example: the MSCM study

247

(6)

Stochastic covariates

253

(6)

Estimation issues with cross-sectional models

254

(2)

A simulation illustration

256

(1)

MSCM data and cross-sectional analysis

257

(1)

Summary

258

(1)

Lagged covariates

259

(6)

A single lagged covariate

259

(1)

Multiple lagged covariates

260

(1)

MSCM data and lagged covariates

261

(4)

Summary

265

(1)

Time-dependent confounders

265

(15)

Feedback: response is an intermediate and a confounder

266

(2)

MSCM data and endogeneity

268

(1)

Targets of inference

269

(4)

Estimation using g-computation

273

(2)

MSCM data and g-computation

275

(1)

Estimation using inverse probability of treatment weights (IPTW)

276

(3)

MSCM data and marginal structural models using IPTW

279

(1)

Summary

280

(1)

Summary and further reading

280

(2)

Missing values in longitudinal data

282

(37)

Introduction

282

(1)

Classification of missing value mechanisms

283

(1)

Intermittent missing values and dropouts

284

(3)

Simple solutions and their limitations

287

(1)

Last observation carried forward

287

(1)

Complete case analysis

288

(1)

Testing for completely random dropouts

288

(5)

Generalized estimating equations under a random missingness mechanism

293

(2)

Modelling the dropout process

295

(10)

Selection models

295

(4)

Pattern mixture models

299

(2)

Random effect models

301

(2)

Contrasting assumptions: a graphical representation

303

(2)

A longitudinal trial of drug therapies for schizophrenia

305

(11)

Discussion

316

(3)

Additional topics

319

(18)

Non-parametric modelling of the mean response

319

(7)

Further reading

326

(1)

Non-linear regression modelling

326

(3)

Correlated errors

328

(1)

Non-linear random effects

329

(1)

Joint modelling of longitudinal measurements and recurrent events

329

(3)

Multivariate longitudinal data

332

(5)

Appendix Statistical background

337

(12)

Introduction

337

(1)

The linear model and the method of least squares

337

(2)

Multivariate Gaussian theory

339

(1)

Likelihood inference

340

(3)

Generalized linear models

343

(3)

Logistic regression

343

(1)

Poisson regression

344

(1)

The general class

345

(1)

Quasi-likelihood

346

(3)

Bibliography

349

(20)

Index

369

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Analysis of Longitudinal Data

Summary

Table of Contents

Supplemental Materials