Analysis of Longitudinal Data

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

• ISBN13: 9780198524847
• ISBN10: 0198524846
• Edition: 2nd
• Format: Hardcover
• Copyright: 2002-08-29
• Publisher: Oxford University Press

Summary

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.

Table of Contents

Introduction	1	(21)
Longitudinal studies	1	(2)
Examples	3	(12)
Notation	15	(1)
Merits of longitudinal studies	16	(1)
Approaches to longitudinal data analysis	17	(3)
Organization of subsequent chapters	20	(2)
Design considerations	22	(11)
Introduction	22	(1)
Bias	22	(2)
Efficiency	24	(2)
Sample size calculations	26	(5)
Continuous responses	28	(2)
Binary responses	30	(1)
Further reading	31	(2)
Exploring longitudinal data	33	(21)
Introduction	33	(1)
Graphical presentation of longitudinal data	34	(7)
Fitting smooth curves to longitudinal data	41	(5)
Exploring correlation structure	46	(6)
Exploring association amongst categorical responses	52	(1)
Further reading	53	(1)
General linear models for longitudinal data	54	(27)
Motivation	54	(1)
The general linear model with correlated errors	55	(4)
The uniform correlation model	55	(1)
The exponential correlation model	56	(1)
Two-stage least-squares estimation and random effects models	57	(2)
Weighted least-squares estimation	59	(5)
Maximum likelihood estimation under Gaussian assumptions	64	(2)
Restricted maximum likelihood estimation	66	(4)
Robust estimation of standard errors	70	(11)
Parametric models for covariance structure	81	(33)
Introduction	81	(1)
Models	82	(11)
Pure serial correlation	84	(5)
Serial correlation plus measurement error	89	(1)
Random intercept plus serial correlation plus measurement error	90	(1)
Random effects plus measurement error	91	(2)
Model-fitting	93	(6)
Formulation	94	(1)
Estimation	95	(2)
Inference	97	(1)
Diagnostics	98	(1)
Examples	99	(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