| Description |
1 online resource |
| Series |
Statistics in practice |
| Contents |
Cover -- Title Page -- Copyright -- Contents -- Preface to third edition -- Mixed models notation -- About the Companion Website -- Chapter 1 Introduction -- 1.1 The use of mixed models -- 1.2 Introductory example -- 1.2.1 Simple model to assess the effects of treatment (Model A) -- 1.2.2 A model taking patient effects into account (Model B) -- 1.2.3 Random effects model (Model C) -- 1.2.4 Estimation (or prediction) of random effects -- 1.3 A multi-centre hypertension trial -- 1.3.1 Modelling the data -- 1.3.2 Including a baseline covariate (Model B) -- 1.3.3 Modelling centre effects (Model C) -- 1.3.4 Including centre-by-treatment interaction effects (Model D) -- 1.3.5 Modelling centre and centre·treatment effects as random (Model E) -- 1.4 Repeated measures data -- 1.4.1 Covariance pattern models -- 1.4.2 Random coefficients models -- 1.5 More about mixed models -- 1.5.1 What is a mixed model? -- 1.5.2 Why use mixed models? -- 1.5.3 Communicating results -- 1.5.4 Mixed models in medicine -- 1.5.5 Mixed models in perspective -- 1.6 Some useful definitions -- 1.6.1 Containment -- 1.6.2 Balance -- 1.6.3 Error strata -- Chapter 2 Normal mixed models -- 2.1 Model definition -- 2.1.1 The fixed effects model -- 2.1.2 The mixed model -- 2.1.3 The random effects model covariance structure -- 2.1.4 The random coefficients model covariance structure -- 2.1.5 The covariance pattern model covariance structure -- 2.2 Model fitting methods -- 2.2.1 The likelihood function and approaches to its maximisation -- 2.2.2 Estimation of fixed effects -- 2.2.3 Estimation (or prediction) of random effects and coefficients -- 2.2.4 Estimation of variance parameters -- 2.3 The Bayesian approach -- 2.3.1 Introduction -- 2.3.2 Determining the posterior density |
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2.3.3 Parameter estimation, probability intervals and p-values -- 2.3.4 Specifying non-informative prior distributions -- 2.3.5 Evaluating the posterior distribution -- 2.4 Practical application and interpretation -- 2.4.1 Negative variance components -- 2.4.2 Accuracy of variance parameters -- 2.4.3 Bias in fixed and random effects standard errors -- 2.4.4 Significance testing -- 2.4.5 Confidence intervals -- 2.4.6 Checking model assumptions -- 2.4.7 Missing data -- 2.4.8 Determining whether the simulated posterior distribution has converged -- 2.5 Example -- 2.5.1 Analysis models -- 2.5.2 Results -- 2.5.3 Discussion of points from Section 2.4 -- Chapter 3 Generalised linear mixed models -- 3.1 Generalised linear models -- 3.1.1 Introduction -- 3.1.2 Distributions -- 3.1.3 The general form for exponential distributions -- 3.1.4 The GLM definition -- 3.1.5 Fitting the GLM -- 3.1.6 Expressing individual distributions in the general exponential form -- 3.1.7 Conditional logistic regression -- 3.2 Generalised linear mixed models -- 3.2.1 The GLMM definition -- 3.2.2 The likelihood and quasi-likelihood functions -- 3.2.3 Fitting the GLMM -- 3.3 Practical application and interpretation -- 3.3.1 Specifying binary data -- 3.3.2 Uniform effects categories -- 3.3.3 Negative variance components -- 3.3.4 Presentation of fixed and random effects estimates -- 3.3.5 Accuracy of variance parameters and potential bias -- 3.3.6 Bias in fixed and random effects standard errors -- 3.3.7 The dispersion parameter -- 3.3.8 Significance testing -- 3.3.9 Confidence intervals -- 3.3.10 Model checking -- 3.3.11 Determining whether the simulated posterior distribution has converged -- 3.4 Example -- 3.4.1 Introduction and models fitted -- 3.4.2 Results -- 3.4.3 Discussion of points from Section 3.3 |
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Chapter 4 Mixed models for categorical data -- 4.1 Ordinal logistic regression (fixed effects model) -- 4.2 Mixed ordinal logistic regression -- 4.2.1 Definition of the mixed ordinal logistic regression model -- 4.2.2 Residual variance matrix -- 4.2.3 Likelihood and quasi-likelihood functions -- 4.2.4 Model fitting methods -- 4.3 Mixed models for unordered categorical data -- 4.3.1 The G matrix -- 4.3.2 The R matrix -- 4.3.3 Fitting the model -- 4.4 Practical application and interpretation -- 4.4.1 Expressing fixed and random effects results -- 4.4.2 The proportional odds assumption -- 4.4.3 Number of covariance parameters -- 4.4.4 Choosing a covariance pattern -- 4.4.5 Interpreting covariance parameters -- 4.4.6 Checking model assumptions -- 4.4.7 The dispersion parameter -- 4.4.8 Other points -- 4.5 Example -- Chapter 5 Multi-centre trials and meta-analyses -- 5.1 Introduction to multi-centre trials -- 5.1.1 What is a multi-centre trial? -- 5.1.2 Why use mixed models to analyse multi-centre data? -- 5.2 The implications of using different analysis models -- 5.2.1 Centre and centre·treatment effects fixed -- 5.2.2 Centre effects fixed, centre·treatment effects omitted -- 5.2.3 Centre and centre·treatment effects random -- 5.2.4 Centre effects random, centre·treatment effects omitted -- 5.3 Example: a multi-centre trial -- 5.4 Practical application and interpretation -- 5.4.1 Plausibility of a centre·treatment interaction -- 5.4.2 Generalisation -- 5.4.3 Number of centres -- 5.4.4 Centre size -- 5.4.5 Negative variance components -- 5.4.6 Balance -- 5.5 Sample size estimation -- 5.5.1 Normal data -- 5.5.2 Binary data -- 5.5.3 Categorical data -- 5.6 Meta-analysis -- 5.7 Example: meta-analysis -- 5.7.1 Analyses -- 5.7.2 Results -- 5.7.3 Treatment estimates in individual trials -- Chapter 6 Repeated measures data |
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6.1 Introduction -- 6.1.1 Reasons for repeated measurements -- 6.1.2 Analysis objectives -- 6.1.3 Fixed effects approaches -- 6.1.4 Mixed models approaches -- 6.2 Covariance pattern models -- 6.2.1 Covariance patterns -- 6.2.2 Choice of covariance pattern -- 6.2.3 Choice of fixed effects -- 6.2.4 General points -- 6.3 Example: covariance pattern models for normal data -- 6.3.1 Analysis models -- 6.3.2 Selection of covariance pattern -- 6.3.3 Assessing fixed effects -- 6.3.4 Model checking -- 6.4 Example: covariance pattern models for count data -- 6.4.1 Analysis models -- 6.4.2 Analysis using a categorical mixed model -- 6.5 Random coefficients models -- 6.5.1 Introduction -- 6.5.2 General points -- 6.5.3 Comparisons with fixed effects approaches -- 6.6 Examples of random coefficients models -- 6.6.1 A linear random coefficients model -- 6.6.2 A polynomial random coefficients model -- 6.7 Sample size estimation -- 6.7.1 Normal data -- 6.7.2 Binary data -- 6.7.3 Categorical data -- Chapter 7 Cross-over trials -- 7.1 Introduction -- 7.2 Advantages of mixed models in cross-over trials -- 7.3 The AB/BA cross-over trial -- 7.3.1 Example: AB/BA cross-over design -- 7.4 Higher order complete block designs -- 7.4.1 Inclusion of carry-over effects -- 7.4.2 Example: four-period, four-treatment cross-over trial -- 7.5 Incomplete block designs -- 7.5.1 Example: Three treatment two-period cross-over trial -- 7.6 Optimal designs -- 7.6.1 Example: Balaam's design -- 7.7 Covariance pattern models -- 7.7.1 Structured by period -- 7.7.2 Structured by treatment -- 7.7.3 Example: four-way cross-over trial -- 7.8 Analysis of binary data -- 7.9 Analysis of categorical data -- 7.10 Use of results from random effects models in trial design -- 7.10.1 Example -- 7.11 General points |
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Chapter 8 Other applications of mixed models -- 8.1 Trials with repeated measurements within visits -- 8.1.1 Covariance pattern models -- 8.1.2 Example -- 8.1.3 Random coefficients models -- 8.1.4 Example: random coefficients models -- 8.2 Multi-centre trials with repeated measurements -- 8.2.1 Example: multi-centre hypertension trial -- 8.2.2 Covariance pattern models -- 8.3 Multi-centre cross-over trials -- 8.4 Hierarchical multi-centre trials and meta-analysis -- 8.5 Matched case -- control studies -- 8.5.1 Example -- 8.5.2 Analysis of a quantitative variable -- 8.5.3 Check of model assumptions -- 8.5.4 Analysis of binary Variables -- 8.6 Different variances for treatment groups in a simple between-patient trial -- 8.6.1 Example -- 8.7 Estimating variance components in an animal physiology trial -- 8.7.1 Sample size estimation for a future experiment -- 8.8 Inter- and intra-observer variation in foetal scan measurements -- 8.9 Components of variation and mean estimates in a cardiology experiment -- 8.10 Cluster sample surveys -- 8.10.1 Example: cluster sample survey -- 8.11 Small area mortality estimates -- 8.12 Estimating surgeon performance -- 8.13 Event history analysis -- 8.13.1 Example -- 8.14 A laboratory study using a within-subject 4 x 4 factorial design -- 8.15 Bioequivalence studies with replicate cross-over designs -- 8.15.1 Example -- 8.16 Cluster randomised trials -- 8.16.1 Example: A trial to evaluate integrated care pathways for treatment of children with asthma in hospital -- 8.16.2 Example: Edinburgh randomised trial of breast screening -- 8.17 Analysis of bilateral data -- 8.18 Incomplete block designs -- 8.18.1 Introduction -- 8.18.2 Balanced incomplete block (BIB) designs |
| Summary |
A fully updated edition of this key text on mixed models, focusing on applications in medical research The application of mixed models is an increasingly popular way of analysing medical data, particularly in the pharmaceutical industry. A mixed model allows the incorporation of both fixed and random variables within a statistical analysis, enabling efficient inferences and more information to be gained from the data. There have been many recent advances in mixed modelling, particularly regarding the software and applications. This third edition of Brown and Prescott's groundbreaking text provides an update on the latest developments, and includes guidance on the use of current SAS techniques across a wide range of applications. Presents an overview of the theory and applications of mixed models in medical research, including the latest developments and new sections on incomplete block designs and the analysis of bilateral data. Easily accessible to practitioners in any area where mixed models are used, including medical statisticians and economists. Includes numerous examples using real data from medical and health research, and epidemiology, illustrated with SAS code and output. Features the new version of SAS, including new graphics for model diagnostics and the procedure PROC MCMC. Supported by a website featuring computer code, data sets, and further material. This third edition will appeal to applied statisticians working in medical research and the pharmaceutical industry, as well as teachers and students of statistics courses in mixed models. The book will also be of great value to a broad range of scientists, particularly those working in the medical and pharmaceutical areas |
| Notes |
CIP data; resource not viewed |
| Subject |
Medicine -- Mathematical models.
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Statistics as Topic -- methods
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Models, Statistical
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Medicine -- Mathematical models
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| Form |
Electronic book
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| Author |
Prescott, Robin, author
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| ISBN |
9781118778241 |
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1118778243 |
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9781118778210 |
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1118778219 |
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