Giáo trình Y dược học: Applied Mixed Models in Medicine 2nd Edition (Mô hình hỗn hợp ứng dụng trong Y học - Bản 2)

HELEN BROWN - ROBIN PRESCOTT

APPLIED MIXED MODELS IN MEDICINE

(MÔ HÌNH HỖN HỢP ỨNG DỤNG TRONG Y HỌC)

PUBLISHER: JOHN WILEY & SONS (UNITED KINGDOM, 2008)

THÔNG TIN CHUNG:

Tiêu đề: Applied Mixed Models in Medicine 2nd Edition (tạm dịch: Mô hình hỗn hợp ứng dụng trong Y học - Bản 2).

Tác giả: Helen Brown - Robin Prescott.

NXB: John Wiley & Sons (2008).

Số trang: 468.

Nội dung cuốn sách này được chia làm 9 chương chính sẽ đề cập đến các mô hình hỗn hợp toán học được áp dụng trong khảo sát, nghiên cứu và điều trị trong Y học. Ứng dụng của các mô hình này rất đa dạng, từ việc thống kê, thử nghiệm vắc-xin, dược phẩm mới, đưa ra dự báo về tỷ lệ thành công trong điều trị, khả năng và thời gian hồi phục; hướng tới việc lập kế hoạch phòng chống bệnh dịch, lập pháp đồ điều trị một cách tổng thể và khoa học....

CONTENTS (MỤC LỤC):

Preface to Second Edition

Mixed Model Notations

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 asrandom (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

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 itsmaximisation

2.2.2 Estimation of fixed effects

2.2.3 Estimation (or prediction) Of random effects andcoefficients

2.2.4 Estimation of variance parameters

2.3 The Bayesian Approach

2.3.1 Introduction

2.3.2 Determining the posterior density

2.3.3 Parameter estimation, probability intervals andp-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 Model checking

2.4.7 Missing data

2.5 Example

2.5.1 Analysis models

2.5.2 Results

2.5.3 Discussion of points from Section 2.4

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 generalexponential 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 Fixed and random effects estimates

3.3.5 Accuracy of variance parameters and randomeffects shrinkage

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

3.4 Example

3.4.1 Introduction and models fitted

3.4.2 Results

3.4.3 Discussion of points from Section 3.3

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 regressionmodel

4.2.2 Residual variance matrix

4.2.3 Alternative specification for random effects models

4.2.4 Likelihood and quasi-likelihood functions

4.2.5 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

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-centredata?

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 effectsomitted

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 Non-normal 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

6 Repeated Measures Data

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 Non-normal data

6.7.3 Categorical data

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-overtrial

7.5 Incomplete Block Designs

7.5.1 The three-treatment, two-period design (Koch’sdesign)

7.5.2 Example: 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

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 carepathways for treatment of children with asthma inhospital

8.16.2 Example: Edinburgh randomised trial of breastscreening

9 Software for Fitting Mixed Models

9.1 Packages for Fitting Mixed Models

9.2 Basic use of PROC MIXED

9.3 Using SAS to Fit Mixed Models to Non-Normal Data

9.3.1 PROC GLIMMIX

9.3.2 PROC GENMOD

Glossary

References

Index

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