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E-raamat: Measuring Agreement: Models, Methods, and Applications

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Measuring Agreement: Models, Methods, and ApplicationsSuurem pilt
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Presents statistical methodologies for analyzing common types of data from method comparison experiments and illustrates their applications through detailed case studies

Measuring Agreement: Models, Methods, and Applications features statistical evaluation of agreement between two or more methods of measurement of a variable with a primary focus on continuous data. The authors view the analysis of method comparison data as a two-step procedure where an adequate model for the data is found, and then inferential techniques are applied for appropriate functions of parameters of the model. The presentation is accessible to a wide audience and provides the necessary technical details and references. In addition, the authors present chapter-length explorations of data from paired measurements designs, repeated measurements designs, and multiple methods; data with covariates; and heteroscedastic, longitudinal, and categorical data. The book also:

Strikes a balance between theory and applications

Presents parametric as well as nonparametric methodologies

Provides a concise introduction to Cohens kappa coefficient and other measures of agreement for binary and categorical data

Discusses sample size determination for trials on measuring agreement

Contains real-world case studies and exercises throughout

Provides a supplemental website containing the related datasets and R code

Measuring Agreement: Models, Methods, and Applications is a resource for statisticians and biostatisticians engaged in data analysis, consultancy, and methodological research. It is a reference for clinical chemists, ecologists, and biomedical and other scientists who deal with development and validation of measurement methods. This book can also serve as a graduate-level text for students in statistics and biostatistics.
Preface xv
1 Introduction 1(52)
1.1 Preview
1(1)
1.2 Notational Conventions
1(1)
1.3 Basic Characteristics of a Measurement Method
2(3)
1.3.1 A Statistical Model for Measurements
3(1)
1.3.2 Quality Characteristics
3(2)
1.4 Method Comparison Studies
5(1)
1.5 Meaning of Agreement
6(2)
1.6 A Measurement Error Model
8(3)
1.6.1 Identifiability Issues
9(1)
1.6.2 Model-Based Moments
10(1)
1.6.3 Conditions for Perfect Agreement
10(1)
1.6.4 Link to Test Theory
11(1)
1.7 Similarity versus Agreement
11(2)
1.7.1 Evaluation of Similarity
11(1)
1.7.2 Evaluation of Agreement
12(1)
1.8 A Toy Example
13(1)
1.9 Controversies and Our View
14(1)
1.10 Concepts Related to Agreement
15(1)
1.11 Role of Confidence Intervals and Hypotheses Testing
16(2)
1.11.1 Formulating the Agreement Hypotheses
16(1)
1.11.2 Testing Hypotheses Using Confidence Bounds
17(1)
1.11.3 Evaluation of Agreement Using Confidence Bounds
17(1)
1.11.4 Evaluation of Similarity Using Confidence Intervals
18(1)
1.12 Common Models for Paired Measurements Data
18(5)
1.12.1 A Measurement Error Model
19(1)
1.12.2 A Mixed-Effects Model
20(1)
1.12.3 A Bivariate Normal Model
21(1)
1.12.4 Limitations of the Paired Measurements Design
22(1)
1.13 The Bland-Altman Plot
23(6)
1.13.1 The Ideal Plot
23(2)
1.13.2 A Linear Trend in the Bland-Altman Plot
25(1)
1.13.3 Heteroscedasticity in the Bland-Altman Plot
26(1)
1.13.4 Variations of the Bland-Altman Plot
27(2)
1.14 Common Regression Approaches
29(5)
1.14.1 Ordinary Linear Regression
29(2)
1.14.2 Deming Regression
31(3)
1.15 Inappropriate Use of Common Tests in Method Comparison Studies
34(5)
1.15.1 Test of Zero Correlation
34(2)
1.15.2 Paired t-test
36(1)
1.15.3 Pitman-Morgan and Bradley-Blackwood Tests
36(2)
1.15.4 Test of Zero Intercept and Unit Slope
38(1)
1.16 Key Steps in the Analysis of Method Comparison Data
39(1)
1.17
Chapter Summary
40(1)
1.18 Bibliographic Note
41(6)
Exercises
47(6)
2 Common Approaches for Measuring Agreement 53(18)
2.1 Preview
53(1)
2.2 Introduction
53(1)
2.3 Mean Squared Deviation
54(1)
2.4 Concordance Correlation Coefficient
54(3)
2.5 A Digression: Tolerance and Prediction intervals
57(2)
2.5.1 Definitions
57(1)
2.5.2 Normally Distributed Data
58(1)
2.6 Lin's Probability Criterion and Bland-Altman Criterion
59(1)
2.7 Limits of Agreement
60(2)
2.7.1 The Approach
60(1)
2.7.2 Why Ignore the Variability?
61(1)
2.7.3 Limits of Agreement versus Prediction and Tolerance Intervals
62(1)
2.8 Total Deviation Index and Coverage Probability
62(2)
2.8.1 The Approaches
62(1)
2.8.2 Normally Distributed Differences
63(1)
2.9 Inference on Agreement Measures
64(1)
2.10
Chapter Summary
64(1)
2.11 Bibliographic Note
65(1)
Exercises
66(5)
3 A General Approach for Modeling and Inference 71(24)
3.1 Preview
71(1)
3.2 Mixed-Effects Models
71(5)
3.2.1 The Model
72(1)
3.2.2 Prediction
73(1)
3.2.3 Model Fitting
74(1)
3.2.4 Model Diagnostics
75(1)
3.3 A Large-Sample Approach to Inference
76(9)
3.3.1 Approximate Distributions
77(1)
3.3.2 Confidence Intervals
78(2)
3.3.3 Parameter Transformation
80(1)
3.3.4 Bootstrap Confidence Intervals
81(2)
3.3.5 Confidence Bands
83(1)
3.3.6 Test of Homogeneity
83(1)
3.3.7 Model Comparison
84(1)
3.4 Modeling and Analysis of Method Comparison Data
85(3)
3.5
Chapter Summary
88(1)
3.6 Bibliographic Note
89(1)
Exercises
89(6)
4 Paired Measurements Data 95(16)
4.1 Preview
95(1)
4.2 Modeling of Data
95(3)
4.2.1 Mixed-Effects Model
95(2)
4.2.2 Bivariate Normal Model
97(1)
4.3 Evaluation of Similarity and Agreement
98(1)
4.4 Case Studies
99(7)
4.4.1 Oxygen Saturation Data
99(2)
4.4.2 Plasma Volume Data
101(2)
4.4.3 Vitamin D Data
103(3)
4.5
Chapter Summary
106(1)
4.6 Technical Details
106(2)
4.6.1 Mixed-Effects Model
106(1)
4.6.2 Bivariate Normal Model
107(1)
4.7 Bibliographic Note
108(1)
Exercises
108(3)
5 Repeated Measurements Data 111(30)
5.1 Preview
111(1)
5.2 Introduction
111(3)
5.2.1 Types of Data
112(1)
5.2.2 Individual versus Average Measurement
113(1)
5.2.3 Example Datasets
113(1)
5.3 Displaying Data
114(3)
5.3.1 Basic Plots
114(2)
5.3.2 Interaction Plots
116(1)
5.4 Modeling of Data
117(6)
5.4.1 Unlinked Data
118(3)
5.4.2 Linked Data
121(2)
5.4.3 Model Fitting and Evaluation
123(1)
5.5 Evaluation of Similarity and Agreement
123(1)
5.6 Evaluation of Repeatability
124(2)
5.6.1 Unlinked Data
125(1)
5.6.2 Linked Data
125(1)
5.7 Case Studies
126(7)
5.7.1 Kiwi Data
126(3)
5.7.2 Oximetry Data
129(4)
5.8
Chapter Summary
133(1)
5.9 Technical Details
134(1)
5.9.1 Unlinked Data
134(1)
5.9.2 Linked Data
134(1)
5.10 Bibliographic Note
135(2)
Exercises
137(4)
6 Heteroscedastic Data 141(36)
6.1 Preview
141(1)
6.2 Introduction
141(3)
6.2.1 Diagnosing Heteroscedasticity
142(1)
6.2.2 Example Datasets
143(1)
6.3 Variance Function Models
144(2)
6.4 Repeated Measurements Data
146(16)
6.4.1 A Heteroscedastic Mixed-Effects Model
147(2)
6.4.2 Specifying the Variance Function
149(1)
6.4.3 Model Fitting and Evaluation
150(1)
6.4.4 Testing for Homoscedasticity
151(1)
6.4.5 Evaluation of Similarity, Agreement, and Repeatability
151(1)
6.4.6 Case Study: Cholesterol Data
152(10)
6.5 Paired Measurements Data
162(9)
6.5.1 A Heteroscedastic Bivariate Normal Model
162(1)
6.5.2 Specifying the Variance Function
163(1)
6.5.3 Model Fitting and Evaluation
164(1)
6.5.4 Testing for Homoscedasticity
164(1)
6.5.5 Evaluation of Similarity and Agreement
164(1)
6.5.6 Case Study: Cyclosporin Data
165(6)
6.6
Chapter Summary
171(1)
6.7 Technical Details
171(3)
6.7.1 Repeated Measurements Data
171(2)
6.7.2 Paired Measurements Data
173(1)
6.8 Bibliographic Note
174(1)
Exercises
174(3)
7 Data from Multiple Methods 177(28)
7.1 Preview
177(1)
7.2 Introduction
177(2)
7.3 Displaying Data
179(1)
7.4 Example Datasets
179(5)
7.4.1 Systolic Blood Pressure Data
180(1)
7.4.2 Tumor Size Data
180(4)
7.5 Modeling Unreplicated Data
184(2)
7.6 Modeling Repeated Measurements Data
186(3)
7.6.1 Unlinked Data
186(1)
7.6.2 Linked Data
187(2)
7.7 Model Fitting and Evaluation
189(1)
7.8 Evaluation of Similarity and Agreement
190(1)
7.9 Evaluation of Repeatability
191(1)
7.10 Case Studies
192(6)
7.10.1 Systolic Blood Pressure Data
192(3)
7.10.2 Tumor Size Data
195(3)
7.11
Chapter Summary
198(1)
7.12 Technical Details
198(2)
7.13 Bibliographic Note
200(1)
Exercises
200(5)
8 Data with Covariates 205(24)
8.1 Preview
205(1)
8.2 Introduction
205(1)
8.3 Modeling of Data
206(5)
8.3.1 Modeling Means of Methods
206(1)
8.3.2 Modeling Variances of Methods
207(1)
8.3.3 Data Models
208(3)
8.3.4 Model Fitting and Evaluation
211(1)
8.4 Evaluation of Similarity, Agreement, and Repeatability
211(3)
8.4.1 Measures of Agreement for Two methods
212(1)
8.4.2 Measures of Agreement for More Than Two Methods
213(1)
8.4.3 Measures of Repeatability
213(1)
8.4.4 Inference on Measures
214(1)
8.5 Case Study
214(10)
8.6
Chapter Summary
224(1)
8.7 Technical Details
225(1)
8.8 Bibliographic Note
226(1)
Exercises
226(3)
9 Longitudinal Data 229(24)
9.1 Preview
229(1)
9.2 Introduction
229(5)
9.2.1 Displaying Data
231(1)
9.2.2 Percentage Body Fat Data
231(3)
9.3 Modeling of Data
234(7)
9.3.1 The Longitudinal Data Model
236(1)
9.3.2 Specifying the Mean Functions
237(1)
9.3.3 Specifying the Correlation Function
237(3)
9.3.4 Model Fitting and Evaluation
240(1)
9.4 Evaluation of Similarity and Agreement
241(1)
9.5 Case Study
242(5)
9.6
Chapter Summary
247(1)
9.7 Technical Details
247(2)
9.8 Bibliographic Note
249(1)
Exercises
250(3)
10 A Nonparametric Approach 253(26)
10.1 Preview
253(1)
10.2 Introduction
253(2)
10.3 The Statistical Functional Approach
255(3)
10.3.1 A Weighted Empirical CDF
256(1)
10.3.2 Distributions Induced by Empirical CDF
256(2)
10.4 Evaluation of Similarity and Agreement
258(1)
10.5 Case Studies
259(8)
10.5.1 Unreplicated Blood Pressure Data
259(4)
10.5.2 Replicated Blood Pressure Data
263(4)
10.6
Chapter Summary
267(1)
10.7 Technical Details
267(4)
10.7.1 The Omega Matrix
268(1)
10.7.2 Estimation of Omega
269(1)
10.7.3 Influence Functions for the Measures
270(1)
10.7.4 TDI Confidence Bounds
270(1)
10.7.5 Summary of Steps
271(1)
10.8 Bibliographic Note
271(1)
Exercises
272(7)
11 Sample Size Determination 279(10)
11.1 Preview
279(1)
11.2 Introduction
279(2)
11.3 The Sample Size Methodology
281(1)
11.3.1 Paired Measurements Design
281(1)
11.3.2 Repeated Measurements Design
281(1)
11.4 Case Study
282(4)
11.5
Chapter Summary
286(1)
11.6 Bibliographic Note
286(1)
Exercises
287(2)
12 Categorical Data 289(30)
12.1 Preview
289(1)
12.2 Introduction
289(1)
12.3 Experimental Setups and Examples
290(3)
12.3.1 Types of Data
290(1)
12.3.2 Illustrative Examples
290(2)
12.3.3 A Graphical Approach
292(1)
12.4 Cohen's Kappa Coefficient for Dichotomous Data
293(10)
12.4.1 Definition and Basic Properties: Two Raters
293(4)
12.4.2 Sample Kappa Coefficient
297(1)
12.4.3 Agreement with a Gold Standard
298(1)
12.4.4 Unbiased Raters: Intraclass Kappa
299(1)
12.4.5 Multiple Raters
300(1)
12.4.6 Combining and Comparing Kappa Coefficients
301(1)
12.4.7 Sample Size Calculations
302(1)
12.5 Kappa Type Measures for More Than Two Categories
303(2)
12.5.1 Two Fixed Raters with Nominal Categories
303(1)
12.5.2 Two Raters with Ordinal Categories: Weighted Kappa
303(1)
12.5.3 Multiple Raters
304(1)
12.6 Case Studies
305(1)
12.6.1 Two Raters with Two Categories
305(1)
12.6.2 Weighted Kappa: Multiple Categories
306(1)
12.7 Models for Exploring Agreement
306(3)
12.7.1 Conditional Logistic Regression Models
306(1)
12.7.2 Log-Linear Models
307(1)
12.7.3 A Generalized Linear Mixed-Effects Model
308(1)
12.8 Discussion
309(1)
12.9
Chapter Summary
310(1)
12.10 Bibliographic Note
311(1)
Exercises
312(7)
References 319(12)
Dataset List 331(2)
Index 333
P. K. CHOUDHARY, PhD, is Professor in the Department of Mathematical Sciences at the University of Texas at Dallas. Currently, he is also the Associate Head of the department. His research interests include development of statistical methodology for biostatistical applications, and he has published extensively in the field of method comparison studies.

H. N. NAGARAJA, PhD, is Professor Emeritus at The Ohio State University where he has served in the Departments of Statistics and Internal Medicine and the Division of Biostatistics. He is a fellow of the American Statistical Association and the American Association for the Advancement of Science, and an elected member of the International Statistical Institute. His published works include Order Statistics, Third Edition (with H. A. David) and Records (with B. C. Arnold and N. Balakrishnan), both published by Wiley.
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