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Applied Multivariate Statistical Analysis in Medicine
- 1st Edition - August 21, 2024
- Author: Jingmei Jiang
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 3 5 8 7 - 0
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 3 5 8 8 - 7
Applied Multivariate Statistical Analysis in Medicine provides a multivariate conceptual framework that allows readers to understand the interconnectivity and interrela… Read more
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Request a sales quoteApplied Multivariate Statistical Analysis in Medicine provides a multivariate conceptual framework that allows readers to understand the interconnectivity and interrelations among variables, which maintains the intrinsic precision of statistical theories. With a strong focus on the fundamental concepts of multivariate statistical analysis, the book also gives insight into the applications of multivariate distribution in biomedical fields.
In 14 chapters, Applied Multivariate Statistical Analysis in Medicine covers the main topics of multivariate analysis methods widely used in health science research. The content is organized progressively from fundamental concepts to sophisticated methods. It begins with basic descriptive statistics in multivariate analysis and follows with parameter estimation, in addition to the hypothesis testing of a multivariate normal distribution, which has heavy applications in biomedical fields where the relationships among approximately normal variables are of great interest. Keeping mathematics to a minimum, considerable emphasis is placed on explanations and real-world applications of core principles to maintain a good balance between introducing theory and cultivating problem-solving skills. This book is a very valuable reference text for clinicians, medical researchers, and other researchers across medical and biomedical disciplines, all of whom confront increasingly complex statistical methods during the analysis and presentation of their results.
- Gives understanding and mastering of the multivariate analysis techniques in the medical sciences
- Maintains a balance between the introduction of statistical analysis theory and the cultivation of practical skills
- Exposes a variety of well-designed real-life cases that integrate concepts and analytical techniques
- Includes substantive exercises, online coding sources, and case discussions to solidify a conceptual understanding
Researchers and students in biostatistics clinicians, medical researchers, and other researchers across medical and biomedical disciplines
1. Overview of multivariate statistical analysis
1.1 Introduction
1.2 Application of multivariate statistical analysis
1.3 Structure of multivariate data
1.4 Descriptive statistics of multivariate data
1.5 Statistical distance
1.6 Statistical software
1.7 Problems
2. Multivariate normal distribution
2.1 Introduction
2.2 Distributions of random vectors
2.3 Numerical characteristics of random vectors
2.4 Multivariate normal distribution
2.5 Parameter estimation of the multivariate normal distribution
2.6 Calculation of the reference region
2.7 Detecting outliers
2.8 Summary
2.9 Problems
3. Hypothesis testing for the parameters of multivariate normal populations
3.1 Introduction
3.2 Distributions of several important statistics
3.3 Hypothesis testing
3.4 Multivariate analysis of variance
3.5 Testing for the homogeneity of covariance matrices
3.6 Data transformation
3.7 Summary
3.8 Problems
4. Multivariate linear regression
4.1 Introduction
4.2 Classical multivariate linear regression model
4.3 Hypothesis tests for models and regression coefficients
4.4 Evaluation of model fit and variable selection
4.5 Diagnosis and treatment of multicollinearity
4.6 Other issues in multivariate linear regression
4.7 Summary
4.8 Problems
5. Generalized linear models
5.1 Introduction
5.2 Overview of generalized linear models
5.3 Data representation of generalized linear models
5.4 Distribution of response variables
5.5 Exponential family and generalized linear models
5.6 Parameter estimation for generalized linear models
5.7 Hypothesis testing for generalized linear models
5.8 Goodness-of-fit test of generalized linear models
5.9 Application of generalized linear models
5.10 Summary
5.11 Problems
6. Logistic regression
6.1 Introduction
6.2 Logit behind logistic regression models
6.3 Binary logistic regression
6.4 Logistic regression for matched case-control studies
6.5 Logistic regression for multinomial outcomes
6.6 Logistic regression for ordinal outcomes
6.7 Other issues for logistic regression
6.8 Summary
6.9 Problems
7. Survival analysis
7.1 Introduction
7.2 Overview for survival analysis
7.3 Modeling the hazard function
7.4 Exponential model
7.5 Weibull model
7.6 Cox proportional hazard model
7.7 Extensions to the Cox proportional hazard model
7.8 Summary
7.9 Problems
8. Principal component analysis
8.1 Introduction
8.2 Population principal components
8.3 Sample principal components
8.4 Steps of principal component analysis
8.5 Application of principal component analysis
8.6 Summary
8.7 Problems
9. Factor analysis
9.1 Introduction
9.2 Exploratory factor analysis
9.3 Confirmatory factor analysis
9.4 Steps of factor analysis
9.5 Other issues in factor analysis
9.6 Summary
9.7 Problems
10. Canonical correlation analysis
10.1 Introduction
10.2 Review of correlation
10.3 Population canonical correlations
10.4 Sample canonical correlations
10.5 Canonical redundancy analysis
10.6 Other issues in canonical correlation analysis
10.7 Summary
10.8 Problems
11. Cluster analysis
11.1 Introduction
11.2 Measures of similarity
11.3 Definition and characteristics of clusters
11.4 Hierarchical clustering methods
11.5 Dynamic clustering method
11.6 Ordered object clustering
11.7 Other issues in cluster analysis
11.8 Summary
11.9 Problems
12. Discriminant analysis
12.1 Introduction
12.2 Discrimination using the mahalanobis distance
12.3 Fisher discriminant
12.4 Bayes discriminant
12.5 Stepwise discriminant
12.6 Other issues for discriminant analysis
12.7 Summary
12.8 Problems
13. matrix algebra
13.1 Introduction
13.2 Basic concept of a vector
13.3 Basic concept of a matrix
13.4 Determinant, inverse, and rank of a matrix
13.5 Eigenvalue, eigenvectors, and trace of a matrix
13.6 Quadratic forms, spectral decomposition, and positive definite matrix
13.7 Elimination transformation
13.8 Derivative of the matrix
13.9 Summary
13.10 Problems
1.1 Introduction
1.2 Application of multivariate statistical analysis
1.3 Structure of multivariate data
1.4 Descriptive statistics of multivariate data
1.5 Statistical distance
1.6 Statistical software
1.7 Problems
2. Multivariate normal distribution
2.1 Introduction
2.2 Distributions of random vectors
2.3 Numerical characteristics of random vectors
2.4 Multivariate normal distribution
2.5 Parameter estimation of the multivariate normal distribution
2.6 Calculation of the reference region
2.7 Detecting outliers
2.8 Summary
2.9 Problems
3. Hypothesis testing for the parameters of multivariate normal populations
3.1 Introduction
3.2 Distributions of several important statistics
3.3 Hypothesis testing
3.4 Multivariate analysis of variance
3.5 Testing for the homogeneity of covariance matrices
3.6 Data transformation
3.7 Summary
3.8 Problems
4. Multivariate linear regression
4.1 Introduction
4.2 Classical multivariate linear regression model
4.3 Hypothesis tests for models and regression coefficients
4.4 Evaluation of model fit and variable selection
4.5 Diagnosis and treatment of multicollinearity
4.6 Other issues in multivariate linear regression
4.7 Summary
4.8 Problems
5. Generalized linear models
5.1 Introduction
5.2 Overview of generalized linear models
5.3 Data representation of generalized linear models
5.4 Distribution of response variables
5.5 Exponential family and generalized linear models
5.6 Parameter estimation for generalized linear models
5.7 Hypothesis testing for generalized linear models
5.8 Goodness-of-fit test of generalized linear models
5.9 Application of generalized linear models
5.10 Summary
5.11 Problems
6. Logistic regression
6.1 Introduction
6.2 Logit behind logistic regression models
6.3 Binary logistic regression
6.4 Logistic regression for matched case-control studies
6.5 Logistic regression for multinomial outcomes
6.6 Logistic regression for ordinal outcomes
6.7 Other issues for logistic regression
6.8 Summary
6.9 Problems
7. Survival analysis
7.1 Introduction
7.2 Overview for survival analysis
7.3 Modeling the hazard function
7.4 Exponential model
7.5 Weibull model
7.6 Cox proportional hazard model
7.7 Extensions to the Cox proportional hazard model
7.8 Summary
7.9 Problems
8. Principal component analysis
8.1 Introduction
8.2 Population principal components
8.3 Sample principal components
8.4 Steps of principal component analysis
8.5 Application of principal component analysis
8.6 Summary
8.7 Problems
9. Factor analysis
9.1 Introduction
9.2 Exploratory factor analysis
9.3 Confirmatory factor analysis
9.4 Steps of factor analysis
9.5 Other issues in factor analysis
9.6 Summary
9.7 Problems
10. Canonical correlation analysis
10.1 Introduction
10.2 Review of correlation
10.3 Population canonical correlations
10.4 Sample canonical correlations
10.5 Canonical redundancy analysis
10.6 Other issues in canonical correlation analysis
10.7 Summary
10.8 Problems
11. Cluster analysis
11.1 Introduction
11.2 Measures of similarity
11.3 Definition and characteristics of clusters
11.4 Hierarchical clustering methods
11.5 Dynamic clustering method
11.6 Ordered object clustering
11.7 Other issues in cluster analysis
11.8 Summary
11.9 Problems
12. Discriminant analysis
12.1 Introduction
12.2 Discrimination using the mahalanobis distance
12.3 Fisher discriminant
12.4 Bayes discriminant
12.5 Stepwise discriminant
12.6 Other issues for discriminant analysis
12.7 Summary
12.8 Problems
13. matrix algebra
13.1 Introduction
13.2 Basic concept of a vector
13.3 Basic concept of a matrix
13.4 Determinant, inverse, and rank of a matrix
13.5 Eigenvalue, eigenvectors, and trace of a matrix
13.6 Quadratic forms, spectral decomposition, and positive definite matrix
13.7 Elimination transformation
13.8 Derivative of the matrix
13.9 Summary
13.10 Problems
- No. of pages: 550
- Language: English
- Edition: 1
- Published: August 21, 2024
- Imprint: Academic Press
- Paperback ISBN: 9780443235870
- eBook ISBN: 9780443235887
JJ
Jingmei Jiang
Jingmei Jiang, Professor of Biostatistics in the Department of Epidemiology and Biostatistics, Institute of Basic Medical Research, Chinese Academy of Medical Sciences and School of Basic Medical Research, Peking Union Medical College, China. Doctoral degree from Peking Union Medical College. As the current Head of Statistics Department, she has been teaching statistics for more than 30 years and has gained much experience in teaching several biostatistics courses to undergraduate and graduate students at PUMC. She has completed four textbooks (one in English) as Editor-in-Chief and five monographs (four in English) as Editor. Since 2000, she has authored more than 100 scientific papers, including more than 70 peer-reviewed research papers as first author or corresponding author. Although the author has a broad research interest in the application of biostatistical methods in medical research, she mainly devotes herself to two research fields: population-based cancer research and clinical patient safety research.
Affiliations and expertise
Professor of Biostatistics, Department of Epidemiology and Biostatistics, Institute of Basic Medical Research, Chinese Academy of Medical Sciences and School of Basic Medical Research, Peking Union Medical College, Beijing, ChinaRead Applied Multivariate Statistical Analysis in Medicine on ScienceDirect