Applied 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.
1. 3.1 Introduction - p. 49 2. 3.2 Distributions of several important statistics - p. 49 3. 3.3 Hypothesis testing - p. 55 4. 3.4 Multivariate analysis of variance - p. 71 5. 3.5 Testing for the homogeneity of covariance matrices - p. 81 6. 3.6 Data transformation - p. 83 7. 3.7 Summary - p. 84 8. 3.8 Problems - p. 84 9. Bibliography - p. 87 10. Chapter 4. Multivariate linear regression - p. 89 11. Chapter 5. Generalized linear models - p. 125 12. Abstract - p. 125 13. 5.1 Introduction - p. 125 14. 5.2 Overview of generalized linear models - p. 125 15. 5.3 Data representation of generalized linear models - p. 133 16. 5.4 Distribution of response variables - p. 137 17. 5.5 Exponential family and generalized linear models - p. 142 18. 5.6 Parameter estimation for generalized linear models - p. 150 19. 5.7 Hypothesis testing for generalized linear models - p. 155 20. 5.8 Goodness-of-fit test of generalized linear models - p. 159 21. 5.9 Application of generalized linear models - p. 162 22. 5.10 Summary - p. 166 23. 5.11 Problems - p. 167 24. Bibliography - p. 168 25. Chapter 6. Logistic regression - p. 169 26. Abstract - p. 169 27. 6.1 Introduction - p. 169 28. 6.2 Logit behind logistic regression models - p. 169 29. 6.3 Binary logistic regression - p. 173 30. 6.4 Logistic regression for matched case-control studies - p. 191 31. 6.5 Logistic regression for multinomial outcomes - p. 198 32. 6.6 Logistic regression for ordinal outcomes - p. 203 33. 6.7 Other issues for logistic regression - p. 208 34. 6.8 Summary - p. 210 35. 6.9 Problems - p. 211 36. Bibliography - p. 216 37. Chapter 7. Survival analysis - p. 217 38. Abstract - p. 217 39. 7.1 Introduction - p. 217 40. 7.2 Overview for survival analysis - p. 217 41. 7.3 Modeling the hazard function - p. 224 42. 7.4 Exponential model - p. 225 43. 7.5 Weibull model - p. 234 44. 7.6 Cox proportional hazard model - p. 239 45. 7.7 Extensions to the Cox proportional hazard model - p. 249 46. 7.8 Summary - p. 255 47. 7.9 Problems - p. 258 48. Bibliography - p. 259 49. Chapter 8. Principal component analysis - p. 265 50. Chapter 9. Factor analysis - p. 303 51. Chapter 10. Canonical correlation analysis - p. 337 52. Chapter 11. Cluster analysis - p. 367 53. Chapter 12. Discriminant analysis - p. 413 54. Abstract - p. 413 55. 12.1 Introduction - p. 413 56. 12.2 Discrimination using the mahalanobis distance - p. 414 57. 12.3 Fisher discriminant - p. 429 58. 12.4 Bayes discriminant - p. 442 59. 12.5 Stepwise discriminant - p. 452 60. 12.6 Other issues for discriminant analysis - p. 461 61. 12.7 Summary - p. 462 62. 12.8 Problems - p. 463 63. Bibliography - p. 464 64. Basic matrixalgebra - p. 467 65. Abstract - p. 467 66. 13.1 Introduction - p. 467 67. 13.2 Basic concept of a vector - p. 467 68. 13.3 Basic concept of a matrix - p. 473 69. 13.4 Determinant, inverse, and rank of a matrix - p. 479 70. 13.5 Eigenvalue, eigenvectors, and trace of a matrix - p. 484 71. 13.6 Quadratic forms, spectral decomposition, and positive definite matrix - p. 487 72. 13.7 Elimination transformation - p. 491 73. 13.8 Derivative of the matrix - p. 492 74. 13.9 Summary - p. 493 75. 13.10 Problems - p. 494 76. Bibliography - p. 495 77. Index - p. 497
Applied 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.
1. 3.1 Introduction - p. 49 2. 3.2 Distributions of several important statistics - p. 49 3. 3.3 Hypothesis testing - p. 55 4. 3.4 Multivariate analysis of variance - p. 71 5. 3.5 Testing for the homogeneity of covariance matrices - p. 81 6. 3.6 Data transformation - p. 83 7. 3.7 Summary - p. 84 8. 3.8 Problems - p. 84 9. Bibliography - p. 87 10. Chapter 4. Multivariate linear regression - p. 89 11. Chapter 5. Generalized linear models - p. 125 12. Abstract - p. 125 13. 5.1 Introduction - p. 125 14. 5.2 Overview of generalized linear models - p. 125 15. 5.3 Data representation of generalized linear models - p. 133 16. 5.4 Distribution of response variables - p. 137 17. 5.5 Exponential family and generalized linear models - p. 142 18. 5.6 Parameter estimation for generalized linear models - p. 150 19. 5.7 Hypothesis testing for generalized linear models - p. 155 20. 5.8 Goodness-of-fit test of generalized linear models - p. 159 21. 5.9 Application of generalized linear models - p. 162 22. 5.10 Summary - p. 166 23. 5.11 Problems - p. 167 24. Bibliography - p. 168 25. Chapter 6. Logistic regression - p. 169 26. Abstract - p. 169 27. 6.1 Introduction - p. 169 28. 6.2 Logit behind logistic regression models - p. 169 29. 6.3 Binary logistic regression - p. 173 30. 6.4 Logistic regression for matched case-control studies - p. 191 31. 6.5 Logistic regression for multinomial outcomes - p. 198 32. 6.6 Logistic regression for ordinal outcomes - p. 203 33. 6.7 Other issues for logistic regression - p. 208 34. 6.8 Summary - p. 210 35. 6.9 Problems - p. 211 36. Bibliography - p. 216 37. Chapter 7. Survival analysis - p. 217 38. Abstract - p. 217 39. 7.1 Introduction - p. 217 40. 7.2 Overview for survival analysis - p. 217 41. 7.3 Modeling the hazard function - p. 224 42. 7.4 Exponential model - p. 225 43. 7.5 Weibull model - p. 234 44. 7.6 Cox proportional hazard model - p. 239 45. 7.7 Extensions to the Cox proportional hazard model - p. 249 46. 7.8 Summary - p. 255 47. 7.9 Problems - p. 258 48. Bibliography - p. 259 49. Chapter 8. Principal component analysis - p. 265 50. Chapter 9. Factor analysis - p. 303 51. Chapter 10. Canonical correlation analysis - p. 337 52. Chapter 11. Cluster analysis - p. 367 53. Chapter 12. Discriminant analysis - p. 413 54. Abstract - p. 413 55. 12.1 Introduction - p. 413 56. 12.2 Discrimination using the mahalanobis distance - p. 414 57. 12.3 Fisher discriminant - p. 429 58. 12.4 Bayes discriminant - p. 442 59. 12.5 Stepwise discriminant - p. 452 60. 12.6 Other issues for discriminant analysis - p. 461 61. 12.7 Summary - p. 462 62. 12.8 Problems - p. 463 63. Bibliography - p. 464 64. Basic matrixalgebra - p. 467 65. Abstract - p. 467 66. 13.1 Introduction - p. 467 67. 13.2 Basic concept of a vector - p. 467 68. 13.3 Basic concept of a matrix - p. 473 69. 13.4 Determinant, inverse, and rank of a matrix - p. 479 70. 13.5 Eigenvalue, eigenvectors, and trace of a matrix - p. 484 71. 13.6 Quadratic forms, spectral decomposition, and positive definite matrix - p. 487 72. 13.7 Elimination transformation - p. 491 73. 13.8 Derivative of the matrix - p. 492 74. 13.9 Summary - p. 493 75. 13.10 Problems - p. 494 76. Bibliography - p. 495 77. Index - p. 497
