Applied Multivariate Statistical Analysis in Medicine / Jingmei Jiang.

Format:

Book

Author/Creator:

Jiang, Jingmei, 1958- author.

Language:

English

Subjects (All):

Multivariate analysis.

Medical statistics.

Physical Description:

1 online resource (526 pages)

Edition:

First edition.

Place of Publication:

London, England : Academic Press, [2024]

Summary:

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.- 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

Contents:

Front Cover

Applied Multivariate Statistical Analysis in Medicine

Copyright

Contents

Preface

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

1.4.1 Sample mean vector

1.4.2 Sample covariance matrix

1.4.3 Sample correlation matrix

1.5 Statistical distance

1.6 Statistical software

1.7 Problems

Bibliography

2 - Multivariate normal distribution

2.1 Introduction

2.2 Distributions of random vectors

2.2.1 Review of distributions of univariate variables

2.2.2 Joint distributions

2.2.3 Marginal distributions

2.2.4 Statistical independence

2.2.5 Conditional distributions

2.3 Numerical characteristics of random vectors

2.3.1 Mean vector and covariance matrix

2.3.2 Properties of the mean vector and covariance matrix

2.4 Multivariate normal distribution

2.4.1 Multivariate normal probability density function

2.4.2 Geometric characteristics of the multivariate normal distribution

2.4.3 Properties of the multivariate normal distribution

2.5 Parameter estimation of the multivariate normal distribution

2.5.1 Definition of maximum likelihood estimation

2.5.2 Maximum likelihood estimation of μ and Σ

2.5.3 Properties of the maximum likelihood estimators of μ and Σ

2.6 Calculation of the reference region

2.7 Detecting outliers

2.7.1 Outliers in univariate samples

2.7.2 Outliers in multivariate samples

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

3.2.1 Distribution of the sample mean vector.

3.2.2 Wishart distribution

3.2.3 Properties of the Wishart distribution

3.2.4 Hotelling's T2 distribution

3.2.5 Properties of Hotelling's T2 distribution

3.2.6 Wilks' Λ statistic and its distribution

3.3 Hypothesis testing

3.3.1 Review of the basic principles of hypothesis testing

3.3.2 Testing the mean vector for one multivariate normal population

3.3.3 Testing the mean vector in paired design

3.3.4 Testing the mean vectors of two independent multivariate normal populations

3.4 Multivariate analysis of variance

3.4.1 Review of univariate analysis of variance

3.4.2 Multivariate analysis of variance for independent group design

3.4.3 Multivariate analysis of variance in randomized block design

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

4.2.1 Model definition

4.2.2 Model assumptions

4.2.3 Least squares estimation of parameters

4.2.4 Sampling properties of the least squares estimator

4.2.5 Interpretation of regression coefficients

4.3 Hypothesis tests for models and regression coefficients

4.3.1 Hypothesis testing for the regression model

4.3.2 Hypothesis testing of the regression coefficients

4.3.3 Standardized regression coefficients

4.4 Evaluation of model fit and variable selection

4.4.1 Goodness-of-fit of the regression model

4.4.2 Choosing the optimal regression subset

4.4.3 Strategies and methods for variable selection

4.5 Diagnosis and treatment of multicollinearity

4.5.1 Diagnosis of multicollinearity

4.5.2 Treatment of multicollinearity

4.6 Other issues in multivariate linear regression

4.6.1 Checking the normality assumptions for the model.

4.6.2 Diagnosis and treatment of outliers

4.6.3 Sample size requirement

4.7 Summary

4.8 Problems

5 - Generalized linear models

5.1 Introduction

5.2 Overview of generalized linear models

5.2.1 Review of the classical linear regression model

5.2.2 Concept of generalized linear models

5.2.3 Explanation of model parameters

5.3 Data representation of generalized linear models

5.3.1 Representation of observational data

5.3.2 Quantification of categorical data

5.4 Distribution of response variables

5.4.1 Exponential family of distributions

5.4.2 Mean and variance of distributions in the exponential family

5.5 Exponential family and generalized linear models

5.5.1 Generalized linear model of non-normal distributed data

5.5.2 Generalized linear model of two-point distributed data

5.5.3 Generalized linear model of counting data

5.6 Parameter estimation for generalized linear models

5.6.1 Maximum likelihood estimation

5.6.2 Weighted least squares estimation

5.7 Hypothesis testing for generalized linear models

5.7.1 Likelihood-ratio test

5.7.2 Wald test

5.7.3 Score test

5.7.4 Characteristics and applications of the three statistics

5.8 Goodness-of-fit test of generalized linear models

5.8.1 Pearson test

5.8.2 Deviance test

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

6.2.1 Probability, odds, and the logarithm of the odds

6.2.2 Odds ratio

6.3 Binary logistic regression

6.3.1 Model definition

1 Single predictor models

2 Multi-predictor models

6.3.2 Parameter estimation of logistic regression

1 Maximum likelihood estimation

6.3.3 Interpretation of the partial regression coefficient.

1 Single binary predictive variable

2 Multiple predictive variables

3 Interval estimation of the partial regression coefficient βj and ORj

6.3.4 Hypothesis testing of models and parameters

1 Likelihood ratio test

2 Wald test

3 Score test

6.3.5 Goodness-of-fit test for the model

1 Pearson test

2 Deviance test

3 Hosmer-Lemeshow test

6.4 Logistic regression for matched case-control studies

6.4.1 Rationale for a matched study

6.4.2 Model definition

6.4.3 Estimation of partial regression coefficients

6.5 Logistic regression for multinomial outcomes

6.5.1 Basic principles

1 Multinomial distribution

2 Baseline-category logit

6.5.2 Multinomial logistic regression

6.6 Logistic regression for ordinal outcomes

6.6.1 Basic principles

6.6.2 Cumulative probability and logit

6.6.3 Ordinal logit model

6.7 Other issues for logistic regression

6.7.1 Sample sizes

6.7.2 Variable types

6.7.3 Variable selection

6.7.4 Missing data problem

6.8 Summary

6.9 Problems

7 - Survival analysis

7.1 Introduction

7.2 Overview for survival analysis

7.2.1 Terminology and notation for survival analysis

1. Initial event and endpoint event

2. Survival time

7.2.2 Basic lifetime functions

1. Probability density function

2. Survival function

3. Hazard function

7.3 Modeling the hazard function

7.4 Exponential model

7.4.1 Lifetime functions of the exponential survival distribution

7.4.2 Parameter estimation of the exponential survival distribution

1. For data without censored observations

2. For data with censored observations

7.4.3 Assessment of whether the survival time follows the exponential distribution

7.4.4 Exponential regression model based on the hazard function.

7.4.5 Parameter estimation and hypothesis testing of the exponential regression model

7.5 Weibull model

7.5.1 Lifetime functions of the Weibull survival distribution

7.5.2 Parameter estimation of the Weibull survival distribution

7.5.3 Weibull regression model based on the hazard function

7.6 Cox proportional hazard model

7.6.1 Basics for the Cox proportional hazard model

7.6.2 Partial likelihood

7.6.3 Parameter estimation and hypothesis testing using the partial likelihood

7.6.4 Applications of the Cox proportional hazard model

1. Calculating the hazard ratio

2. Calculating the hazard index

7.6.5 Assessment of the proportional hazard assumption

1. Graphical method

2. Checking proportionality with scaled Schoenfield residuals

7.7 Extensions to the Cox proportional hazard model

7.7.1 Hazard rate model with time-dependent covariates

7.7.2 Hazard rate model with repeated events

7.8 Summary

7.9 Problems

8 - Principal component analysis

8.1 Introduction

8.2 Population principal components

8.2.1 Understanding principal components

8.2.2 Determining principal components

8.2.3 Properties of principal components

8.2.4 Principal components of standardized variables and properties

8.3 Sample principal components

8.3.1 Sample principal component scores

8.3.2 Determining the number of sample principal components

8.4 Steps of principal component analysis

8.5 Application of principal component analysis

8.5.1 Comprehensive evaluation

8.5.2 Principal component regression

8.5.3 Variable selection

8.5.4 Cluster analysis

8.6 Summary

8.7 Problems

9 - Factor analysis

9.1 Introduction

9.2 Exploratory factor analysis.

9.2.1 Definition of the orthogonal factor model.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Other Format:

Print version: Jiang, Jingmei Applied Multivariate Statistical Analysis in Medicine

ISBN:

9780443235887

OCLC:

1453194483