Applied multivariate statistical analysis in medicine /
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
London ; San Diego, CA :
Academic Press,
2024.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- 4.6.2 Diagnosis and treatment of outliers
- 4.6.3 Sample size requirement
- 4.7 Summary
- 4.8 Problems
- Bibliography
- 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
- Bibliography
- 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.
- 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
- 1. For data without censored observations
- 2. For data with censored observations
- 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
- Bibliography
- 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
- Bibliography
- 9
- Factor analysis
- 9.1 Introduction
- 9.2 Exploratory factor analysis.