 Multivariable Model - Building: A Pragmatic Approach to Regression Anaylsis based on Fractional Polynomials for Modelling Continuous Variables
ISBN: 978-0-470-02842-1
Hardcover
322 pages
July 2008
US $130.00
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Preface
1 Introduction
1.1 Real-Life Problems as Motivation for Model Building
1.2 Issues in Modelling Continuous Predictors
1.3 Types of Regression Model Considered
1.4 Role of Residuals
1.5 Role of Subject-Matter Knowledge in Model Development
1.6 Scope of Model Building in our Book
1.7 Modelling Preferences
1.8 General Notation
2 Selection of Variables
2.1 Introduction
2.2 Background
2.3 Preliminaries for a Multivariable Analysis
2.4 Aims of Multivariable Models
2.5 Prediction: Summary Statistics and Comparisons
2.6 Procedures for Selecting Variables,
2.7 Comparison of Selection Strategies in Examples
2.8 Selection and Shrinkage
2.9 Discussion
3 Handling Categorical and Continuous Predictors
3.1 Introduction
3.2 Types of Predictor
3.3 Handling Ordinal Predictors
3.4 Handling Counting and Continuous Predictors: Categorization
3.5 Example: Issues in Model Building with Categorized Variables
3.6 Handling Counting and Continuous Predictors: Functional Form
3.7 Empirical Curve Fitting
3.8 Discussion
4 Fractional Polynomials for One Variable
4.1 Introduction
4.2 Background
4.3 Definition and Notation
4.4 Characteristics
4.5 Examples of Curve Shapes with FP1 and FP2 Functions
4.6 Choice of Powers
4.7 Choice of Origin
4.8 Model Fitting and Estimation
4.9 Inference
4.10 Function Selection Procedure
4.11 Scaling and Centring
4.12 Fractional Polynomial Powers as Approximations to Continuous Powers
4.13 Presentation of Fractional Polynomial Functions
4.14 Worked Example
4.15 Modelling Covariates with a Spike at Zero
4.16 Power of Fractional Polynomial Analysis
4.17 Discussion
5 Some Issues with Univariate Fractional Polynomial Models
5.1 Introduction
5.2 Susceptibility to Influential Covariate Observations
5.3 A Diagnostic Plot for Influential Points in Fractional Polynomial Models
5.4 Dependence on Choice of Origin
5.5 Improving Robustness by Preliminary Transformation
5.6 Improving Fit by Preliminary Transformation
5.7 Higher Order Fractional Polynomials
5.8 When Fractional Polynomial Models are Unsuitable
5.9 Discussion
6 Multivariable Fractional Polynomial: Multivariable Model-Building with Fractional Polynomials
6.1 Introduction
6.2 Motivation
6.3 The Multivariable Fractional Polynomial Algorithm
6.4 Presenting the Model
6.5 Model Criticism
6.6 Further Topics
6.7 Further Examples
6.8 Simple Versus Complex Fractional Polynomial Models
6.9 Discussion
7 Interactions
7.1 Introduction
7.2 Background
7.3 General Considerations
7.4 The Multivariable Fractional Polynomial Interaction Procedure
7.5 Example 1: Advanced Prostate Cancer
7.6 Example 2: GBSG Breast Cancer Study
Interaction
7.7 Categorization
7.8 STEPP
7.9 Example 3: Comparison of STEPP with Multivariable Fractional Polynomial Interaction
7.10 Comment on Type I Error of Multivariable Fractional Polynomial Interaction
7.11 Continuous-by-Continuous Interactions
7.12 Multi-Category Variables
7.13 Discussion
8 Model Stability
8.1 Introduction
8.2 Background
8.3 Using the Bootstrap to Explore Model Stability
8.4 Example 1: Glioma Data
8.5 Example 2: Educational Body-Fat Data
8.6 Example 3: Breast Cancer Diagnosis
8.7 Model Stability for Functions
8.8 Example 4: GBSG Breast Cancer Data
8.9 Discussion
9 Some Comparisons of Multivariable Fractional Polynomials with Splines
9.1 Introduction
9.2 Background
9.3 MVRS: A Procedure for Model Building with Regression Splines
9.4 MVSS: A Procedure for Model Building with Cubic Smoothing Splines
9.5 Example 1: Boston Housing Data
9.6 Example 2: GBSG Breast Cancer Study
9.7 Example 3: Pima Indians
9.8 Example 4: PBC
9.9 Discussion
10 How ToWork with Multivariable Fractional Polynomials
10.1 Introduction
10.2 The Dataset
10.3 Univariate Analyses
10.4 Multivariable Fractional Polynomial Analysis
10.5 Model Criticism
10.6 Stability Analysis
10.7 Final Model
10.8 Issues to be Aware of
10.9 Discussion
11 Special Topics Involving Fractional Polynomials
11.1 Time-Varying Hazard Ratios in the Cox Model
11.2 Age-specific Reference Intervals
11.3 Other Topics
12 Epilogue
12.1 Introduction
12.2 Towards Recommendations for Practice
12.3 Omitted Topics and Future Directions
12.4 Conclusion
13 Data and Software Resources
13.1 Summaries of Datasets
13.2 Datasets used more than once
13.3 Software
Appendix: Glossary of Abbreviations
References
