Multivariable Model - Building A Pragmatic

Multivariable regression models are of fundamental importance in all areas of science in which empirical data must be analyzed. This book proposes a systematic approach to building such models based on standard principles of statistical modeling. The main emphasis is on the fractional polynomial method for modeling the influence of continuous variables in a multivariable context, a topic for which there is no standard approach. Existing options range from very simple step functions to highly complex adaptive methods such as multivariate splines with many knots and penalisation. This new approach, developed in part by the authors over the last decade, is a compromise which promotes interpretable, comprehensible and transportable models.

Patrick Royston DSc,is a senior statistician and cancer clinical realist at the MRC Clinical Trials Unit, London, an honorary professor of statistics at University College London and a fellow of the Royal Statistical Society. he has authored many research papers in biostatistics, and has published over 150 articles in leading statistical journals. Patrick is an experienced statistical consultant, Stata programmer and software author.

Willi Sauerbrei PhD, is a senior statistician and professor in medical biometry at the IMBI, University Medical Center Freiburg. He has authored many research papers in biostatistics and has published over 100 articles in leading statistical and clinical journals. He worked for more than two decades as an academic biostatistician and has extensive experience of cancer research, with a particular concern for breast cancer.

Preface
Introduction
Real-Life Problems as Motivation for Model Building
Issues in Modelling Continuous Predictors
Types of Regression Model Considered
Role of Residuals
Role of Subject-Matter Knowledge in Model Development
Scope of Model Building in our Book
Modelling Preferences
General Notation
Selection of Variables
Introduction
Background
Preliminaries for a Multivariable Analysis
Aims of Multivariable Models
Prediction: Summary Statistics and Comparisons
Procedures for Selecting Variables
Comparison of Selection Strategies in Examples
Selection and Shrinkage
Discussion
Handling Categorical and Continuous Predictors
Introduction
Types of Predictor
Handling Ordinal Predictors
Handling Counting and Continuous Predictors: Categorization
Example: Issues in Model Building with Categorized Variables
Handling Counting and Continuous Predictors: Functional Form
Empirical Curve Fitting
Discussion
Fractional Polynomials for One Variable
Introduction
Background
Definition and Notation
Characteristics
Examples of Curve Shapes with FP1 and FP2 Functions
Choice of Powers
Choice of Origin
Model Fitting and Estimation
Inference
Function Selection Procedure
Scaling and Centering
FP Powers as Approximations to Continuous Powers
Presentation of Fractional Polynomial Functions
Worked Example
Modelling Covariates with a Spike at Zero
Power of Fractional Polynomial Analysis
Discussion
Some Issues with Univariate Fractional Polynomial Models
Introduction
Susceptibility to Influential Covariate Observations
A Diagnostic Plot for Influential Points in FP Models
Dependence on Choice of Origin
Improving Robustness by Preliminary Transformation
Improving Fit by Preliminary Transformation
Higher Order Fractional Polynomials
When Fractional Polynomial Models are Unsuitable
Discussion
MFP: Multivariable Model-Building with Fractional Polynomials
Introduction
Motivation
The MFP Algorithm
Presenting the Model
Model Criticism
Further Topics
Further Examples
Simple Versus Complex Fractional Polynomial Models
Discussion
Interactions
Introduction
Background
General Considerations
The MFPI Procedure
Example 1: Advanced Prostate Cancer
Example 2: GBSG Breast Cancer Study
Categorization
STEPP
Example 3: Comparison of STEPP with MFPI
Comment on Type I Error of MFPI
Continuous-by-Continuous Interactions
Multi-Category Variables
Discussion
Model Stability
Introduction
Background
Using the Bootstrap to Explore Model Stability
Example 1: Glioma Data
Example 2: Educational Body-Fat Data
Example 3: Breast Cancer Diagnosis
Model Stability for Functions
Example 4: GBSG Breast Cancer Data
Discussion
Some Comparisons of MFP with Splines
Introduction
Background
MVRS: A Procedure for Model Building with Regression Splines
MVSS: A Procedure for Model Building with Cubic Smoothing Splines
Example 1: Boston Housing Data
Example 2: GBSG Breast Cancer Study
Example 3: Pima Indians
Examp
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Multivariable Model - Building A Pragmatic Approach to Regression Anaylsis based on Fractional Polynomials for Modelling Continuous Variables

Summary

Author Biography

Table of Contents

Supplemental Materials