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Regression Models as a Tool in Medical Research 

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Comment from the Stata technical groupRegression Models as a Tool in Medical Research, by Werner Vach, is a practical guide to regression analysis for medical researchers. It describes the important aspects of regression models for continuous, binary, survival, and count outcomes—all commonly encountered in medical research. The regression models covered include linear regression, logistic regression, Cox regression, and Poisson regression. The book also discusses methods to handle different types of data structures such as matched case–control data and longitudinal data. The “handson” examples reinforce the concepts described in each chapter, and the “inanutshell” summaries after each chapter provide a quick refresher of the topics covered. The book has five parts. The first part covers the basic concepts of the linear, logistic, and Cox regressions commonly used to analyze medical data. The second part discusses more advanced topics such as modeling of nonlinear effects and analysis of longitudinal and clustered data, as well as samplesize and power considerations when designing a study. The third part concentrates on prediction, and the fourth part briefly covers some alternatives to regression modeling. Finally, the fifth part provides mathematical details behind the main regression concepts. The numerical examples and graphs are produced with Stata; all datasets used in the examples and solutions to all exercises are available at www.imbi.unifreiburg.de/RegModToolInMedRes. 

Table of contentsView table of contents >> Preface
Acknowledgments
About the Author
I The Basics
1 Why Use Regression Models?
1.1 Why Use Simple Regression Models?
1.2 Why Use Multiple Regression Models? 1.3 Some Basic Notation 2 An Introductory Example
2.1 A Single Line Model
2.2 Fitting a Single Line Model 2.3 Taking Uncertainty into Account 2.4 A TwoLine Model 2.5 How to Perform These Steps with Stata 2.6 Exercise 5HIAA and Serotonin 2.7 Exercise Haemoglobin 2.8 Exercise Scaling of Variables 3 The Classical Multiple Regression Model
4 Adjusted Effects
4.1 Adjusting for Confounding
4.2 Adjusting for Imbalances 4.3 Exercise Physical Activity in Schoolchildren 5 Inference for the Classical Multiple Regression Model
5.1 The Traditional and the Modern Way of Inference
5.2 How to Perform the Modern Way of Inference with Stata 5.3 How Valid and Good are Least Squares Estimates? 5.4 A Note on the Use and Interpretation of pValues in Regression Analyses 6 Logistic Regression
6.1 The Definition of the Logistic Regression Model
6.2 Analysing a Dose Response Experiment by Logistic Regression 6.3 How to Fit a Dose Response Model with Stata 6.4 Estimating Odds Ratios and Adjusted Odds Ratios Using Logistic Regression 6.5 How to Compute (Adjusted) Odds Ratios Using Logistic Regression in Stata 6.6 Exercise Allergy in Children 6.7 More on Logit Scale and Odds Scale 7 Inference for the Logistic Regression Model
7.1 The Maximum Likelihood Principle
7.2 Properties of the ML Estimates for Logistic Regression 7.3 Inference for a Single Regression Parameter 7.4 How to Perform Wald Tests and Likelihood Ratio Tests in Stata 8 Categorical Covariates
8.1 Incorporating Categorical Covariates in a Regression Model
8.2 Some Technicalities in Using Categorical Covariates 8.3 Testing the Effect of a Categorical Covariate 8.4 The Handling of Categorical Covariates in Stata 8.5 Presenting Results of a Regression Analysis Involving Categorical Covariates in a Table 8.6 Exercise Physical Occupation and Back Pain 8.7 Exercise Odds Ratios and Categorical Covariates 9 Handling Ordered Categories: A First Lesson in Regression Modelling Strategies
10 The Cox Proportional Hazards Model
10.1 Modelling the Risk of Dying
10.2 Modelling the Risk of Dying in Continuous Time 10.3 Using the Cox Proportional Hazards Model to Quantify the Difference in Survival Between Groups 10.4 How to Fit a Cox Proportional Hazards Model with Stata 10.5 Exercise Prognostic Factors in Breast Cancer Patients—Part 1 11 Common Pitfalls in Using Regression Models
11.1 Association versus Causation
11.2 Difference between Subjects versus Difference within Subjects 11.3 RealWorld Models versus Statistical Models 11.4 Relevance versus Significance 11.5 Exercise Prognostic Factors in Breast Cancer Patients— Part 2 II Advanced Topics and Techniques
12 Some Useful Technicalities
12.1 Illustrating Models by Using ModelBased Predictions
12.2 How to Work with Predictions in Stata 12.3 Residuals and the Standard Deviation of the Error Term 12.4 Working with Residuals and the RMSE in Stata 12.5 Linear and Nonlinear Functions of Regression Parameters 12.6 Transformations of Regression Parameters 12.7 Centering of Covariate Values 12.8 Exercise Paternal Smoking versus Maternal Smoking 13 Comparing Regression Coefficients
13.1 Comparing Regression Coefficients among Continuous Covariates
13.2 Comparing Regression Coefficients among Binary Covariates 13.3 Measuring the Impact of Changing Covariate Values 13.4 Translating Regression Coefficients 13.5 How to Compare Regression Coefficients in Stata 13.6 Exercise Health in Young People 14 Power and Sample Size
14.1 The Power of a Regression Analysis
14.2 Determinants of Power in Regression Models with a Single Covariate 14.3 Determinants of Power in Regression Models with Several Covariates 14.4 Power and Sample Size Calculations When a Sample from the Covariate Distribution Is Given 14.5 Power and Sample Size Calculations Given a Sample from the Covariate Distribution with Stata 14.6 The Choice of the Values of the Regression Parameters in a Simulation Study 14.7 Simulating a Covariate Distribution 14.8 Simulating a Covariate Distribution with Stata 14.9 Choosing the Parameters to Simulate a Covariate Distribution 14.10 Necessary Sample Sizes to Justify Asymptotic Methods 14.11 Exercise Power Considerations for a Study on Neck Pain 14.12 Exercise Choosing between Two Outcomes 15 Selection of the Sample
15.1 Selection in Dependence on the Covariates
15.2 Selection in Dependence on the Outcome 15.3 Sampling in Dependence on Covariate Values 16 Selection of Covariates
16.1 Fitting Regression Models with Correlated Covariates
16.2 The “Adjustment versus Power” Dilemma 16.3 The “Adjustment Makes Effects Small” Dilemma 16.4 Adjusting for Mediators 16.5 Adjusting for Confounding — A Useful Academic Game 16.6 Adjusting for Correlated Confounders 16.7 Including Predictive Covariates 16.8 Automatic Variable Selection 16.9 How to Choose Relevant Sets of Covariates 16.10 Preparing the Selection of Covariates: Analysing the Association Among Covariates 16.11 Preparing the Selection of Covariates: Univariate Analyses? 16.12 Exercise Vocabulary Size in Young Children—Part 1 16.13 Preprocessing of the Covariate Space 16.14 How to Preprocess the Covariate Space with Stata 16.15 Exercise Vocabulary Size in Young Children— Part 2 16.16 What Is a Confounder? 17 Modelling Nonlinear Effects
17.1 Quadratic Regression
17.2 Polynomial Regression 17.3 Splines 17.4 Fractional Polynomials 17.5 Gain in Power by Modelling Nonlinear Effects? 17.6 Demonstrating the Effect of a Covariate 17.7 Demonstrating a Nonlinear Effect 17.8 Describing the Shape of a Nonlinear Effect 17.9 Detecting Nonlinearity by Analysis of Residuals 17.10 Judging of Nonlinearity May Require Adjustment 17.11 How to Model Nonlinear Effects in Stata 17.12 The Impact of Ignoring Nonlinearity 17.13 Modelling the Nonlinear Effect of Confounders 17.14 Nonlinear Models 17.15 Exercise Serum Makers for AMI 18 Transformation of Covariates
18.1 Transformations to Obtain a Linear Relationship
18.2 Transformation of Skewed Covariates 18.3 To Categorise or Not to Categorise 19 Effect Modification and Interactions
19.1 Modelling Effect Modification
19.2 Adjusted Effect Modifications 19.3 Interactions 19.4 Modelling Effect Modifications in Several Covariates 19.5 The Effect of a Covariate in the Presence of Interactions 19.6 Interactions as Deviations from Additivity 19.7 Scales and Interactions 19.8 Ceiling Effects and Interactions 19.9 Hunting for Interactions 19.10 How to Analyse Effect Modification and Interactions with Stata 19.11 Exercise Treatment Interactions in a Randomised Clinical Trial for the Treatment of Malignant Glioma 20 Applying Regression Models to Clustered Data
20.1 Why Clustered Data Can Invalidate Inference
20.2 Robust Standard Errors 20.3 Improving the Efficiency 20.4 Within and BetweenCluster Effects 20.5 Some Unusual but Useful Usages of Robust Standard Errors in Clustered Data 20.6 How to Take Clustering into Account in Stata 21 Applying Regression Models to Longitudinal Data
21.1 Analysing Time Trends in the Outcome
21.2 Analysing Time Trends in the Effect of Covariates 21.3 Analysing the Effect of Covariates 21.4 Analysing Individual Variation in Time Trends 21.5 Analysing Summary Measures 21.6 Analysing the Effect of Change 21.7 How to Perform Regression Modelling of Longitudinal Data in Stata 21.8 Exercise Increase of Body Fat in Adolescents 22 The Impact of Measurement Error
22.1 The Impact of Systematic and Random Measurement Error
22.2 The Impact of Misclassification 22.3 The Impact of Measurement Error in Confounders 22.4 The Impact of Differential Misclassification and Measurement Error 22.5 Studying the Measurement Error 22.6 Exercise Measurement Error and Interactions 23 The Impact of Incomplete Covariate Data
23.1 Missing Value Mechanisms
23.2 Properties of a Complete Case Analysis 23.3 Bias Due to Using ad hoc Methods 23.4 Advanced Techniques to Handle Incomplete Covariate Data 23.5 Handling of Partially Defined Covariates III Risk Scores and Predictors
24 Risk Scores
24.1 What Is a Risk Score?
24.2 Judging the Usefulness of a Risk Score 24.3 The Precision of Risk Score Values 24.4 The Overall Precision of a Risk Score 24.5 Using Stata’s predict Command to Compute Risk Scores 24.6 Categorisation of Risk Scores 24.7 Exercise Computing Risk Scores for Breast Cancer Patients 25 Construction of Predictors
25.1 From Risk Scores to Predictors
25.2 Predictions and Prediction Intervals for a Continuous Outcome 25.3 Predictions for a Binary Outcome 25.4 Construction of Predictions for TimetoEvent Data 25.5 How to Construct Predictions with Stata 25.6 The Overall Precision of a Predictor 26 Evaluating the Predictive Performance
26.1 The Predictive Performance of an Existing Predictor
26.2 How to Assess the Predictive Performance of an Existing Predictor in Stata 26.3 Estimating the Predictive Performance of a New Predictor 26.4 How to Assess the Predictive Performance via CrossValidation in Stata 26.5 Exercise Assessing the Predictive Performance of a Prognostic Score in Breast Cancer Patients 27 Outlook: Construction of Parsimonious Predictors
IV Miscellaneous
28 Alterations to Regression Modelling
28.1 Stratification
28.2 Measures of Association: Correlation Coefficients 28.3 Measures of Association: The Odds Ratio 28.4 Propensity Scores 28.5 Classification and Regression Trees 29 Specific Regression Models
29.1 Probit Regression for Binary Outcomes
29.2 Generalised Linear Models 29.3 Regression Models for Count Data 29.4 Regression Models for Ordinal Outcome Data 29.5 Quantile Regression and Robust Regression 29.6 ANOVA and Regression 30 Specific Usages of Regression Models
30.1 Logistic Regression for the Analysis of CaseControl Studies
30.2 Logistic Regression for the Analysis of Matched CaseControl Studies 30.3 Adjusting for Baseline Values in Randomised Clinical Trials 30.4 Assessing Predictive Factors 30.5 Incorporating TimeVarying Covariates in a Cox Model 30.6 TimeDependent Effects in a Cox Model 30.7 Using the Cox Model in the Presence of Competing Risks 30.8 Using the Cox Model to Analyse MultiState Models 31 What Is a Good Model?
31.1 Does the Model Fit the Data?
31.2 How Good Are Predictions? 31.3 Explained Variation 31.4 Goodness of Fit 31.5 Model Stability 31.6 The Usefulness of a Model 32 Final Remarks on the Role of Prespecified Models and Model Development
V Mathematical Details
A Mathematics Behind the Classical Linear Regression Model
A.1 Computing Regression Parameters in Simple Linear Regression
A.2 Computing Regression Parameters in the Classical Multiple Regression Model A.3 Estimation of the Standard Error A.4 Construction of Confidence Intervals and pValues B Mathematics Behind the Logistic Regression Model
B.1 The Least Squares Principle as a Maximum Likelihood Principle
B.2 Maximising the Likelihood of a Logistic Regression Model B.3 Estimating the Standard Error of the ML Estimates B.4 Testing Composite Hypotheses C The Modern Way of Inference
C.1 Robust Estimation of Standard Errors
C.2 Robust Estimation of Standard Errors in the Presence of Clustering D Mathematics for Risk Scores and Predictors
D.1 Computing Individual Survival Probabilities after Fitting a Cox Model
D.2 Standard Errors for Risk Scores D.3 The Delta Rule Bibliography
Index

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