Statistics at Square Two

Michael J. Campbell is Emeritus Professor of Medical Statistics at the University of Sheffield in the United Kingdom. Richard M. Jacques is a Senior Lecturer in Medical Statistics at the University of Sheffield in the United Kingdom.

• Preface xi1 Models, Tests and Data 11.1 Types of Data 11.2 Confounding, Mediation and Effect Modification 21.3 Causal Inference 31.4 Statistical Models 51.5 Results of Fitting Models 61.6 Significance Tests 71.7 Confidence Intervals 81.8 Statistical Tests Using Models 81.9 Many Variables 91.10 Model Fitting and Analysis: Exploratory and Confirmatory Analyses 101.11 Computer-intensive Methods 111.12 Missing Values 111.13 Bayesian Methods 121.14 Causal Modelling 121.15 Reporting Statistical Results in the Medical Literature 141.16 Reading Statistics in the Medical Literature 142 Multiple Linear Regression 172.1 The Model 172.2 Uses of Multiple Regression 182.3 Two Independent Variables 182.3.1 One Continuous and One Binary Independent Variable 192.3.2 Two Continuous Independent Variables 222.3.3 Categorical Independent Variables 222.4 Interpreting a Computer Output 232.4.1 One Continuous Variable 242.4.2 One Continuous Variable and One Binary Independent Variable 252.4.3 One Continuous Variable and One Binary Independent Variable with Their Interaction 262.4.4 Two Independent Variables: Both Continuous 272.4.5 Categorical Independent Variables 292.5 Examples in the Medical Literature 312.5.1 Analysis of Covariance: One Binary and One Continuous Independent Variable 312.5.2 Two Continuous Independent Variables 322.6 Assumptions Underlying the Models 322.7 Model Sensitivity 332.7.1 Residuals, Leverage and Influence 332.7.2 Computer Analysis: Model Checking and Sensitivity 342.8 Stepwise Regression 352.9 Reporting the Results of a Multiple Regression 362.10 Reading about the Results of a Multiple Regression 362.11 Frequently Asked Questions 372.12 Exercises: Reading the Literature 383 Multiple Logistic Regression 413.1 Quick Revision 413.2 The Model 423.2.1 Categorical Covariates 443.3 Model Checking 443.3.1 Lack of Fit 453.3.2 “Extra-binomial” Variation or “Over Dispersion” 453.3.3 The Logistic Transform is Inappropriate 463.4 Uses of Logistic Regression 463.5 Interpreting a Computer Output 473.5.1 One Binary Independent Variable 473.5.2 Two Binary Independent Variables 513.5.3 Two Continuous Independent Variables 533.6 Examples in the Medical Literature 543.6.1 Comment 553.7 Case-control Studies 563.8 Interpreting Computer Output: Unmatched Case-control Study 563.9 Matched Case-control Studies 583.10 Interpreting Computer Output: Matched Case-control Study 583.11 Example of Conditional Logistic Regression in the Medical Literature 603.11.1 Comment 603.12 Alternatives to Logistic Regression 613.13 Reporting the Results of Logistic Regression 613.14 Reading about the Results of Logistic Regression 613.15 Frequently Asked Questions 623.16 Exercise 624 Survival Analysis 654.1 Introduction 654.2 The Model 664.3 Uses of Cox Regression 684.4 Interpreting a Computer Output 684.5 Interpretation of the Model 704.6 Generalisations of the Model 704.6.1 Stratified Models 704.6.2 Time Dependent Covariates 714.6.3 Parametric Survival Models 714.6.4 Competing Risks 714.7 Model Checking 724.8 Reporting the Results of a Survival Analysis 734.9 Reading about the Results of a Survival Analysis 744.10 Example in the Medical Literature 744.10.1 Comment 754.11 Frequently Asked Questions 764.12 Exercises 775 Random Effects Models 795.1 Introduction 795.2 Models for Random Effects 805.3 Random vs Fixed Effects 815.4 Use of Random Effects Models 815.4.1 Cluster Randomised Trials 815.4.2 Repeated Measures 825.4.3 Sample Surveys 835.4.4 Multi-centre Trials 835.5 Ordinary Least Squares at the Group Level 845.6 Interpreting a Computer Output 855.6.1 Different Methods of Analysis 855.6.2 Likelihood and gee 855.6.3 Interpreting Computer Output 865.7 Model Checking 895.8 Reporting the Results of Random Effects Analysis 895.9 Reading about the Results of Random Effects Analysis 905.10 Examples of Random Effects Models in the Medical Literature 905.10.1 Cluster Trials 905.10.2 Repeated Measures 915.10.3 Comment 915.10.4 Clustering in a Cohort Study 915.10.5 Comment 915.11 Frequently Asked Questions 915.12 Exercises 926 Poisson and Ordinal Regression 956.1 Poisson Regression 956.2 The Poisson Model 956.3 Interpreting a Computer Output: Poisson Regression 966.4 Model Checking for Poisson Regression 976.5 Extensions to Poisson Regression 996.6 Poisson Regression Used to Estimate Relative Risks from a 2 × 2 Table 996.7 Poisson Regression in the Medical Literature 1006.8 Ordinal Regression 1006.9 Interpreting a Computer Output: Ordinal Regression 1016.10 Model Checking for Ordinal Regression 1036.11 Ordinal Regression in the Medical Literature 1046.12 Reporting the Results of Poisson or Ordinal Regression 1046.13 Reading about the Results of Poisson or Ordinal Regression 1046.14 Frequently Asked Question 1056.15 Exercises 1057 Meta-analysis 1077.1 Introduction 1077.2 Models for Meta-analysis 1087.3 Missing Values 1117.4 Displaying the Results of a Meta-analysis 1117.5 Interpreting a Computer Output 1137.6 Examples from the Medical Literature 1147.6.1 Example of a Meta-analysis of Clinical Trials 1147.6.2 Example of a Meta-analysis of Case-control Studies 1157.7 Reporting the Results of a Meta-analysis 1157.8 Reading about the Results of a Meta-analysis 1167.9 Frequently Asked Questions 1167.10 Exercise 1188 Time Series Regression 1218.1 Introduction 1218.2 The Model 1228.3 Estimation Using Correlated Residuals 1228.4 Interpreting a Computer Output: Time Series Regression 1238.5 Example of Time Series Regression in the Medical Literature 1248.6 Reporting the Results of Time Series Regression 1258.7 Reading about the Results of Time Series Regression 1258.8 Frequently Asked Questions 1258.9 Exercise 126Appendix 1 Exponentials and Logarithms 129Appendix 2 Maximum Likelihood and Significance Tests 133A2. 1 Binomial Models and Likelihood 133A. 2 The Poisson Model 135A2. 3 The Normal Model 135A2. 4 Hypothesis Testing: the Likelihood Ratio Test 137A2. 5 The Wald Test 138A2. 6 The Score Test 138A2. 7 Which Method to Choose? 139A2. 8 Confidence Intervals 139A2. 9 Deviance Residuals for Binary Data 140A2. 10 Example: Derivation of the Deviances and Deviance Residuals Given in Table 3.3 140A2.10.1 Grouped Data 140A2.10.2 Ungrouped Data 140Appendix 3 Bootstrapping and Variance Robust Standard Errors 143A3.1 The Bootstrap 143A3.2 Example of the Bootstrap 144A3.3 Interpreting a Computer Output: The Bootstrap 145A3.3.1 Two-sample T-test with Unequal Variances 145A3.4 The Bootstrap in the Medical Literature 145A3.5 Robust or Sandwich Estimate SEs 146A3.6 Interpreting a Computer Output: Robust SEs for Unequal Variances 147A3.7 Other Uses of Robust Regression 149A3.8 Reporting the Bootstrap and Robust SEs in the Literature 149A3.9 Frequently Asked Question 150Appendix 4 Bayesian Methods 151A4.1 Bayes’ Theorem 151A4.2 Uses of Bayesian Methods 152A4.3 Computing in Bayes 153A4.4 Reading and Reporting Bayesian Methods in the Literature 154A4.5 Reading about the Results of Bayesian Methods in the Medical Literature 154Appendix 5 R codes 157A5. 1 R Code for Chapter 2 157A5. 3 R Code for Chapter 3 163A5. 4 R Code for Chapter 4 166A. 5 R Code for Chapter 5 168A5. 6 R Code for Chapter 6 170A5. 7 R Code for Chapter 7 171A5. 8 R Code for Chapter 8 173A5. 9 R Code for Appendix 1 173A5. 10 R Code for Appendix 2 174A5. 11 R Code for Appendix 3 175Answers to Exercises 179Glossary 185Index 191