Statistics at Square Two

46 3.4 Uses of Logistic Regression 46 3.5 Interpreting a Computer Output 47 3.5.1 One Binary Independent Variable 47 3.5.2 Two Binary Independent Variables 51 3.5.3 Two Continuous Independent Variables 53 3.6 Examples in the Medical Literature 54 3.6.1 Comment 55 3.7 Case-control Studies 56 3.8 Interpreting Computer Output: Unmatched Case-control Study 56 3.9 Matched Case-control Studies 58 3.10 Interpreting Computer Output: Matched Case-control Study 58 3.11 Example of Conditional Logistic Regression in the Medical Literature 60 3.11.1 Comment 60 3.12 Alternatives to Logistic Regression 61 3.13 Reporting the Results of Logistic Regression 61 3.14 Reading about the Results of Logistic Regression 61 3.15 Frequently Asked Questions 62 3.16 Exercise 62 4 Survival Analysis 65 4.1 Introduction 65 4.2 The Model 66 4.3 Uses of Cox Regression 68 4.4 Interpreting a Computer Output 68 4.5 Interpretation of the Model 70 4.6 Generalisations of the Model 70 4.6.1 Stratified Models 70 4.6.2 Time Dependent Covariates 71 4.6.3 Parametric Survival Models 71 4.6.4 Competing Risks 71 4.7 Model Checking 72 4.8 Reporting the Results of a Survival Analysis 73 4.9 Reading about the Results of a Survival Analysis 74 4.10 Example in the Medical Literature 74 4.10.1 Comment 75 4.11 Frequently Asked Questions 76 4.12 Exercises 77 5 Random Effects Models 79 5.1 Introduction 79 5.2 Models for Random Effects 80 5.3 Random vs Fixed Effects 81 5.4 Use of Random Effects Models 81 5.4.1 Cluster Randomised Trials 81 5.4.2 Repeated Measures 82 5.4.3 Sample Surveys 83 5.4.4 Multi-centre Trials 83 5.5 Ordinary Least Squares at the Group Level 84 5.6 Interpreting a Computer Output 85 5.6.1 Different Methods of Analysis 85 5.6.2 Likelihood and gee 85 5.6.3 Interpreting Computer Output 86 5.7 Model Checking 89 5.8 Reporting the Results of Random Effects Analysis 89 5.9 Reading about the Results of Random Effects Analysis 90 5.10 Examples of Random Effects Models in the Medical Literature 90 5.10.1 Cluster Trials 90 5.10.2 Repeated Measures 91 5.10.3 Comment 91 5.10.4 Clustering in a Cohort Study 91 5.10.5 Comment 91 5.11 Frequently Asked Questions 91 5.12 Exercises 92 6 Poisson and Ordinal Regression 95 6.1 Poisson Regression 95 6.2 The Poisson Model 95 6.3 Interpreting a Computer Output: Poisson Regression 96 6.4 Model Checking for Poisson Regression 97 6.5 Extensions to Poisson Regression 99 6.6 Poisson Regression Used to Estimate Relative Risks from a 2 × 2 Table 99 6.7 Poisson Regression in the Medical Literature 100 6.8 Ordinal Regression 100 6.9 Interpreting a Computer Output: Ordinal Regression 101 6.10 Model Checking for Ordinal Regression 103 6.11 Ordinal Regression in the Medical Literature 104 6.12 Reporting the Results of Poisson or Ordinal Regression 104 6.13 Reading about the Results of Poisson or Ordinal Regression 104 6.14 Frequently Asked Question 105 6.15 Exercises 105 7 Meta-analysis 107 7.1 Introduction 107 7.2 Models for Meta-analysis 108 7.3 Missing Values 111 7.4 Displaying the Results of a Meta-analysis 111 7.5 Interpreting a Computer Output 113 7.6 Examples from the Medical Literature 114 7.6.1 Example of a Meta-analysis of Clinical Trials 114 7.6.2 Example of a Meta-analysis of Case-control Studies 115 7.7 Reporting the Results of a Meta-analysis 115 7.8 Reading about the Results of a Meta-analysis 116 7.9 Frequently Asked Questions 116 7.10 Exercise 118 8 Time Series Regression 121 8.1 Introduction 121 8.2 The Model 122 8.3 Estimation Using Correlated Residuals 122 8.4 Interpreting a Computer Output: Time Series Regression 123 8.5 Example of Time Series Regression in the Medical Literature 124 8.6 Reporting the Results of Time Series Regression 125 8.7 Reading about the Results of Time Series Regression 125 8.8 Frequently Asked Questions 125 8.9 Exercise 126 Appendix 1 Exponentials and Logarithms 129 Appendix 2 Maximum Likelihood and Significance Tests 133 A2. 1 Binomial Models and Likelihood 133 A. 2 The Poisson Model 135 A2. 3 The Normal Model 135 A2. 4 Hypothesis Testing: the Likelihood Ratio Test 137 A2. 5 The Wald Test 138 A2. 6 The Score Test 138 A2. 7 Which Method to Choose? 139 A2. 8 Confidence Intervals 139 A2. 9 Deviance Residuals for Binary Data 140 A2. 10 Example: Derivation of the Deviances and Deviance Residuals Given in Table 3.3 140 A2.10.1 Grouped Data 140 A2.10.2 Ungrouped Data 140 Appendix 3 Bootstrapping and Variance Robust Standard Errors 143 A3.1 The Bootstrap 143 A3.2 Example of the Bootstrap 144 A3.3 Interpreting a Computer Output: The Bootstrap 145 A3.3.1 Two-sample T-test with Unequal Variances 145 A3.4 The Bootstrap in the Medical Literature 145 A3.5 Robust or Sandwich Estimate SEs 146 A3.6 Interpreting a Computer Output: Robust SEs for Unequal Variances 147 A3.7 Other Uses of Robust Regression 149 A3.8 Reporting the Bootstrap and Robust SEs in the Literature 149 A3.9 Frequently Asked Question 150 Appendix 4 Bayesian Methods 151 A4.1 Bayes' Theorem 151 A4.2 Uses of Bayesian Methods 152 A4.3 Computing in Bayes 153 A4.4 Reading and Reporting Bayesian Methods in the Literature 154 A4.5 Reading about the Results of Bayesian Methods in the Medical Literature 154 Appendix 5 R codes 157 A5. 1 R Code for Chapter 2 157 A5. 3 R Code for Chapter 3 163 A5. 4 R Code for Chapter 4 166 A. 5 R Code for Chapter 5 168 A5. 6 R Code for Chapter 6 170 A5. 7 R Code for Chapter 7 171 A5. 8 R Code for Chapter 8 173 A5. 9 R Code for Appendix 1 173 A5. 10 R Code for Appendix 2 174 A5. 11 R Code for Appendix 3 175 Answers to Exercises 179 Glossary 185 Index 191