Medical Statistics

STEPHEN J. WALTERS is Professor of Medical Statistics and Clinical Trials in the School of Health and Related Research (ScHARR) at the University of Sheffield, UK. Stephen is a prolific researcher and writer, including the popular textbooks How to Display Data and How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research. He is a National Institute for Health Research (NIHR) Senior Investigator, and has developed several courses on teaching medical statistics to medical and health science students, clinicians and allied health professionals. MICHAEL J. CAMPBELL is Emeritus Professor of Medical Statistics in the School of Health and Related Research (ScHARR) at the University of Sheffield, UK. Mike is a leading researcher in medical statistics and clinical trials with a national and international reputation. A prolific writer, Mike has written many best-selling textbooks on medical statistics and clinical trials including: Statistics at Square One, Statistics at Square Two, Sample Size Tables for Clinical Studies, and How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research. DAVID MACHIN is Emeritus Professor of Medical Statistics in the School of Health and Related Research (ScHARR) at the University of Sheffield, UK. He was Foundation Director of the National Medical Research Council, Clinical Trials and Epidemiology Research Unit, Singapore, and Head of the MRC Cancer Trials Office, Cambridge, UK. He has published more than 250 peer reviewed articles, and several books on a wide variety of topics in statistics and medicine. His earlier experience included posts at the Universities of Wales, Leeds, Stirling, Southampton and Sheffield, a period with the European Organisation for Research and Treatment of Cancer in Brussels, Belgium, and at the World Health Organization in Geneva, Switzerland.

• Preface xi1 Uses and Abuses of Medical Statistics 11.1 Introduction 21.2 Why Use Statistics? 21.3 Statistics is About Common Sense and Good Design 31.4 How a Statistician Can Help 52 Displaying and Summarising Data 92.1 Types of Data 102.2 Summarising Categorical Data 132.3 Displaying Categorical Data 152.4 Summarising Continuous Data 172.5 Displaying Continuous Data 242.6 Within-Subject Variability 282.7 Presentation 302.8 Points When Reading the Literature 312.9 Technical Details 322.10 Exercises 333 Summary Measures for Binary Data 373.1 Summarising Binary and Categorical Data 383.2 Points When Reading the Literature 463.3 Exercises 464 Probability and Distributions 494.1 Types of Probability 504.2 The Binomial Distribution 544.3 The Poisson Distribution 554.4 Probability for Continuous Outcomes 574.5 The Normal Distribution 584.6 Reference Ranges 634.7 Other Distributions 644.8 Points When Reading the Literature 664.9 Technical Section 664.10 Exercises 675 Populations, Samples, Standard Errors and Confidence Intervals 715.1 Populations 725.2 Samples 735.3 The Standard Error 745.4 The Central Limit Theorem 755.5 Standard Errors for Proportions and Rates 775.6 Standard Error of Differences 795.7 Confidence Intervals for an Estimate 805.8 Confidence Intervals for Differences 835.9 Points When Reading the Literature 845.10 Technical Details 855.11 Exercises 866 Hypothesis Testing, P-values and Statistical Inference 916.1 Introduction 926.2 The Null Hypothesis 926.3 The Main Steps in Hypothesis Testing 946.4 Using Your P-value to Make a Decision About Whether to Reject, or Not Reject, Your Null Hypothesis 966.5 Statistical Power 996.6 One-sided and Two-sided Tests 1016.7 Confidence Intervals (CIs) 1016.8 Large Sample Tests for Two Independent Means or Proportions 1046.9 Issues with P-values 1076.10 Points When Reading the Literature 1086.11 Exercises 1087 Comparing Two or More Groups with Continuous Data 1117.1 Introduction 1127.2 Comparison of Two Groups of Paired Observations – Continuous Outcomes 1137.3 Comparison of Two Independent Groups – Continuous Outcomes 1197.4 Comparing More than Two Groups 1277.5 Non-Normal Distributions 1307.6 Degrees of Freedom 1317.7 Points When Reading the Literature 1327.8 Technical Details 1327.9 Exercises 1408 Comparing Groups of Binary and Categorical Data 1458.1 Introduction 1468.2 Comparison of Two Independent Groups – Binary Outcomes 1468.3 Comparing Risks 1518.4 Comparison of Two Groups of Paired Observations – Categorical Outcomes 1528.5 Degrees of Freedom 1538.6 Points When Reading the Literature 1548.7 Technical Details 1548.8 Exercises 1609 Correlation and Linear Regression 1639.1 Introduction 1649.2 Correlation 1659.3 Linear Regression 1719.4 Comparison of Assumptions Between Correlation and Regression 1789.5 Multiple Regression 1799.6 Correlation is not Causation 1819.7 Points When Reading the Literature 1829.8 Technical Details 1829.9 Exercises 19010 Logistic Regression 19310.1 Introduction 19410.2 Binary Outcome Variable 19410.3 The Multiple Logistic Regression Equation 19610.4 Conditional Logistic Regression 20010.5 Reporting the Results of a Logistic Regression 20110.6 Additional Points When Reading the Literature When Logistic Regression Has Been Used 20210.7 Technical Details 20210.8 The Wald Test 20410.9 Evaluating the Model and its Fit: The Hosmer–Lemeshow Test 20410.10 Assessing Predictive Efficiency (1): 2 × 2 Classification Table 20510.11 Assessing Predictive Efficiency (2): The ROC Curve 20610.12 Investigating Linearity 20610.13 Exercises 20711 Survival Analysis 21111.1 Time to Event Data 21211.2 Kaplan–Meier Survival Curve 21411.3 The Logrank Test 21711.4 The Hazard Ratio 22111.5 Modelling Time to Event Data 22311.6 Points When Reading Literature 22611.7 Exercises 22912 Reliability and Method Comparison Studies 23312.1 Introduction 23412.2 Repeatability 23412.3 Agreement 23712.4 Validity 23912.5 Method Comparison Studies 24012.6 Points When Reading the Literature 24312.7 Technical Details 24312.8 Exercises 24513 Evaluation of Diagnostic Tests 24913.1 Introduction 25013.2 Diagnostic Tests 25013.3 Prevalence, Overall Accuracy, Sensitivity, and Specificity 25113.4 Positive and Negative Predictive Values 25213.5 The Effect of Prevalence 25313.6 Confidence Intervals 25413.7 Functions of a Screening and Diagnostic Test 25513.8 Likelihood Ratio, Pre-test Odds and Post-test Odds 25613.9 Receiver Operating Characteristic (ROC) Curve 25713.10 Points When Reading the Literature About a Diagnostic Test 26113.11 Exercises 26214 Observational Studies 26514.1 Introduction 26614.2 Risk and Rates 26614.3 Taking a Random Sample 27214.4 Questionnaire and Form Design 27314.5 Cross-sectional Surveys 27414.6 Non-randomised Studies 27514.7 Cohort Studies 27814.8 Case–Control Studies 28214.9 Association and Causality 28714.10 Modern Causality Methods and Big Data 28714.11 Points When Reading the Literature 28814.12 Technical Details 28814.13 Exercises 29015 The Randomised Controlled Trial 29315.1 Introduction 29415.2 The Protocol 29415.3 Why Randomise? 29515.4 Methods of Randomisation 29615.5 Design Features 29815.6 Design Options 30315.7 Meta-analysis 30915.8 Checklists for Design, Analysis and Reporting 30915.9 Consort 31115.10 Points When Reading the Literature About a Trial 31115.11 Exercises 31116 Sample Size Issues 31316.1 Introduction 31416.2 Study Size 31516.3 Continuous Data 31816.4 Binary Data 31916.5 Prevalence 32116.6 Subject Withdrawals 32216.7 Other Aspects of Sample Size Calculations 32316.8 Points When Reading the Literature 32516.9 Technical Details 32516.10 Exercises 32717 Other Statistical Methods 33117.1 Analysing Serial or Longitudinal Data 33217.2 Poisson Regression 34117.3 Missing Data 34317.4 Bootstrap Methods 35017.5 Points When Reading the Literature 35317.6 Exercises 35318 Meta-analysis 35518.1 Introduction 35618.2 What is a Meta-analysis? 35618.3 Meta-analysis Methods 35818.4 Example: Mobile Phone Based Intervention for Smoking Cessation 35918.5 Discussion 36318.6 Technical Details 36318.7 Exercises 36519 Common Mistakes and Pitfalls 36919.1 Introduction 37019.2 Misleading Graphs and Tables 37019.3 Plotting Change Against Initial Value 37619.4 Within Group Versus Between Group Analyses 38019.5 Analysing Paired Data Ignoring the Matching 38119.6 Unit of Analysis 38219.7 Testing for Baseline Imbalances in an RCT 38219.8 Repeated Measures 38319.9 Clinical and Statistical Significance 38719.10 Post Hoc Power Calculations 38719.11 Predicting or Extrapolating Beyond the Observed Range of Data 38819.12 Exploratory Data Analysis 39019.13 Misuse of P-values 39119.14 Points When Reading the Literature 391Appendix: Statistical Tables 393Solutions to Multiple-Choice Exercises 403References 413Index 423