Preface xi 1 Uses and Abuses of Medical Statistics 1 1.1 Introduction 2 1.2 Why Use Statistics? 2 1.3 Statistics is About Common Sense and Good Design 3 1.4 How a Statistician Can Help 5 2 Displaying and Summarising Data 9 2.1 Types of Data 10 2.2 Summarising Categorical Data 13 2.3 Displaying Categorical Data 15 2.4 Summarising Continuous Data 17 2.5 Displaying Continuous Data 24 2.6 Within-Subject Variability 28 2.7 Presentation 30 2.8 Points When Reading the Literature 31 2.9 Technical Details 32 2.10 Exercises 33 3 Summary Measures for Binary Data 37 3.1 Summarising Binary and Categorical Data 38 3.2 Points When Reading the Literature 46 3.3 Exercises 46 4 Probability and Distributions 49 4.1 Types of Probability 50 4.2 The Binomial Distribution 54 4.3 The Poisson Distribution 55 4.4 Probability for Continuous Outcomes 57 4.5 The Normal Distribution 58 4.6 Reference Ranges 63 4.7 Other Distributions 64 4.8 Points When Reading the Literature 66 4.9 Technical Section 66 4.10 Exercises 67 5 Populations, Samples, Standard Errors and Confidence Intervals 71 5.1 Populations 72 5.2 Samples 73 5.3 The Standard Error 74 5.4 The Central Limit Theorem 75 5.5 Standard Errors for Proportions and Rates 77 5.6 Standard Error of Differences 79 5.7 Confidence Intervals for an Estimate 80 5.8 Confidence Intervals for Differences 83 5.9 Points When Reading the Literature 84 5.10 Technical Details 85 5.11 Exercises 86 6 Hypothesis Testing, P-values and Statistical Inference 91 6.1 Introduction 92 6.2 The Null Hypothesis 92 6.3 The Main Steps in Hypothesis Testing 94 6.4 Using Your P-value to Make a Decision About Whether to Reject, or Not Reject, Your Null Hypothesis 96 6.5 Statistical Power 99 6.6 One-sided and Two-sided Tests 101 6.7 Confidence Intervals (CIs) 101 6.8 Large Sample Tests for Two Independent Means or Proportions 104 6.9 Issues with P-values 107 6.10 Points When Reading the Literature 108 6.11 Exercises 108 7 Comparing Two or More Groups with Continuous Data 111 7.1 Introduction 112 7.2 Comparison of Two Groups of Paired Observations – Continuous Outcomes 113 7.3 Comparison of Two Independent Groups – Continuous Outcomes 119 7.4 Comparing More than Two Groups 127 7.5 Non-Normal Distributions 130 7.6 Degrees of Freedom 131 7.7 Points When Reading the Literature 132 7.8 Technical Details 132 7.9 Exercises 140 8 Comparing Groups of Binary and Categorical Data 145 8.1 Introduction 146 8.2 Comparison of Two Independent Groups – Binary Outcomes 146 8.3 Comparing Risks 151 8.4 Comparison of Two Groups of Paired Observations – Categorical Outcomes 152 8.5 Degrees of Freedom 153 8.6 Points When Reading the Literature 154 8.7 Technical Details 154 8.8 Exercises 160 9 Correlation and Linear Regression 163 9.1 Introduction 164 9.2 Correlation 165 9.3 Linear Regression 171 9.4 Comparison of Assumptions Between Correlation and Regression 178 9.5 Multiple Regression 179 9.6 Correlation is not Causation 181 9.7 Points When Reading the Literature 182 9.8 Technical Details 182 9.9 Exercises 190 10 Logistic Regression 193 10.1 Introduction 194 10.2 Binary Outcome Variable 194 10.3 The Multiple Logistic Regression Equation 196 10.4 Conditional Logistic Regression 200 10.5 Reporting the Results of a Logistic Regression 201 10.6 Additional Points When Reading the Literature When Logistic Regression Has Been Used 202 10.7 Technical Details 202 10.8 The Wald Test 204 10.9 Evaluating the Model and its Fit: The Hosmer–Lemeshow Test 204 10.10 Assessing Predictive Efficiency (1): 2 × 2 Classification Table 205 10.11 Assessing Predictive Efficiency (2): The ROC Curve 206 10.12 Investigating Linearity 206 10.13 Exercises 207 11 Survival Analysis 211 11.1 Time to Event Data 212 11.2 Kaplan–Meier Survival Curve 214 11.3 The Logrank Test 217 11.4 The Hazard Ratio 221 11.5 Modelling Time to Event Data 223 11.6 Points When Reading Literature 226 11.7 Exercises 229 12 Reliability and Method Comparison Studies 233 12.1 Introduction 234 12.2 Repeatability 234 12.3 Agreement 237 12.4 Validity 239 12.5 Method Comparison Studies 240 12.6 Points When Reading the Literature 243 12.7 Technical Details 243 12.8 Exercises 245 13 Evaluation of Diagnostic Tests 249 13.1 Introduction 250 13.2 Diagnostic Tests 250 13.3 Prevalence, Overall Accuracy, Sensitivity, and Specificity 251 13.4 Positive and Negative Predictive Values 252 13.5 The Effect of Prevalence 253 13.6 Confidence Intervals 254 13.7 Functions of a Screening and Diagnostic Test 255 13.8 Likelihood Ratio, Pre-test Odds and Post-test Odds 256 13.9 Receiver Operating Characteristic (ROC) Curve 257 13.10 Points When Reading the Literature About a Diagnostic Test 261 13.11 Exercises 262 14 Observational Studies 265 14.1 Introduction 266 14.2 Risk and Rates 266 14.3 Taking a Random Sample 272 14.4 Questionnaire and Form Design 273 14.5 Cross-sectional Surveys 274 14.6 Non-randomised Studies 275 14.7 Cohort Studies 278 14.8 Case–Control Studies 282 14.9 Association and Causality 287 14.10 Modern Causality Methods and Big Data 287 14.11 Points When Reading the Literature 288 14.12 Technical Details 288 14.13 Exercises 290 15 The Randomised Controlled Trial 293 15.1 Introduction 294 15.2 The Protocol 294 15.3 Why Randomise? 295 15.4 Methods of Randomisation 296 15.5 Design Features 298 15.6 Design Options 303 15.7 Meta-analysis 309 15.8 Checklists for Design, Analysis and Reporting 309 15.9 Consort 311 15.10 Points When Reading the Literature About a Trial 311 15.11 Exercises 311 16 Sample Size Issues 313 16.1 Introduction 314 16.2 Study Size 315 16.3 Continuous Data 318 16.4 Binary Data 319 16.5 Prevalence 321 16.6 Subject Withdrawals 322 16.7 Other Aspects of Sample Size Calculations 323 16.8 Points When Reading the Literature 325 16.9 Technical Details 325 16.10 Exercises 327 17 Other Statistical Methods 331 17.1 Analysing Serial or Longitudinal Data 332 17.2 Poisson Regression 341 17.3 Missing Data 343 17.4 Bootstrap Methods 350 17.5 Points When Reading the Literature 353 17.6 Exercises 353 18 Meta-analysis 355 18.1 Introduction 356 18.2 What is a Meta-analysis? 356 18.3 Meta-analysis Methods 358 18.4 Example: Mobile Phone Based Intervention for Smoking Cessation 359 18.5 Discussion 363 18.6 Technical Details 363 18.7 Exercises 365 19 Common Mistakes and Pitfalls 369 19.1 Introduction 370 19.2 Misleading Graphs and Tables 370 19.3 Plotting Change Against Initial Value 376 19.4 Within Group Versus Between Group Analyses 380 19.5 Analysing Paired Data Ignoring the Matching 381 19.6 Unit of Analysis 382 19.7 Testing for Baseline Imbalances in an RCT 382 19.8 Repeated Measures 383 19.9 Clinical and Statistical Significance 387 19.10 Post Hoc Power Calculations 387 19.11 Predicting or Extrapolating Beyond the Observed Range of Data 388 19.12 Exploratory Data Analysis 390 19.13 Misuse of P-values 391 19.14 Points When Reading the Literature 391 Appendix: Statistical Tables 393 Solutions to Multiple-Choice Exercises 403 References 413 Index 423

Medical Statistics A TEXTBOOK FOR THE HEALTH SCIENCES FIFTH EDITION The fifth edition of this popular introduction to statistics for the medical and health sciences has undergone a significant revision, with several new chapters added and examples refreshed throughout the book. It retains its central philosophy to explain medical statistics with as little technical detail as possible, making it accessible to a wide audience. Helpful multi-choice exercises are included at the end of each chapter, with answers provided at the end of the book. Each analysis technique is carefully explained and the mathematics kept to a minimum. Written in a style suitable for statisticians and clinicians alike, this edition features many real and original examples, taken from the authors' combined many years' experience of designing and analysing clinical trials and teaching statistics. Students of the health sciences, such as medicine, nursing, dentistry, physiotherapy, occupational therapy, and radiography should find the book useful, with examples relevant to their disciplines. The aim of training courses in medical statistics pertinent to these areas is not to turn the students into medical statisticians but rather to help them interpret the published scientific literature and appreciate how to design studies and analyse data arising from their own projects. The reader who is about to design their own study and collect, analyse and report on their own data will benefit from this clearly written book, which provides practical guidance to such issues. The practical guidance provided by this book will be of use to professionals both working in and managing clinical trials, in academic, public health, government and industry settings, particularly medical statisticians, clinicians, and trial co-ordinators. Its practical approach will appeal to applied statisticians and biomedical researchers, in particular those in the biopharmaceutical industry, medical and public health organisations.