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

<p><b>STEPHEN J. WALTERS</b> 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 <i>How to Display Data</i> and <i>How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research</i>. 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. <p><b>MICHAEL J. CAMPBELL</b> 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: <i>Statistics at Square One, Statistics at Square Two, Sample Size Tables for Clinical Studies,</i> and <i>How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research</i>. <p><b>DAVID MACHIN</b> 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.

<p><b> Medical Statistics</b></br> A TEXTBOOK FOR THE HEALTH SCIENCES</br> FIFTH EDITION <p>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. <p>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. <p>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. <p>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.

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