Preface to the second edition, xv Preface to the first edition, xvii Abbreviations, xxi 1 Basic ideas in clinical trial design, 1 1.1 Historical perspective, 1 1.2 Control groups, 2 1.3 Placebos and blinding, 3 1.4 Randomisation, 3 1.4.1 Unrestricted randomisation, 4 1.4.

2 Block randomisation, 4 1.4.3 Unequal randomisation, 5 1.4.4 Stratified randomisation, 6 1.4.5 Central randomisation, 7 1.4.

6 Dynamic allocation and minimisation, 8 1.4.7 Cluster randomisation, 9 1.5 Bias and precision, 9 1.6 Between- and within-patient designs, 11 1.7 Crossover trials, 12 1.8 Signal, noise and evidence, 13 1.8.

1 Signal, 13 1.8.2 Noise, 13 1.8.3 Signal-to-noise ratio, 14 1.9 Confirmatory and exploratory trials, 15 1.10 Superiority, equivalence and non-inferiority trials, 16 1.11 Data and endpoint types, 17 1.

12 Choice of endpoint, 18 1.12.1 Primary variables, 18 1.12.2 Secondary variables, 19 1.12.3 Surrogate variables, 20 1.12.

4 Global assessment variables, 21 1.12.5 Composite variables, 21 1.12.6 Categorisation, 21 2 Sampling and inferential statistics, 23 2.1 Sample and population, 23 2.2 Sample statistics and population parameters, 24 2.2.

1 Sample and population distribution, 24 2.2.2 Median and mean, 25 2.2.3 Standard deviation, 25 2.2.4 Notation, 26 2.2.

5 Box plots, 27 2.3 The normal distribution, 28 2.4 Sampling and the standard error of the mean, 31 2.5 Standard errors more generally, 34 2.5.1 The standard error for the difference between two means, 34 2.5.2 Standard errors for proportions, 37 2.

5.3 The general setting, 37 3 Confidence intervals and p-values, 38 3.1 Confidence intervals for a single mean, 38 3.1.1 The 95 per cent Confidence interval, 38 3.1.2 Changing the confidence coefficient, 40 3.1.

3 Changing the multiplying constant, 40 3.1.4 The role of the standard error, 41 3.2 Confidence interval for other parameters, 42 3.2.1 Difference between two means, 42 3.2.2 Confidence interval for proportions, 43 3.

2.3 General case, 44 3.2.4 Bootstrap Confidence interval, 45 3.3 Hypothesis testing, 45 3.3.1 Interpreting the p-value, 46 3.3.

2 Calculating the p-value, 47 3.3.3 A common process, 50 3.3.4 The language of statistical significance, 53 3.3.5 One-sided and two-sided tests, 54 4 Tests for simple treatment comparisons, 56 4.1 The unpaired t-test, 56 4.

2 The paired t-test, 57 4.3 Interpreting the t-tests, 60 4.4 The chi-square test for binary data, 61 4.4.1 Pearson chi-square, 61 4.4.2 The link to a ratio of the signal to the standard error, 64 4.5 Measures of treatment benefit, 64 4.

5.1 Odds ratio, 65 4.5.2 Relative risk, 65 4.5.3 Relative risk reduction, 66 4.5.4 Number needed to treat, 66 4.

5.5 Confidence intervals, 67 4.5.6 Interpretation, 68 4.6 Fisher''s exact test, 69 4.7 Tests for categorical and ordinal data, 71 4.7.1 Categorical data, 71 4.

7.2 Ordered categorical (ordinal) data, 73 4.7.3 Measures of treatment benefit, 74 4.8 Extensions for multiple treatment groups, 75 4.8.1 Between-patient designs and continuous data, 75 4.8.

2 Within-patient designs and continuous data, 76 4.8.3 Binary, categorical and ordinal data, 76 4.8.4 Dose-ranging studies, 77 4.8.5 Further discussion, 77 5 Adjusting the analysis, 78 5.1 Objectives for adjusted analysis, 78 5.

2 Comparing treatments for continuous data, 78 5.3 Least squares means, 82 5.4 Evaluating the homogeneity of the treatment effect, 83 5.4.1 Treatment-by-factor interactions, 83 5.4.2 Quantitative and qualitative interactions, 85 5.5 Methods for binary, categorical and ordinal data, 86 5.

6 Multi-centre trials, 87 5.6.1 Adjusting for centre, 87 5.6.2 Significant treatment-by-centre interactions, 87 5.6.3 Combining centres, 88 6 Regression and analysis of covariance, 89 6.1 Adjusting for baseline factors, 89 6.

2 Simple linear regression, 89 6.3 Multiple regression, 91 6.4 Logistic regression, 94 6.5 Analysis of covariance for continuous data, 94 6.5.1 Main effect of treatment, 94 6.5.2 Treatment-by-covariate interactions, 96 6.

5.3 A single model, 98 6.5.4 Connection with adjusted analyses, 98 6.5.5 Advantages of ANCOVA, 99 6.5.6 Least squares means, 100 6.

6 Binary, categorical and ordinal data, 101 6.7 Regulatory aspects of the use of covariates, 103 6.8 Baseline testing, 105 7 Intention-to-treat and analysis sets, 107 7.1.