Sample Size Tables for Clinical Studies

This book provides statisticians and researchers with the statistical tools - equations, formulae and numerical tables - to design and plan clinical studies and carry out accurate, reliable and reproducible analysis of the data so obtained. There is no way around this as incorrect procedure in clinical studies means that the researcher's paper will not be accepted by a peer-reviewed journal. Planning and analysing clinical studies is a very complicated business and this book provides indispensible factual information. David Machin , Children's Cancer and Leukaemia Group, University of Leicester, UK; Division of Clinical Trials and Epidemiological Sciences, National Cancer Centre, Singapore; Medical Statistics Unit, School of Health and Related Sciences, University of Sheffield, UK - Michael J. Campbell, Medical Statistics Unit, School of Health and Related Sciences, University of Sheffield, UK - Say Beng Tan, Singapore Clinical Research Institute, Singapore; Duke-NUS Graduate Medical School, Singapore - Sze Huey Tan, Division of Clinical Trials and Epidemiological Sciences, National Cancer Centre, Singapore CONTENTS 1 Basic design considerations, 1. 2 Distributions and confidence intervals, 14. Table 2.1 The Normal distribution functionaprobability that a Normally. distributed variable is less than z, 27. Table 2.2 Percentage points of the Normal distribution for α and 1 − β, 28. Table 2.3 Values of θ(α, β) = (z1−α/2 + z1−β)2, 28. Table 2.4 The t-distribution, 29. 3 Comparing two independent groups for binary data, 30. Table 3.1 Sample size for the comparison of two proportions, 38. Table 3.2 Sample size for the comparison of two proportions using the odds. ratio (OR), 40. 4 Comparing two independent groups for ordered. categorical data, 42. 5 Comparing two independent groups for continuous data, 47. Table 5.1 Sample sizes for the two sample t-test with two-sided α = 0.05, 54. Table 5.2 Sample sizes for the two sample t-test with unequal variances, 55. Table 5.3 Sample sizes for the one sample t-test with two-sided α = 0.05, 57. 6 Cluster designs, repeated measures data and more than. two groups, 58. Table 6.1 Multiplying factor for repeated measures designs, 66. 7 Comparing paired groups for binary, ordered categorical and. continuous outcomes, 67. Table 7.1 Sample sizes for paired binary data, 80. Table 7.2 Sample sizes for paired continuous data with two-sided α = 0.05, 81. 8 Comparing survival curves, 82. Table 8.1 Number of critical events for comparison of survival rates (Logrank test), 95. Table 8.2 Number of subjects for comparison of survival rates (Logrank test), 97. Table 8.3 Number of critical events for comparison of two exponential survival. distributions with two-sided α = 0.05, 99. 9 Equivalence, 100. Table 9.1 Sample sizes for bioequivalence studiesadifference between two means or. ratio of two means, 115. Table 9.2 Sample sizes for testing the equivalence of two means, 116. Table 9.3 Sample sizes for testing the equivalence of two proportions, 118. 10 Confidence intervals, 120. Table 10.1 Sample sizes required to observe a given confidence interval width for a. given proportion in a sample from a large population, 134. Table 10.2 Sample sizes required to observe a given confidence interval width for the. difference between two proportionsaindependent groups, 135. Table 10.3 Sample sizes required to observe a proportionate confidence interval width. for the difference between two groups expressed via the odds ratio (OR), 136. Table 10.4 Sample sizes required to observe a given confidence interval width for the. difference between two proportions from paired or matched groups, 137. Table 10.5 Sample sizes required to observe a given confidence interval width to. estimate a single mean or the difference between two means for independent or. matched groups, 139. 11 Post-marketing surveillance, 140. Table 11.1 Sample sizes required to observe a total of a adverse reactions with a given. probability 1 − β and anticipated incidence λ, 147. Table 11.2 Sample sizes required for detection of a specific adverse reaction with. background incidence, λ0, known, 148. Table 11.3 Sample sizes required for detection of a specific adverse reaction with. background incidence unknown, 149. Table 11.4 Number of cases to be observed in a case-control study, 150. 12 The correlation coefficient, 151. Table 12.1 Sample sizes for detecting a statistically significant correlation coefficient,. 155. 13 Reference intervals and receiver operating curves, 156. Table 13.1 Sample sizes in order to obtain a required reference intervalaNormal. distribution, 167. Table 13.2 Sample sizes in order to obtain a required reference intervalanon-Normal. distribution, 168. Table 13.3 Sample sizes required to observe a given sensitivity and specificity in. diagnostic accuracy studiesasingle sample, 169. Table 13.4 Sample sizes required to observe a given sensitivity and specificity in. diagnostic accuracy studiesatwo sample unpaired design, 171. Table 13.5 Sample sizes required to observe a given sensitivity and specificity in. diagnostic accuracy studiesatwo sample matched paired design, 173. Table 13.6 Sample sizes required to observe a given confidence interval width for. receiver operating curves (ROC), 175. 14 Observer agreement studies, 177. Table 14.1 Sample sizes required to observe a given confidence interval to estimate. the proportion of disagreements between two observers, 187. Table 14.2 Sample sizes required to observe a given confidence interval to estimate. the within observer variation, 188. Table 14.3 Sample sizes required to observe a given confidence interval to minimise. the number of subjects required to achieve the desired precision in the probability of. their disagreement, ΘDis, 189. Table 14.4 Sample sizes required to observe a given confidence interval width for. inter-observer agreement using Cohen's Kappa, κ, 190. Table 14.5 Sample sizes required to observe a given intra-class correlation using. confidence interval approach, 191. Table 14.6 Sample sizes required to observe a given intra-class correlation using. hypothesis testing approach with two-sided α = 0.05, 192. 15 Dose finding studies, 193. 16 Phase II trials, 205. Table 16.1 Fleming-A'Hern single-stage Phase II design, 223. Table 16.2 Gehan two-stage Phase II designaStage 1, 224. Table 16.3 Gehan two-stage Phase II designaStage 2, 225. Table 16.4 Simon Optimal and Minimax designs, 226. Table 16.5 Bayesian single threshold design (STD), 227. Table 16.6 Bayesian dual threshold design (DTD), 228. Table 16.7 Case and Morgan design (EDA) with α = 0.05, 229. Table 16.8 Case and Morgan design (ETSL) with α = 0.05, 230. Table 16.9 Simon, Wittes and Ellenberg design, 231. Table 16.10 Bryant and Day design, 233. 17 Sample size software , 235. Cumulative references, 237. Index, 247