Sample Sizes for Clinical Trials

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ISBN: 9781584887393 | 1584887397
Cover: Hardcover
Copyright: 8/26/2009

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With worked examples and problems based on real-world scenarios, this book takes readers through the process of calculating the sample size for many types of clinical trials. It covers the most common types of clinical trials across all phases. The author discusses how assumptions made in a sample size calculation can impact the calculation. He provides calculations for many of the trials and offers hints and tips on how to optimize the calculations. He also illustrates the steps involved in determining sample size, from defining the trial objective to selecting an appropriate endpoint.

Preface	p. xvii
List of Figures	p. xix
List of Tables	p. xxi
Introduction	p. 1
Background to Randomised Controlled Trials	p. 1
Types of Clinical Trial	p. 2
Assessing Evidence from Trials	p. 3
The Normal Distribution	p. 3
The Central Limit Theorem	p. 3
Frequentist Approaches	p. 5
Hypothesis Testing and Estimation	p. 6
Hypothesis Testing: Superiority Trials	p. 6
Statistical and Clinical Significance or Importance	p. 10
Superiority Trials	p. 11
Equivalence Trials	p. 13
General Case	p. 15
Special Case of No Treatment Difference	p. 16
Non-inferiority Trials	p. 16
As-Good-as-or-Better Trials	p. 18
A Test of Non-inferiority and One-Sided Test of Superiority	p. 18
A Test of Non-inferiority and Two-Sided Test of Superiority	p. 19
Assessment of Bioequivalence	p. 20
Justification for Log Transformation	p. 23
Rationale for Using Coefficients of Variation	p. 23
Individual and Population Bioequivalence	p. 24
Estimation to a Given Precision	p. 24
Seven Key Steps to Cook Up a Sample Size	p. 27
Introduction	p. 27
Step 1: Deciding on the Trial Objective	p. 27
Step 2: Deciding on the Endpoint	p. 28
Step 3: Determining the Effect Size (or Margin)	p. 28
Obtaining an Estimate of the Treatment Effects	p. 28
Worked Example with a Binary Endpoint	p. 30
Worked Example with Normal Endpoint	p. 30
Point Estimate	p. 32
Choice of Equivalence or Non-inferiority Limit	p. 33
Step 4: Assessing the Population Variability	p. 34
Binary Data	p. 35
Worked Example of a Variable Control Response with Binary Data	p. 35
Normal Data	p. 36
Worked Example of Assessing Population Differences with Normal Data	p. 37
Step 5: Type I Error	p. 40
Superiority Trials	p. 41
Non-Inferiority and Equivalence Trials	p. 41
Step 6: Type II Error	p. 42
Step 7: Other Factors	p. 43
Sample Sizes for Parallel Group Superiority Trials with Normal Data	p. 45
Introduction	p. 45
Sample Sizes Estimated Assuming the Population Variance to Be Known	p. 45
Worked Example 3.1	p. 49
Initial Wrong Calculation	p. 50
Correct Calculations	p. 51
Accounting for Dropout	p. 52
Worked Example 3.2	p. 53
Design Considerations	p. 53
Inclusion of Baselines or Covariates	p. 53
Post-dose Measures Summarised by Summary Statistics	p. 55
Inclusion of Baseline or Covariates as Well as Post-dose Measures Summarised by Summary Statistics	p. 56
Revisiting Worked Example 3.1	p. 57
Reinvestigating the Type II Error	p. 58
Sensitivity Analysis	p. 59
Worked Example 3.3	p. 60
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 61
Worked Example 3.4	p. 63
Interim Analyses and Sample Size Re-estimation	p. 63
Interim Analyses	p. 64
Worked Example 3.5	p. 64
Sample Size Re-estimation	p. 67
Cluster Randomised Trials	p. 69
Quantifying the Effect of Clustering	p. 70
Sample Size Requirements for Cluster-Randomised Designs	p. 71
Sample Size Calculations for Superiority Cross-over Trials with Normal Data	p. 73
Introduction	p. 73
Sample Sizes Estimated Assuming the Population Variance to Be Known	p. 73
Analysis of Variance	p. 73
Paired t-tests	p. 74
Period-Adjusted t-tests	p. 74
Summary of Statistical Analysis Approaches	p. 75
Sample Size Calculations	p. 75
Worked Example 4.1	p. 77
Worked Example 4.2	p. 78
Worked Example 4.3	p. 79
Sensitivity Analysis about the Variance Used in the Sample Size Calculations	p. 80
Worked Example 4.4	p. 80
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 80
Sample Size Calculations for Equivalence Clinical Trials with Normal Data	p. 83
Introduction	p. 83
Parallel Group Trials	p. 83
Sample Sizes Estimated Assuming the Population Variance to Be Known	p. 83
General Case	p. 83
Special Case of No Treatment Difference	p. 85
Worked Example 5.1	p. 87
Worked Example 5.2	p. 87
Sensitivity Analysis about the Variance Used in the Sample Size Calculations	p. 87
Worked Example 5.3	p. 88
Calculations Taking Account of the Imprecision of the Variances Used in the Sample Size Calculations	p. 88
General Case	p. 88
Special Case of No Treatment Difference	p. 89
Cross-over Trials	p. 90
Sample Size Estimated Assuming the Population Variance to Be Known	p. 91
General Case	p. 91
Special Case of No Treatment Difference	p. 92
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 92
General Case	p. 92
Special Case of No Treatment Difference	p. 94
Sample Size Calculations for Non-Inferiority Clinical Trials with Normal Data	p. 95
Introduction	p. 95
Parallel Group Trials	p. 95
Sample Size Estimated Assuming the Population Variance to Be Known	p. 95
Non-inferiority versus Superiority Trials	p. 97
Worked Example 6.1	p. 99
Sensitivity Analysis about the Mean Difference Used in the Sample Size Calculations	p. 100
Worked Example 6.2	p. 101
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 101
Cross-over Trials	p. 102
Sample Size Estimated Assuming the Population Variance to Be Known	p. 102
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 103
As-Good-as-or-Better Trials	p. 105
Worked Example 6.3	p. 106
Sample Size Calculations for Bioequivalence Trials	p. 107
Introduction	p. 107
Cross-over Trials	p. 107
Sample Sizes Estimated Assuming the Population Variance to Be Known	p. 107
General Case	p. 107
Special Case of the Mean Ratio Equalling Unity	p. 108
Replicate Designs	p. 109
Worked Example 7.1	p. 112
Sensitivity Analysis about the Variance Used in the Sample Size Calculations	p. 113
Worked Example 7.2	p. 113
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 114
General Case	p. 114
Special Case of the Mean Ratio Equalling Unity	p. 115
Parallel Group Studies	p. 116
Sample Size Estimated Assuming the Population Variance to Be Known	p. 116
General Case	p. 116
Special Case of the Ratio Equalling Unity	p. 117
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 118
General Case	p. 118
Special Case of the Mean Ratio Equalling Unity	p. 121
Sample Size Calculations for Precision-Based Clinical Trials with Normal Data	p. 123
Introduction	p. 123
Parallel Group Trials	p. 124
Sample Size Estimated Assuming the Population Variance to Be Known	p. 124
Worked Example 8.1: Standard Results	p. 125
Worked Example 8.2: Using Results from Superiority Trials	p. 125
Worked Example 8.3: Sample Size Is Based on Feasibility	p. 126
Sensitivity Analysis about the Variance Used in the Sample Size Calculations	p. 127
Worked Example 8.4	p. 127
Accounting for the Imprecision of the Variance in the Future Trial	p. 127
Worked Example 8.5: Accounting for the Imprecision in the Variance in the Future Trial	p. 128
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 128
Worked Example 8.6: Accounting for the Imprecision in the Variance of the Variance Used in Calculations	p. 130
Allowing for the Imprecision in the Variance Used in the Sample Size Calculations and in Future Trials	p. 131
Worked Example 8.7: Allowing for the Imprecision in the Variance Used in the Sample Size Calculations and in Future Trials	p. 131
Cross-over Trials	p. 133
Sample Size Estimated Assuming the Population Variance to Be Known	p. 133
Sensitivity Analysis about the Variance Used in the Sample Size Calculations	p. 133
Accounting for the Imprecision of the Variance in the Future Trial	p. 134
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 134
Allowing for the Imprecision in the Variance Used in the Sample Size Calculations and in Future Trials	p. 136
Sample Size Calculations for Parallel Group Superiority Clinical Trials with Binary Data	p. 139
Introduction	p. 139
Inference and Analysis of Clinical Trials with Binary Data	p. 139
&pi's or p's	p. 140
Absolute Risk Difference	p. 141
Calculation of Confidence Intervals	p. 141
Normal Approximation	p. 141
Normal Approximation with Continuity Correction	p. 141
Exact Confidence Intervals	p. 142
Odds Ratio	p. 142
Calculation of Confidence Intervals	p. 143
Sample Sizes with the Population Effects Assumed Known	p. 144
Odds Ratio	p. 144
Absolute Risk Difference	p. 145
Method 1: Using the Anticipated Responses	p. 146
Method 2: Using the Responses under the Null and Alternative Hypotheses	p. 148
Accounting for Continuity Correction	p. 149
Equating Odds Ratios with Absolute Risks	p. 151
Equating Odds Ratios with Absolute Risks: Revisited	p. 152
Worked Example 9.1	p. 153
Worked Example 9.2	p. 154
Worked Example 9.3	p. 154
Inclusion of Baselines or Covariates	p. 155
Sample Size Re-estimation	p. 156
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 157
Worked Example 9.4	p. 157
Worked Example 9.5	p. 158
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations	p. 159
Odds Ratio	p. 160
Absolute Risk Difference	p. 160
Worked Example 9.6	p. 161
Calculations Taking Account of the Imprecision of the Estimates Used in the Sample Size Calculations: Bayesian Methods	p. 161
Prior Response	p. 162
Anticipated Response	p. 163
Posterior Response	p. 163
Worked Example 9.7	p. 163
Non-informative	p. 163
Sceptical Prior	p. 164
Optimistic	p. 164
Sample Size Calculations for Superiority Cross-over Clinical Trials with Binary Data	p. 167
Introduction	p. 167
Analysis of a Trial	p. 167
Sample Size Estimation with the Population Effects Assumed Known	p. 168
Worked Example 10.1	p. 170
Worked Example 10.2	p. 170
Comparison of Cross-over and Parallel Group Results	p. 171
Worked Example 10.3	p. 172
Worked Example 10.4	p. 173
Analysis of a Trial Revisited	p. 174
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 176
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations	p. 176
Calculations Taking Account of the Imprecision of the Estimates Used in the Sample Size Calculations: Bayesian Methods	p. 177
Sample Size Calculations for Non-inferiority Trials with Binary Data	p. 179
Introduction	p. 179
Choice of Non-inferiority Limit	p. 180
Parallel Group Trials Sample Size with the Population Effects Assumed Known	p. 182
Absolute Risk Difference	p. 182
Method 1: Using Anticipated Responses	p. 183
Method 2: Using Anticipated Responses in Conjunction with the Non-inferiority Limit	p. 183
Method 3: Using Maximum Likelihood Estimates	p. 184
Comparison of the Three Methods of Sample Size Estimation	p. 184
Odds Ratio	p. 184
Worked Example 11.1	p. 186
Superiority Trials Revisited	p. 187
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 187
Worked Example 11.2	p. 189
Absolute Risk Difference versus Odds Ratios Revisited	p. 190
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations	p. 190
Worked Example 11.3	p. 191
Calculations Taking Account of the Imprecision of the Estimates Used in the Calculation of Sample Sizes: Bayesian Methods	p. 191
Worked Example 11.4	p. 192
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects with Respect to the Assumptions about the Mean Difference and the Variance Used in the Sample Size Calculations	p. 192
Worked Example 11.5	p. 195
Calculations That Take Account of the Imprecision of the Estimate Effects with Respect to the Assumptions about the Mean Difference and the Variance Used in the Sample Size Calculations: Bayesian Methods	p. 195
Worked Example 11.6	p. 195
Cross-over Trials	p. 195
As-Good-as-or-Better Trials	p. 196
Sample Size Calculations for Equivalence Trials with Binary Data	p. 197
Introduction	p. 197
Parallel Group Trials	p. 197
Sample Sizes with the Population Effects Assumed Known: General Case	p. 197
Absolute Risk Difference	p. 197
Odds Ratio	p. 199
Sample Sizes with the Population Effects Assumed Known: No Treatment Difference	p. 200
Absolute Risk Difference	p. 201
Odds Ratio	p. 202
Worked Example 12.1	p. 203
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 203
Worked Example 12.2	p. 203
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations	p. 203
Worked Example 12.3	p. 205
Calculations That Take Account of the Imprecision in the Estimates of the Effects Used in the Sample Size Calculations: Bayesian Methods	p. 205
Worked Example 12.4	p. 206
Calculations Taking Account of the Imprecision of the Population Effects with Respect to the Assumptions about the Mean Difference and the Variance Used in the Sample Size Calculations	p. 206
Worked Example 12.5	p. 208
Calculations That Take Account of the Imprecision of the Population Effects with Respect to the Assumptions about the Mean Difference and the Variance Used in the Sample Size Calculations: Bayesian Methods	p. 208
Worked Example 12.6	p. 208
Cross-over Trials	p. 208
Sample Size Calculations for Precision-Based Trials with Binary Data	p. 209
Introduction	p. 209
Parallel Group Trials	p. 209
Absolute Risk Difference	p. 209
Odds Ratio	p. 211
Equating Odds Ratios with Proportions	p. 211
Worked Example 13.1	p. 213
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 213
Worked Example 13.2	p. 214
Cross-over Trials	p. 214
Sample Size Calculations for Clinical Trials with Ordinal Data	p. 215
Introduction	p. 215
The Quality-of-Life Data	p. 216
Superiority Trials	p. 217
Parallel Group Trials	p. 217
Sample Sizes That Are Estimated Assuming That the Population Effects Are Known	p. 217
Whitehead's Method	p. 217
Noether's Method	p. 223
Comparison of Methods	p. 226
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 226
Worked Example 14.8: Full Ordinal Scale	p. 228
Worked Example 14.9: Four-Point Scale	p. 229
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations	p. 230
Worked Example 14.10: Full Ordinal Scale	p. 230
Worked Example 14.11: Four-Point Scale	p. 231
Cross-over Trials	p. 232
Sample Sizes That Are Estimated Assuming That the Population Effects Are Known	p. 232
Worked Example 14.12: Full Ordinal Scale	p. 233
Worked Example 14.13: Applying Parallel Group Methodology	p. 234
Worked Example 14.14: Applying Binary Methodology	p. 234
Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations	p. 235
Worked Example 14.15	p. 235
Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations	p. 235
Worked Example 14.16	p. 235
Non-inferiority Trials	p. 236
Parallel Group Trials	p. 237
Sample Sizes That Are Estimated Assuming That the Population Effects Are Known	p. 237
Sensitivity Analysis about the Variance That Is Used in the Sample Size Calculations	p. 238
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 238
Cross-over Trials	p. 238
Sample Sizes That Are Estimated Assuming That the Population Effects Are Known	p. 238
Sensitivity Analysis About the Variance That Is Used in the Sample Size Calculations	p. 239
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 239
As-Good-as-or-Better Trials	p. 239
Equivalence Trials	p. 239
Parallel Group Trials	p. 240
Sample Sizes That Are Estimated Assuming That the Population Variance Is Known	p. 240
Sensitivity Analysis about the Variance That Is Used in the Sample Size Calculations	p. 240
Calculations Taking Account of the Imprecision of the Variances Used in the Sample Size Calculations	p. 241
Cross-over Trials	p. 241
Sample Sizes That Are Estimated Assuming That the Population Variance Is Known	p. 241
Sensitivity Analysis about the Variance that is Used in the Sample Size Calculations	p. 242
Calculations Taking Account of the Imprecision of the Variances Used in the Sample Size Calculations	p. 242
Estimation to a Given Precision	p. 243
Parallel Group Trials	p. 243
Sample Sizes That Are Estimated Assuming That the Population Variance Is Known	p. 243
Worked Example 14.17	p. 243
Sensitivity Analysis about the Variance That Is Used in the Sample Size Calculations	p. 244
Worked Example 14.18	p. 244
Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations	p. 244
Worked Example 14.19	p. 244
Cross-over Trials	p. 244
Sample Size Calculations for Clinical Trials with Survival Data	p. 247
Introduction	p. 247
Superiority Trials	p. 248
Primary Endpoint Is Negative	p. 248
Sample Size Calculations: Number of Events	p. 249
Worked Example 15.1	p. 251
Sample Size Calculations: Total Number of Subjects	p. 252
Loss to Follow-up	p. 252
Worked Example 15.2	p. 252
Total Sample Size Revisited	p. 253
Worked Example 15.3: Uniform Recruitment	p. 256
Worked Example 15.4: Truncated Exponential Recruitment	p. 257
Worked Example 15.5: Uniform and Truncated Exponential Recruitment Revisited	p. 258
Comment on the Results	p. 260
Primary Endpoint Is Positive	p. 260
Sample Size Calculations: Number of Events and Total Sample Size	p. 262
Worked Example 15.6: Noether Approach	p. 262
Worked Example 15.7: Normal Approach	p. 263
Non-inferiority Trials	p. 264
If Primary Endpoint Is Negative	p. 264
If Primary Endpoint Is Positive	p. 266
Equivalence Trials	p. 266
If Primary Endpoint Is Negative	p. 266
Precision Trials	p. 267
If Primary Endpoint Is Negative	p. 267
References	p. 269
Bibliography	p. 277
Appendix	p. 285
Index	p. 291
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Sample Sizes for Clinical Trials

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