Medical Statistics: Clinical Trials

1 Medical Statistics: Clinical Trials Nick Fieller Clinical Trials ; Contents NRJF, 1996 i Contents 0. Introduction .. 1 Books .. 1 Objectives .. 2 Organization of course material .. 3 A Note on R, S-PLUS and MINITAB .. 4 Data sets .. 5 R data sets .. 5 Data sets in other formats .. 6 R libraries required .. 6 Outline of Course .. 7 1. Background and Basic Concepts .. 9 Definition of Clinical Trial (from Pocock, 1983) .. 9 Historical Background .. 10 Field Trial of Salk Polio Vaccine .. 11 Types of Trial .. 14 Further notes: .. 15 Placebo Effect .. 18 Nocebo Effect .. 18 Blindness of Trials .. 18 Ethical Considerations .. 19 Publication Ethics.

2 21 Evidence-Based Medicine .. 22 The Bradford-Hill Criteria .. 22 Summary & Conclusions .. 24 Tasks 1 .. 25 2. Basic Trial 27 Comments on Tests .. 27 One-sided and two-sided tests .. 27 Separate and Pooled Variance t-tests .. 29 Test equality of variances? .. 31 Parallel Group Designs .. 33 In series designs .. 34 Crossover Design .. 36 Factorial Designs .. 39 Sequential Designs .. 41 Summary & 43 Tasks 2 .. 44 Clinical Trials ; Contents NRJF, 1996 ii 3. Randomization .. 47 Simple randomization .. 47 Restricted Randomization .. 50 Blocking .. 50 Unequal Allocation .. 52 Stratified Randomization .. 53 Minimization .. 55 Note: Minimization/Adaptive Randomization.

3 58 Why Randomize? .. 58 Historical/database controls .. 59 Randomization Software .. 60 Summary and Conclusions .. 61 Tasks 3 .. 62 Exercises 1 .. 64 4. Protocol Deviations .. 66 Protocol .. 66 Protocol deviations .. 67 Summary and Conclusions .. 73 5. Size of the trial .. 74 Introduction .. 74 Binary Data .. 76 Quantitative Data .. 81 One-Sample Tests .. 84 Practical problems .. 85 Computer 86 Implementation in R .. 86 Example: test of two proportions .. 87 Example: t-test of two means .. 87 Summary and Conclusions .. 88 Tasks 4 .. 90 Exercises 2 .. 94 6. Multiplicity and interim analysis .. 95 Introduction .. 95 Example: Signs of the Zodiac.

4 96 Multiplicity .. 99 Fundamentals .. 99 Bonferroni Corrections .. 101 Examples: .. 101 Multiple End-points .. 103 Clinical Trials ; Contents NRJF, 1996 iii Cautionary Examples .. 106 Subgroup analyses .. 107 Fundamentals .. 107 Example: Zodiac (Cont.) .. 109 More Cautionary Examples .. 112 Interim analyses .. 114 Fundamentals .. 114 Remedy: .. 115 Notes: .. 119 Further Notes: .. 121 Repeated Measures .. 122 Fundamentals .. 122 Miscellany .. 124 Regrouping .. 124 Multiple Regression .. 125 Example: shaving & risk of stroke .. 126 Summary and Conclusions .. 127 7. Crossover Trials .. 131 Introduction .. 131 Illustration of different types of effects.

5 132 Model .. 134 Carryover effect .. 136 Notes .. 138 Treatment & period effects .. 139 Treatment test .. 139 Period test .. 141 Analysis with Linear Models .. 142 Introduction .. 142 Fixed effects analysis .. 143 Random effects analysis .. 145 Deferment of example .. 145 Notes .. 146 Binary Responses .. 149 Example: (Senn, 2002) .. 149 Summary and Conclusions .. 152 Tasks 5 .. 154 Exercises 3 .. 156 Clinical Trials ; Contents NRJF, 1996 iv 8. Combining Trials .. 160 Small Trials .. 160 Pooling Trials and meta analysis .. 161 Mantel-Haenszel Test .. 163 Comments .. 164 Possible limitations of M-H test .. 165 Relative merits of M-H & Logistic Regression approaches.

6 165 Example: pooling Trials .. 166 Example of Mantel-Haenszel Test in R .. 170 Summary and Conclusions .. 172 Tasks 6 .. 173 9. Binary Response Data .. 175 Background .. 175 Observational Studies .. 175 Inroduction .. 175 Prospective Studies Relative Risks .. 176 Example .. 178 Retrospective Studies Odds Ratios .. 179 Example .. 180 Matched pairs .. 181 Introduction .. 181 McNemar s Test .. 182 Logistic Modelling .. 184 Introduction .. 184 Interpretation .. 186 Inference .. 187 Example (Pocock ) .. 189 Interactions .. 192 Combining Trials .. 193 Summary and Conclusions .. 194 Exercises 4 .. 195 Clinical Trials ; Contents NRJF, 1996 v 10.

7 Comparing Methods of Measurement .. 197 Introduction .. 197 Bland & Altman Plots .. 198 The Kappa Statistic for Categorical Variables .. 201 Examples .. 202 Two Categories .. 202 More than Two Categories .. 203 Further Modifications .. 204 Summary and Conclusions .. 205 Notes & Solutions for Tasks 1 .. 206 Notes & Solutions for Tasks 2 .. 208 Notes & Solutions for Tasks 3 .. 214 Notes & Solutions for Tasks 4 .. 222 Notes & Solutions for Tasks 5 .. 229 Notes & Solutions for Tasks 6 .. 236 Notes & Solutions for Exercises 240 Notes & Solutions for Exercises 245 Notes & Solutions for Exercises 247 Notes & Solutions for Exercises 253 Clinical Trials ; Introduction NRJF, 1996 1 Statistical Methods in Clinical Trials 0.

8 I n t ro d u ct i o n Books Altman, (1991) Practical Statistics for Medical Research. Chapman & Hall Andersen, B. (1990) Methodological Errors in Medical Research. Blackwell Armitage, P., Berry, G. & Matthews, (2002) Statistical Methods in Medical Research (4th Ed.). Blackwell. Bland, Martin (2000) An Introduction to Medical Statistics (3rd Ed). OUP. Campbell, M. J. & Swainscow, T. D. V. (2009) Statistics at Square One (11th Ed). Wiley-Blackwell Campbell, M. J. (2006) Statistics at Square Two (2nd Ed). Wiley-Blackwell Julious, S. A. (2010) Sample Sizes for Clinical Trials , CRC Press. Kirkwood, B. R. & Stone, (2003) Medical Statistics (2nd Ed).

9 Blackwell Campbell, M. J., Machin, D. & Walters, S. (2007) Medical Statistics: a textbook for the health sciences. (4th Ed.) Wiley Machin, D. & Campbell, M. J. (1997) Statistical Tables for the Design of Clinical Trials . (2nd Ed.) Wiley Matthews, J. N. S. (2006), An Introduction to Randomized Controlled Clinical Trials . (2nd Ed.) Chapman & Hall Pocock, S. J. (1983) Clinical Trials , A Practical Approach. Wiley Schumacher, Martin & Schulgen, Gabi (2002) Methodik Klinischer Studien. Springer. (In German) Senn, Stephen (2002) Cross-over Trials in Clinical Research. Wiley Senn, Stephen (2003) Dicing with Death: Chance, Risk & Health. CUP Clinical Trials ; Introduction NRJF, 1996 2 The two texts which are highlighted cover most of the Clinical Trials section of the Medical Statistics module; the first also has material relevant to the Survival Data Analysis section.

10 Indicates a book which goes considerably further than is required for this course (Chapter 5) but is also highly relevant for those taking the second semester course MAS6062 Further Clinical Trials . Indicates a book which contains much material that is relevant to this course but it is primarily a book about Medical Statistics and is strongly recommended to those planning to go for interviews for jobs in the biomedical areas (including the pharmaceutical industry) Objectives The objective of this book is to provide an introduction to some of the statistical methods and statistical issues that arise in Medical experiments which involve, in particular, human patients.