ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

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TABLE OF CONTENTS ST 520, A. Tsiatis and D. Zhang Contents 1 Introduction 1 1.1 Scope and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Brief Introduction to Epidemiology . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Brief Introduction and History of Clinical Trials . . . . . . . . . . . . . . . . . . . 12 2 Phase I and II clinical trials 18 2.1 Phases of Clinical Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Phase II clinical trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 Statistical Issues and Methods . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.2 Gehan’s Two-Stage Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.3 Simon’s Two-Stage Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3 Phase III Clinical Trials 35 3.1 Why are clinical trials needed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Issues to consider before designing a clinical trial . . . . . . . . . . . . . . . . . . 36 3.3 Ethical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 The Randomized Clinical Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Review of Conditional Expectation and Conditional Variance . . . . . . . . . . . . 43 4 Randomization 49 4.1 Design-based Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Fixed Allocation Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.1 Simple Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.2 Permuted block randomization . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.3 Stratified Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Adaptive Randomization Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3.1 Efron biased coin design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3.2 Urn Model (L.J. Wei) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3.3 Minimization Method of Pocock and Simon . . . . . . . . . . . . . . . . . 67 i
TABLE OF CONTENTS ST 520, A. Tsiatis and D. Zhang 4.4 Response Adaptive Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.5 Mechanics of Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5 Some Additional Issues in Phase III Clinical Trials 74 5.1 Blinding and Placebos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3 The Protocol Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6 Sample Size Calculations 81 6.1 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Deriving sample size to achieve desired power . . . . . . . . . . . . . . . . . . . . 87 6.3 Comparing two response rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.3.1 Arcsin square root transformation . . . . . . . . . . . . . . . . . . . . . . . 92 7 Comparing More Than Two Treatments 96 7.1 Testing equality using independent normally distributed estimators . . . . . . . . 97 7.2 Testing equality of dichotomous response rates . . . . . . . . . . . . . . . . . . . . 98 7.3 Multiple comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7.4 K-sample tests for continuous response . . . . . . . . . . . . . . . . . . . . . . . . 109 7.5 Sample size computations for continuous response . . . . . . . . . . . . . . . . . . 112 7.6 Equivalency Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8 Causality, Non-compliance and Intent-to-treat 118 8.1 Causality and Counterfactual Random Variables . . . . . . . . . . . . . . . . . . . 118 8.2 Noncompliance and Intent-to-treat analysis . . . . . . . . . . . . . . . . . . . . . . 122 8.3 A Causal Model with Noncompliance . . . . . . . . . . . . . . . . . . . . . . . . . 124 9 Survival Analysis in Phase III Clinical Trials 131 9.1 Describing the Distribution of Time to Event . . . . . . . . . . . . . . . . . . . . . 132 9.2 Censoring and Life-Table Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 136 9.3 Kaplan-Meier or Product-Limit Estimator . . . . . . . . . . . . . . . . . . . . . . 140 ii
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