Scientific Inference in Clinical Trials with R

책 소개

Statistical analysis in clinical trials determines which conclusions the available data support.

This book is intended for readers who design trials, analyze their data, and explain the

resulting inferences to colleagues, review committees, and regulators.

The examples work through calculations that statistical software usually performs internally.

A p value is obtained using matrix algebra, maximum likelihood or numerical

optimization, then checked against the package result. Design matrices are written out and

their estimable functions identified. Likelihoods are profiled to examine their shape. The

objective function of a nonlinear mixed-effects model is evaluated step by step and compared

with the output from NONMEM®. These calculations help readers interpret a procedure’s

results and investigate unexpected output.

The book is organized around three principles.

• Inference. Frequentist, likelihood and Bayesian approaches are compared using the same

data. The ECMO trials illustrate the ethical consequences of the choice of inferential

framework.

• Reproducible calculations. The R code printed in the text is available in the repository

(https://github.com/AMC-CPT/CTDA). The console output and figures were generated by

running that code, allowing readers to reproduce the calculations.

• Regulatory reasoning. ICH E9(R1)’s estimand framework, two-stage sequential designs

for bioequivalence, alpha-spending in group sequential trials and adaptive early-phase

designs are explained through the scientific questions they address.

The final chapter draws on my twenty-five years of reviewing protocols for an institutional

review board. It follows a statistical review from the initial questions through the response

to an inadequate answer. Readers who review protocols may find it useful to begin there.

Each chapter ends with computational exercises and discussion questions for seminars.

The discussion questions invite reasoned judgments and need not have a single answer. A

solutions manual is available to instructors on request.

The intended readers are graduate students and researchers in clinical pharmacology,

biostatistics and regulatory science, and clinicians who must read quantitative evidence critically.

Calculus, elementary probability and a minimal familiarity with R are enough to

begin. The installation of R and its basic syntax are summarized in Appendices A and B.

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목차

Preface .............................................................................. iii

1 Drug Development and Clinical Trials ................................................. 1

1.1 The course of drug development ................................................. 2

1.2 The phases of clinical trials .................................................. 5

1.3 Regulation and standards: the ICH framework .................................... 6

1.4 What a clinical trial is, and why it matters ................................... 7

1.5 Three requirements of a good trial: science, ethics, credibility ............... 9

1.6 The core vocabulary of design and analysis .................................... 10

1.7 The structure of development decisions ........................................ 14

1.8 Interpretation of Quantitative Evidence ....................................... 19

1.9 Portfolio arithmetic: the economics of go/no-go ............................... 25

1.10 Recognizing and communicating risk ........................................... 29

1.11 The viewpoint and plan of this book .......................................... 32

1.12 Summary ...................................................................... 33

Exercises ......................................................................... 33

Discussion questions .............................................................. 34

Further reading ................................................................... 35

References ........................................................................ 36

2 Quantitative Decision Making under Uncertainty ...................................... 39

2.1 Introduction: the probabilistic nature of drug development .................... 40

2.2 Distinguishing observation from inference ..................................... 41

2.3 What evidence requires ........................................................ 51

2.4 Effect size, uncertainty, and the value of information ........................ 58

2.5 Tools for quantitative decision making ........................................ 60

2.6 Summary ....................................................................... 63

Exercises ......................................................................... 65

Discussion questions .............................................................. 66

Further reading ................................................................... 67

References ........................................................................ 67

3 Analysis of a Single Variable ....................................................... 69

3.1 Continuous variables .......................................................... 69

3.2 Categorical variables ......................................................... 77

3.3 Time variables ................................................................ 82

3.4 Summary ....................................................................... 84

Exercises ......................................................................... 84

Discussion questions .............................................................. 86

4 Probability ......................................................................... 87

4.1 The definition of probability ................................................. 87

4.2 Conditional probability ....................................................... 88

4.3 Complementary events .......................................................... 88

4.4 Bertrand's paradox ............................................................ 89

4.5 Gambler's ruin ................................................................ 94

4.6 Collecting baseball cards ..................................................... 95

4.7 The Monty Hall problem ........................................................ 96

4.8 The forest fire problem ....................................................... 97

4.9 Summary ....................................................................... 99

Exercises ......................................................................... 99

Discussion questions .............................................................. 99

5 Random Variables ................................................................... 101

5.1 Basic terminology ............................................................ 101

5.2 Expectation .................................................................. 102

5.3 Variance ..................................................................... 102

5.4 Skewness and kurtosis ........................................................ 103

5.5 Joint distributions .......................................................... 104

5.6 Marginal distributions ....................................................... 104

5.7 Conditional distributions .................................................... 105

5.8 Covariance and correlation ................................................... 105

5.9 Independence of two random variables ......................................... 105

5.10 Expectation and variance of a sum ........................................... 106

5.11 The density of a linearly transformed variable .............................. 106

5.12 Expectation and variance of a product ....................................... 107

5.13 Likelihood .................................................................. 107

5.14 Checking it in R ............................................................ 107

5.15 Summary ..................................................................... 108

Exercises ........................................................................ 109

Discussion questions ............................................................. 109

6 Probability Distributions .......................................................... 111

6.1 Discrete distributions .......................................................

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