Statistical Monitoring of Clinical Trials,9780387300597

Statistical Monitoring of Clinical Trials

by ; ;
Edition: 1st
ISBN13: 9780387300597
ISBN10: 0387300597
Format: Hardcover
Pub. Date: 2006-08-03
Publisher(s): Springer Verlag
List Price: $149.99

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Summary

The approach taken in this book is to studies monitored over time, what the Central Limit Theorem is to studies with only one analysis. Just as the Central Limit Theorem shows that test statistics involving very different types of clinical trial outcomes are asymptotically normal, this book shows that the joint distribution of the test statistics at different analysis times is asymptotically multivariate normal with the correlation structure of Brownian motion ("the B-value") irrespective of the test statistic. The so-called B-value approach to monitoring allows us to use, for different types of trials, the same boundaries and the same simple formula for computing conditional power. Although Brownian motion may sound complicated, the authors make the approach easy by starting with a simple example and building on it, one piece at a time, ultimately showing that Brownian motion works for many different types of clinical trials. The book will be very valuable to statisticians involved in clinical trials. The main body of the chapters is accessible to anyone with knowledge of a standard mathematical statistics text. More mathematically advanced readers will find rigorous developments in appendices at the end of chapters. Reading the book will develop insight into not only monitoring, but power, survival analysis, safety, and other statistical issues germane to clinical trials.Michael Proschan, Gordon Lan, and Janet Wittes are elected Fellows of the American Statistical Association. All have spent formative years in the Biostatistics Research Branch of the National Heart, Lung, and Blood Institute (NHLBI/NIH). While there, they were intimately involved in the design and statistical monitoring of large-scale randomized clinical trials, developing methodology to aid in their monitoring. For example, Lan developed, with DeMets, the now widely-used spending function approach to group sequential designs, whose properties were further investigated by Proschan. The B-value approach used in the book was introduced in a very influential paper by Lan and Wittes. The statistical theory behind conditional power was developed by Lan, along with Simon and Halperin, and was the cornerstone for the conditional error approach to adaptive clinical trials introduced by Proschan and Hunsberger. All three authors have expertise in adaptive methodology for clinical trials.Michael Proschan is a Mathematical Statistician at the National Institutes of Health; Gordon Lan is Senior Director of Biometrics at Johnson & Johnson Pharmaceutical Research and Development, L.L.C.; Janet Wittes is President of Statistics Collaborative, a statistical consulting company she founded in 1990.

Author Biography

Janet Wittes is President of Statistics Collaborative, a statistical consulting company she founded in 1990. Gordon Lan is Senior Director of Biometrics at Johnson & Johnson Pharmaceutical Research & Development, L.L.C.

Table of Contents

1 Introduction
1(8)
2 A General Framework
9(34)
2.1 Hypothesis Testing: The Null Distribution of Test Statistics Over Time
10(8)
2.1.1 Continuous Outcomes
10(4)
2.1.2 Dichotomous Outcomes
14(1)
2.1.3 Survival Outcomes
15(2)
2.1.4 Summary of Sums
17(1)
2.2 An Estimation Perspective
18(3)
2.2.1 Information
18(3)
2.2.2 Summary of Treatment Effect Estimators
21(1)
2.3 Connection Between Estimators, Sums, Z-Scores, and Brownian Motion
21(3)
2.4 Maximum Likelihood Estimation
24(4)
2.5 Other Settings Leading to E-Processes and Brownian Motion
28(2)
2.5.1 Minimum Variance Unbiased Estimators
28(1)
2.5.2 Complete Sufficient Statistics
29(1)
2.6 The Normal Linear and Mixed Models
30(6)
2.6.1 The Linear Model
30(1)
2.6.2 The Mixed Model
31(5)
2.7 When Is Brownian Motion Not Appropriate?
36(2)
2.8 Summary
38(1)
2.9 Appendix
39(4)
2.9.1 Asymptotic Validity of Using Estimated Standard Errors
39(1)
2.9.2 Proof of Result 2.1
40(1)
2.9.3 Proof that for the Logrank Test, Di = Oi — Ei Are Uncorrelated Under H0
41(1)
2.9.4 A Rigorous Justification of Brownian Motion with Drift: Local Alternatives
41(1)
2.9.5 Basu's Theorem
42(1)
3 Power: Conditional, Unconditional, and Predictive
43(24)
3.1 Unconditional Power
43(2)
3.2 Conditional Power for Futility
45(8)
3.3 Varied Uses of Conditional Power
53(4)
3.4 Properties of Conditional Power
57(3)
3.5 A Bayesian Alternative: Predictive Power
60(3)
3.6 Summary
63(1)
3.7 Appendix
64(3)
3.7.1 Proof of Result 3.1
64(1)
3.7.2 Formula for corr{Β(t), Θ} and var{Θ|Β(t) = b}
65(1)
3.7.3 Simplification of Formula (3.8)
66(1)
4 Historical Monitoring Boundaries
67(14)
4.1 How Bad Can the Naive Approach Be?
67(2)
4.2 The Pocock Procedure
69(1)
4.3 The Haybittle Procedure and Variants
69(2)
4.4 The O'Brien-Fleming Procedure
71(1)
4.5 A Comparison of the Pocock and O'Brien-Fleming Boundaries
72(3)
4.6 Effect of Monitoring on Power
75(2)
4.7 Appendix: Computation of Boundaries Using Numerical Integration
77(4)
5 Spending Functions
81(18)
5.1 Upper Boundaries
81(9)
5.1.1 Using a Different Time Scale for Spending
87(2)
5.1.2 Data-Driven Looks
89(1)
5.2 Upper and Lower Boundaries
90(2)
5.3 Summary
92(1)
5.4 Appendix
92(7)
5.4.1 Proof of Result 5.1
92(1)
5.4.2 Proof of Result 5.2
93(1)
5.4.3 An S-Plus or R. Program to Compute Boundaries
93(6)
6 Practical Survival Monitoring
99(14)
6.1 Introduction
99(1)
6.2 Survival Trials with Staggered Entry
99(2)
6.3 Stochastic Process Formulation and Linear Trends
101(1)
6.4 A Real Example
102(1)
6.5 Nonlinear Trends of the Statistics: Analogy with Monitoring a t-Test
103(1)
6.6 Considerations for Early Termination
104(1)
6.7 The Information Fraction with Survival Data
105(8)
7 Inference Following a Group-Sequential Trial
113(24)
7.1 Likelihood, Sufficiency, and (Lack of) Completeness
113(3)
7.2 One-Tailed p-Values
116(9)
7.2.1 Definitions of a p-Value
116(6)
7.2.2 Stagewise Ordering
122(2)
7.2.3 Two-Tailed p-Values
124(1)
7.3 Properties of p-Values
125(1)
7.4 Confidence Intervals
126(5)
7.5 Estimation
131(4)
7.6 Summary
135(1)
7.7 Appendix: Proof that B(τ)/τ Overestimates Θ in the One-Tailed Setting
135(2)
8 Options When Brownian Motion Does Not Hold
137(18)
8.1 Small Sample Sizes
137(6)
8.2 Permutation Tests
143(6)
8.2.1 Continuous Outcomes
143(2)
8.2.2 Binary Outcomes
145(4)
8.3 The Bonferroni Method
149(1)
8.4 Summary
150(1)
8.5 Appendix
151(4)
8.5.1 Simulating the Distribution of t-Statistics Over Information Time
151(1)
8.5.2 The Noncentral Hypergeometric Distribution
152(3)
9 Monitoring for Safety
155(20)
9.1 Example: Inference from a Sample Size of One
155(1)
9.2 Example: Inference from Multiple Endpoints
156(1)
9.3 General Considerations
157(3)
9.4 What Safety Data Look Like
160(3)
9.5 Looking for a Single Adverse Event
163(9)
9.5.1 Monitoring for the Flip-Side of the Efficacy Endpoint
164(3)
9.5.2 Monitoring for Unexpected Serious Adverse Events that Would Stop a Study
167(2)
9.5.3 Monitoring for Adverse Events that the DSMB Should Report
169(3)
9.6 Looking for Multiple Adverse Events
172(1)
9.7 Summary
173(2)
10 Bayesian Monitoring 175(10)
10.1 Introduction
175(1)
10.2 The Bayesian Paradigm Applied to B-Values
176(1)
10.3 The Need for a Skeptical Prior
177(3)
10.4 A Comparison of Bayesian and Frequentist Boundaries
180(2)
10.5 Example
182(2)
10.6 Summary
184(1)
11 Adaptive Sample Size Methods 185(28)
11.1 Introduction
185(1)
11.2 Methods Using Nuisance Parameter Estimates: The Continuous Outcome Case
186(13)
11.2.1 Stein's Method
187(4)
11.2.2 The Naive t-Test
191(1)
11.2.3 A Restricted t-Test
192(1)
11.2.4 Variance Shmariance?
193(2)
11.2.5 Incorporating Monitoring
195(2)
11.2.6 Blinded Sample Size Reassessment
197(2)
11.3 Methods Using Nuisance Parameter Estimates: The Binary Outcome Case
199(4)
11.3.1 Blinded Sample Size Reassessment
201(2)
11.4 Adaptive Methods Based on the Treatment Effect
203(7)
11.4.1 Methods
203(6)
11.4.2 Pros and Cons
209(1)
11.5 Summary
210(3)
12 Topics Not Covered 213(8)
12.1 Introduction
213(1)
12.2 Continuous Sequential Boundaries
214(1)
12.3 Other Types of Group-Sequential Boundaries
215(1)
12.4 Reverse Stochastic Curtailing
216(1)
12.5 Monitoring Studies with More Than Two Arms
217(1)
12.6 Monitoring for Equivalence and Noninferiority
218(1)
12.7 Repeated Confidence Intervals
218(3)
13 Appendix I: The Logrank and Related Tests 221(18)
13.1 Hazard Functions
222(3)
13.2 Linear Rank Statistics
225(6)
13.2.1 Complete Survival Times: Which Group Is Better?
226(1)
13.2.2 Ratings, Score Functions, and Payments
227(4)
13.3 Payment Functions and Score Functions
231(2)
13.4 Censored Survival Data
233(1)
13.5 The U-Statistic Approach to the Wilcoxon Statistic
234(1)
13.6 The Logrank and Weighted Mantel-Haenszel Statistics
235(2)
13.7 Monitoring Survival Trials
237(2)
14 Appendix II: Group-Sequential Software 239(8)
14.1 Introduction
239(1)
14.2 Before the Trial Begins: Power and Sample Size
239(2)
14.3 During the Trial: Computation of Boundaries
241(1)
14.3.1 A Note on Upper and Lower Boundaries
242(1)
14.4 After the Trial: p-Value, Parameter Estimate, and Confidence Interval
242(2)
14.5 Other Features of the Program
244(3)
References 247(8)
Index 255

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