The Design and Analysis of Sequential Clinical Trials

by Whitehead, John

• ISBN13: 9780471975502
• ISBN10: 0471975508
• Edition: 2nd
• Format: Hardcover
• Copyright: 1997-08-04
• Publisher: Wiley

Summary

This book details all aspects of sequential clinical trials from preliminary planning, through the monitoring of the trial, to the final analysis of the results. Emphasis is placed on the triangular test and other procedures based on straight line stopping boundaries. These methods allow for frequent or occasional interim analyses and permit the analysis of a wide variety of patient responses. Alternative procedures are also covered in detail, and these include -spending function methods, repeated confidence intervals and Bayesian approaches to sequential clinical trials.

Author Biography

John Whitehead is the author of The Design and Analysis of Sequential Clinical Trials, Revised, 2nd Edition, published by Wiley.

Table of Contents

Preface	xi	(2)
Series Preface	xiii
1 Clinical Trials	1	(16)
1.1 Sequential experimentation	1	(1)
1.2 The rationale of clinical trials	2	(2)
1.3 Historically and prospectively controlled studies	4	(1)
1.4 Parallel group and crossover studies	5	(1)
1.5 General design features	6	(2)
1.6 Frequentist inference	8	(2)
1.7 Sample size criteria for fixed-sample designs	10	(1)
1.8 Sequential designs	11	(1)
1.9 An example of a sequential clinical trial, and the plan of this book	12	(4)
1.10 Bibliographic notes and further comments	16	(1)
2 Allocating Patients to Treatments	17	(12)
2.1 The purpose of allocation schemes	17	(1)
2.2 Stratification variables	18	(1)
2.3 Allocation schemes using a single categorization	19	(3)
2.4 Allocation schemes using several categorizations (minimization)	22	(1)
2.5 Modifications for allocation ratios other than 1	23	(1)
2.6* Allocation to more than two treatments	24	(2)
2.7 Bibliographic notes and further comments	26	(3)
3 Measurement of Treatment Difference	29	(40)
3.1 Measures of difference and of information	29	(2)
3.2 Binary responses	31	(3)
3.3 Poisson responses	34	(2)
3.4 Survival data	36	(5)
3.5 Interval-censored survival data	41	(4)
3.6 Ordinal responses	45	(3)
3.7 Normally distributed responses	48	(3)
3.8* The general form of the test statistics	51	(8)
3.8.1 The definition of Z and V	51	(1)
3.8.2 The derivation of Z and V	52	(2)
3.8.3 Comparative studies	54	(3)
3.8.4 A further example: comparison of Weibull survivor curves	57	(2)
3.9* Bibliographic notes and further comments	59	(10)
3.9.1 Relationship with fixed-sample likelihood ratio tests	59	(1)
3.9.2 Sequential t-tests	60	(1)
3.9.3 Relationships with other methods	61	(1)
3.9.4 The accuracy of the approximation to normality	62	(2)
3.9.5 Use of approximate forms for V	64	(5)
4 The Design of a Sequential Trial Using the Boundaries Approach	69	(66)
4.1 Introduction	69	(1)
4.2 Monitoring a clinical trial	70	(3)
4.3 Power requirements	73	(3)
4.4 The triangular test	76	(11)
4.5 The truncated sequential probability ratio test	87	(5)
4.6 The restricted procedure	92	(5)
4.7 The reverse triangular and double triangular tests	97	(4)
4.8 Some other sequential stopping boundaries	101	(2)
4.9 Other aspects of interim analysis	103	(1)
4.10* The theory of the open sequential probability ratio test	104	(10)
4.10.1 Assumptions, and a transformation	104	(2)
4.10.2 The power function C+	106	(1)
4.10.3 The moments of V*	107	(2)
4.10.4 The distribution function of V*	109	(5)
4.11* The theory of the triangular test	114	(5)
4.11.1 The continuation region	114	(1)
4.11.2 The distribution function of V*	115	(4)
4.12* The theory of the restricted procedure and the truncated sequential probability ratio test	119	(3)
4.13* The theory of the Christmas tree adjustment	122	(4)
4.14 Bibliographic notes and further comments	126	(9)
4.14.1 The development of sequential methods	126	(2)
4.14.2 Sample size reviews	128	(2)
4.14.3* An alternative view of the triangular test	130	(2)
4.14.4 The one-look triangular test	132	(3)
5 The Analysis of a Sequential Trial	135	(48)
5.1 Decision-making and inference	135	(1)
5.2 The P-value function	136	(4)
5.3 The case of continuous monitoring	140	(6)
5.4 The case of discrete monitoring	146	(5)
5.5 Underrunning and overrunning	151	(6)
5.6 The bias-adjusted maximum likelihood estimate	157	(2)
5.7 Estimation of absolute treatment effects	159	(3)
5.8 Analysis of secondary responses	162	(5)
5.9 The reliability of the terminal analysis	167	(5)
5.10 Bibliographic notes and further comments	172	(11)
5.10.1 Sequential estimation	172	(1)
5.10.2* Exact calculation of trial properties for discrete monitoring of Brownian motion	173	(4)
5.10.3* Alternative orderings of the sample space	177	(3)
5.10.4 Alternative methods of post-trial estimation	180	(3)
6 Alternative Approaches to the Design and Analysis of Sequential Clinical Trials	183	(30)
6.1 Repeated significance testing procedures	183	(3)
6.2 The XXX-spending function approach	186	(6)
6.3 Stochastic curtailment	192	(5)
6.4 Repeated confidence intervals	197	(5)
6.5 Bayesian approaches to sequential clinical trials	202	(11)
6.5.1 Bayesian inference	202	(2)
6.5.2 Bayesian decision theory	204	(4)
6.5.3 Pure Bayesian methods	208	(3)
6.5.4 Shrinkage of estimators	211	(1)
6.5.5 Predictive probability	211	(2)
7 Prognostic Factors	213	(40)
7.1 Introduction	213	(2)
7.2 Stratification	215	(4)
7.3 Covariate adjustment	219	(1)
7.4* The theory of the generalized linear model	220	(3)
7.5* The sequential analysis of generalized linear models	223	(6)
7.5.1 The statistics Z and V	223	(2)
7.5.2 The analysis of the selected set of prognostic factors	225	(2)
7.5.3 The analysis of treatment by prognostic factor interactions	227	(1)
7.5.4 Implementation	228	(1)
7.6* Special cases of the generalized linear model	229	(7)
7.6.1 The purpose of this section	229	(1)
7.6.2 The analysis of binary responses	230	(2)
7.6.3 The analysis of normally distributed responses	232	(1)
7.6.4 Cox's regression model	233	(3)
7.7 Simulated clinical trials	236	(15)
7.7.1 Calculating the statistics Z and V, using SAS	236	(1)
7.7.2 A trial with binary responses	237	(9)
7.7.3 A trial with normally distributed responses	246	(5)
7.8 Bibliographic notes and further comments	251	(2)
8 The Comparison of More than Two Treatments	253	(12)
8.1 Introduction	253	(1)
8.2 Elimination procedures	254	(2)
8.3 Orthogonal comparisons	256	(6)
8.3.1 General principles and examples	256	(3)
8.3.2* Mathematical details	259	(3)
8.4 Dose-response relationships	262	(1)
8.5 Bibliographic notes and further comments	263	(2)
9 Implementation of Sequential Methods: Some Examples	265	(20)
9.1 Some general considerations	265	(4)
9.2 The program PEST	269	(1)
9.3 Immunosuppression prior to bone marrow transplantation (a survival study with covariates)	270	(2)
9.4 Treatment of inoperable lung cancer (a survival study)	272	(3)
9.5 A comparison of anti-depressives (a study with ordinal responses)	275	(2)
9.6 Bioequivalence	277	(3)
9.7 Safety monitoring	280	(2)
9.8 The current status of sequential methodology in clinical trials	282	(3)
References	285	(12)
Appendix Simulated Data Used in the Examples of Section 7.7	297	(12)
Table I Simulated binary data for the trial of section 7.7.2	297	(4)
Table II Simulated normally distributed data for the trial of section 7.7.3	301	(8)
Index	309