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Statistical Monitoring of Clinical Trials A Unified Approach

:	Michael A. Proschan, K. K. Gordon Lan, Janet Turk Wittes
:	Statistical Monitoring of Clinical Trials A Unified Approach
:	Springer-Verlag
:	9780387449708
:	1
:	CHF 129.40
:

:	Allgemeines
:	English

:	268
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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. Thus, this book offers statisticians an accessible, incremental approach to understanding Brownian motion as related to clinical trials.

	Preface	7
	Contents	9
	1 Introduction	14
	2 A General Framework	21
	2.1 Hypothesis Testing: The Null Distribution of Test Statistics Over Time	22
	2.2 An Estimation Perspective	30
	2.3 Connection Between Estimators, Sums, Z-Scores, and Brownian Motion	33
	2.4 Maximum Likelihood Estimation	36
	2.5 Other Settings Leading to E-Processes and Brownian Motion	40
	2.6 The Normal Linear and Mixed Models	42
	2.7 When Is Brownian Motion Not Appropriate?	48
	2.8 Summary	50
	2.9 Appendix	51
	3 Power: Conditional, Unconditional, and Predictive	55
	3.1 Unconditional Power	55
	3.2 Conditional Power for Futility	57
	3.3 Varied Uses of Conditional Power	65
	3.4 Properties of Conditional Power	69
	3.5 A Bayesian Alternative: Predictive Power	72
	3.6 Summary	75
	3.7 Appendix	76
	4 Historical Monitoring Boundaries	79
	4.1 How Bad Can the Naive Approach Be?	79
	4.2 The Pocock Procedure	81
	4.3 The Haybittle Procedure and Variants	81
	4.4 The O’Brien-Fleming Procedure	83
	4.5 A Comparison of the Pocock and O’Brien-Fleming Boundaries	84
	4.6 Effect of Monitoring on Power	87
	4.7 Appendix: Computation of Boundaries Using Numerical Integration	89
	5 Spending Functions	92
	5.1 Upper Boundaries	92
	5.2 Upper and Lower Boundaries	101
	5.3 Summary	103
	5.4 Appendix	103
	6 Practical Survival Monitoring	109
	6.1 Introduction	109
	6.2 Survival Trials with Staggered Entry	109
	6.3 Stochastic Process Formulation and Linear Trends	111
	6.4 A Real Example	112
	6.5 Nonlinear Trends of the Statistics: Analogy with Monitoring a t-Test	113
	6.6 Considerations for Early Termination	114
	6.7 The Information Fraction with Survival Data	115
	7 Inference Following a Group-Sequential Trial	122
	7.1 Likelihood, Sufficiency, and (Lack of) Completeness	122
	7.2 One-Tailed p-Values	125
	7.3 Properties of p-Values	134
	7.4 Confidence Intervals	135
	7.5 Estimation	140
	7.6 Summary	144
	7.7 Appendix: Proof that B( t ) t Overestimates 0 in the One-Tailed Setting	144
	8 Options When Brownian Motion Does Not Hold	146
	8.1 Small Sample Sizes	146
	8.2 Permutation Tests	152
	8.3 The Bonferroni Method	158
	8.4 Summary	159
	8.5 Appendix	160
	9 Monitoring for Safety	163
	9.1 Example: Inference from a Sample Size of One	163
	9.2 Example: Inference from Multiple Endpoints	164
	9.3 General Considerations	165
	9.4 What Safety Data Look Like	168
	9.5 Looking for a Single Adverse Event	171
	9.6 Looking for Multiple Adverse Events	180
	9.7 Summary	181
	10 Bayesian Monitoring	183
	10.1 Introduction	183
	10.2 The Bayesian Paradigm Applied to B-Values	184
	10.3 The Need for a Skeptical Prior	185
	10.4 A Comparison of Bayesian and Frequentist Boundaries	188
	10.5 Example	190
	10.6 Summary	192
	11 Adaptive Sample Size Methods	193
	11.1 Introduction	193
	11.2 Methods Using Nuisance Parameter Estimates: The Continuous Outcome Case	194
	11.3 Methods Using Nuisance Parameter Estimates: The Binary Outcome Case	207
	11.4 Adaptive Methods Based on the Treatment Effect	211
	11.5 Summary	218
	12 Topics Not Covered	220
	12.1 Introduction	220
	12.2 Continuous Sequential Boundaries	221
	12.3 Other Types of Group-Sequential Boundaries	222
	12.4 Reverse Stochastic Curtailing	223
	12.5 Monitoring Studies with More Than Two Arms	224
	12.6 Monitoring for Equivalence and Noninferiority	225
	12.7 Repeated Confidence Intervals	225
	13 Appendix I: The Logrank and Related Tests	227
	13.1 Hazard Functions	228
	13.2 Linear Rank Statistics	231
	13.3 Payment Functions and Score Functions	237
	13.4 Censored Survival Data	239
	13.5 The U-Statistic Approach to the Wilcoxon Statistic	240
	13.6 The Logrank and Weighted Mantel-Haenszel Statistics	241
	13.7 Monitoring Survival Trials	243
	14 Appendix II: Group-Sequential Software	244
	14.1 Introduction	244
	14.2 Before the Trial Begins: Power and Sample Size	244
	14.3 During the Trial: Computation of Boundaries	246
	14.4 After the Trial: p-Value, Parameter Estimate, and Confidence Interval	247
	14.5 Other Features of the Program	249
	References	252
	Index	260