Statistics Applied to Clinical Trials

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Format: Paperback
Pub. Date: 2003-03-01
Publisher(s): Kluwer Academic Pub
List Price: $146.99

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Summary

The current book can be studied together with the texbook Statistics Applied To Clinical Trials by the same authors, or separately. The authors often hear that students have difficulties in understanding statistics from a textbook and that self-assessment through exercises and examples is required. Rather than trying to be complete, this book focuses on the main aspects, including the test statistics generally used for the primary analysis of continuous and proportional data from randomized controlled clinical trials. In the past few years statistical analysis has increasingly been left to the computer, and clinical investigators are at a loss to understand the limitations of the research and its statistical analysis, on the one hand, while on the other hand, statistical results are often overemphasized. This self-assessment book is not only useful for investigators involved in the field of clinical trials, but also for every physician who wishes to better understand the data from trials as published currently.

Author Biography

Ton J. Cleophas, MD, PhD, Associate-Professor, President American College of Angiology, Co-Chair Module Statistics Applied to Clinical Trials, European Interuniversity College of Pharmaceutical Medicine Lyon, France, Internist-clinical pharmacologist, Department Medicine, Albert Schweitzer Hospital, Dordrecht, Netherlands Aeilko H. Zwinderman, Math D, PhD, Professor, Co-Chair Module Statistics Applied to Clinical Trials, European Interuniversity College of Pharmaceutical Medicine Lyon, France, Professor of Statistics, Department Biostatistics and Epidemiology, Academic Medical Center Amsterdam, Netherlands Toine F. Cleophas, D Techn, Technical University, Delft, Netherlands

Table of Contents

Preface xiii
Foreword xv
Introduction to the Statistical Analysis of Clinical Trials, Continuous Data Analysis
Scientific rigor
1(1)
Two types of data
1(1)
Historical controls
2(1)
Factorial designs
2(1)
Biology is full of variations
2(1)
Summarize the data
3(1)
Two Gaussian curves
4(1)
Human brain
4(1)
Null-hypothesis
5(1)
Alpha, the Type I error
6(1)
T-table
7(1)
Reject the null-hypothesis
8(1)
Negative trial
9(1)
Borderline result
9(1)
Testing two means
10(2)
Testing paired samples
12(2)
Unpaired testing of paired samples
14(1)
Positive and negative correlations
15(1)
Unpaired analysis of variance (ANOVA)
15(2)
Paired analysis of variance (ANOVA)
17(1)
Non-parametric testing for skewed data
18(1)
Paired non-parametric test (Mann-Whitney)
19(1)
Unpaired non-parametric test (Wilcoxon rank sum)
20(2)
Summary
22(1)
Exercises to chapter 1
22(3)
Equivalence Testing
A negative study ≠ equivalent study, why so?
25(1)
Summarize the data
25(1)
Two Gaussian curves
26(1)
Null-hypothesis
27(1)
Negative study
28(1)
Equivalence testing
29(1)
Equivalent and at the same time significantly different
29(1)
Overview of all possibilities
30(1)
Defining D-boundaries
31(1)
Robustness of equivalence trials
31(1)
Example
31(1)
Crossover equivalence studies with different levels of correlation
32(1)
Conclusions
33(1)
Exercises to chapter 2
34(3)
Power, Sample Size
Definition of statistical power
37(1)
Statistics gives no certainties
37(1)
Summarize the data
38(1)
Two Gaussian curves
39(1)
Important hypotheses
39(1)
Hypothesis 1
40(1)
Alpha, beta, 1-beta
41(1)
Power gets larger when the mean gets larger
41(1)
Example of poor power
42(1)
How to calculate power
43(1)
Use of T-table to find power
43(2)
Use of T-table to find power, one more example
45(2)
Use of T-table to find power, one more example
47(2)
Power formulas
49(1)
Sample size requirements
49(1)
A simple method to calculate required sample size
49(1)
A more accurate method to calculate required sample size, power index method
50(1)
Sample size computations for continuous variables, example
50(1)
Other formulas to calculate required sample size
51(1)
Type I, type II and Type III errors
52(1)
Conclusions
53(1)
Exercises to chapter 3
54(3)
Proportional Data Analysis, Part I
Safety data are, generally, summaries of patients with side effects
57(1)
Example
57(1)
Standard deviation of proportion
58(1)
Why is SD of proportion √[p (1-p)]
58(1)
Method-1 to test difference between two groups of proportional data
58(2)
Normal table rather than t-table must be used for proportional data
60(1)
More easy way to test proportions is the χ2 test
61(1)
How to use the squared curve
62(1)
How the χ2 test for proportions works in practice: 1x2 table
63(1)
How the χ2 test for proportions works in practice: 2x2 table
63(1)
Alternative way to find the adequate χ2 -value: 2x2 table
64(1)
One more way to find the adequate χ2 -value, Fisher-exact test: 2x2 table
64(1)
With χ2 welcome to the real world of statistics because it can be used for kx2 tables
65(1)
McNemar's test for paired yes/no observations
65(1)
Differences between proportions can also be assessed by calculating the odds ratios (or) and its 95% confidence intervals (cis) and checking whether the confidence intervals cross 1.0
66(1)
How to calculate 95% confidence intervals of an odds ratio with paired observations
66(1)
Survival analysis (Kaplan-Meier method)
67(1)
Testing significance of difference between 2 Kaplan-Meier curves
67(1)
Conclusions: what you should know
68(1)
Questions to chapter 4
68(5)
Proportional Data Analysis, Part II
Examples
73(1)
Choice of statistical method: A
74(1)
Choice of statistical method: B
74(1)
Choice of statistical method: C
75(1)
Elements of statistical analysis
75(1)
Example 1: one group of patients measured once
76(1)
Example 1: quantification
76(1)
Example 1: confidence interval
77(1)
Example 1: hypothesis test
78(1)
Standard normal distribution
79(1)
Standard normal distribution: p-value
79(1)
Example 1: graphical illustration
80(1)
Example 2: comparing two groups of patients
80(1)
Example 2: data
81(1)
Example 2: graphical illustration
81(1)
Example 2: risk difference
82(1)
Example 2: confidence interval
82(1)
Example 2: graphical illustration
83(1)
Example 2: hypothesis testing
83(2)
Example 2: 2x2 table
85(1)
Example 2: graphical illustration of risk ratio (RR) and odds ratio (OR)
85(1)
Example 2: hypothesis testing
86(1)
Example 2: chi-square (= χ2) test
87(1)
Example 2: Fisher exact test
87(1)
Sample size calculation
88(1)
Discussed so far...
88(1)
Example 3: 1 sample, two measurements
89(1)
McNemar's test
90(1)
Example 3: McNemar's test
91(1)
Example 4: >2 repeated measurements
91(1)
Example 4: Cochran's test
92(1)
Other repeated measurements designs
92(1)
Other repeated measurements designs: special techniques
93(1)
Censored data
93(1)
Kaplan-Meier curve
94(1)
Kaplan-Meier curve: definition
95(1)
Hazard, cumulative hazard, survival curve
96(1)
Cumulative hazard function: example
96(1)
Hazard function: example
97(1)
Comparing survival curves: logrank test
98(1)
Comparing survival curves: comments
98(1)
Finally: software
99(1)
Questions to chapter 5
100(3)
Meta-Analysis
Review of the past
103(1)
A lot of misunderstanding
103(1)
What is a meta-analysis
104(1)
A summary of meta-analyses helpful to cardiologists for everyday decision-making
104(1)
Proportions, standard errors of proportions, odds, odds ratios
105(1)
How to calculate 95% confidence intervals of an odds ratio
106(1)
Another summary of meta-analyses helpful to cardiologists for everyday decision-making
107(1)
Example of an epidemiological meta-analysis
107(1)
Important matters need few words
108(1)
Clearly defined prior hypotheses
108(1)
Thorough search of trials
109(1)
Strict inclusion criteria
110(1)
Uniform guidelines for data analysis
110(1)
Data analysis: first pitfall, publication bias
110(1)
Data analysis:second pitfall, heterogeneity
111(1)
Testing heterogeneity
111(1)
How to test heterogeneity, calculate and pool odds ratios of various studies and to test whether pooled odds ratios are different from 1.0, example
112(1)
What to do in case of heterogeneity
113(2)
Data analysis: third pitfall, lack of robustness
115(1)
Criticizms of meta-analyses
116(1)
Example of published meta-analysis
117(4)
Additional exercises to chapter 6
121(2)
Interim-Analyses
Interim analysis: looking at the data before closure
123(1)
Monitoring
123(1)
Data consistency and availability
124(1)
Patient accrual
124(1)
Changing inclusion criteria
125(1)
Interim analsis
125(1)
Dangers, random high
126(1)
Significance level
126(1)
Correction for increasing type-I error rate
127(1)
Some rules
128(1)
Decision rules
128(1)
Sequential trials
129(1)
Efficacy (Z)
130(1)
Difference of two means (V)
130(1)
Conclusion
131(1)
Exercises to chapter 7
131(2)
Multiple Testing
Two situations
133(1)
Type-I error rate
133(1)
Multiple comparisons
134(1)
Example 1: data summary
134(1)
Example 1: graphical display
135(1)
Two strategies
136(1)
LSD test
136(1)
Alternatives
137(1)
Multiple ranging
137(1)
Example 1: results
138(1)
Example 1: another graphical display
139(1)
Corrected confidence intervals
139(1)
No method is best
139(1)
Multiple testing
140(1)
What to do
140(1)
Correction
141(1)
Example 2: data
141(1)
Example 2: graphical display
142(1)
Alternatives
142(1)
Composite
143(1)
Example 2: graphical display
143(1)
Conclusion
144(1)
Exercises to chapter 8
144(3)
Principles of Linear Regression
Paired observations: regression analysis is for predicting one observations from another
147(1)
Paired data plotted first
148(1)
Regression line, the equation
148(1)
Correlation coefficient
149(1)
SPSS Statistical software to analyze data from paragraph 1 (stool data)
150(1)
Three columns of paired observations instead of two
151(1)
SPSS Statistical software to analyze the above data
151(1)
Another example of multiple linear regression model
152(1)
Multicollinearity testing of the above example
153(1)
Results from the above example
153(1)
Conclusions
154(1)
Questions to Chapter 9
154(5)
Subgroup Analysis Using Regression Modeling
Subgroup questions
159(1)
Different regression models
160(1)
General form of regression models
160(1)
Link-functions
161(1)
Assumptions of the linear regression model
162(1)
Logistic and Cox regression model
163(1)
An example where the Cox model fits
164(1)
An example where the Cox model does not fit
165(1)
Increasing precision: example
166(1)
Increasing precision using a regression model
166(1)
Increasing precision: example of a regression model
167(1)
Increasing precision: graphical illustration
168(1)
Increasing precision
168(1)
Confounding
169(1)
Confounding: some rules
169(1)
Confounding: warning
170(1)
Interaction/synergism
170(1)
Interaction/synergism: example
171(1)
Interaction/synergism: graphical illustration
171(1)
Interaction/synergism: graphical illustration
172(1)
Interaction/synergism: warnings
172(1)
Conclusion
172(1)
Questions to chapter 10
173(2)
Relationship Among Statistical Distributions
Variables to assess clinical data
175(1)
Central tendency and spread of data
175(1)
Creating a chi-square distribution
176(1)
How to use squared curve
176(1)
How χ2 works in practice: 1 x 2 table
177(1)
How χ2 works in practice: 2 x 2 table
178(1)
With χ2 welcome to the real world of statistics because it can be used for k x 2 tables
178(1)
Why not χ2 for continuous data
179(1)
What is the advantage of a χ2 -test compared to a z -test (normal test) or t-test
180(1)
With chi-square welcome to the real world of statistics, because variance can be simply added up
180(1)
Examples
181(1)
More examples, how to calculate 95% confidence intervals of an odds ratio with unpaired observations
181(1)
More examples, how to calculate 95% confidence intervals of an odds ratio with paired observations
182(1)
More examples, how to calculate and pool odds ratios of various studies (unpaired data)
182(2)
More examples: heterogeneity of trials in a meta-analysis
184(1)
More examples, extension of chi-square is the F-distribution
184(1)
Limitations of statistical tests as discussed and conclusions
185(1)
Questions and exercises to Chapter 11
186(3)
Statistics Is Not Bloodless Algebra
Biological processes are full of variations
189(1)
Statistics is fun for clinical investigators
189(1)
Use simple tests
189(1)
Statistical principles improve quality of trial
190(1)
Statistics provides extras
190(1)
Statistics provides extras, special designs can manage what parallel designs cannot
190(1)
For example, interim analyses
190(1)
Statistics is not like algebra and requires biological thinking and just a bit of maths
191(1)
Statistics turns art into science
191(1)
Statistics for support rather than illumination?
192(1)
Statistics helps the clinician to better understand the limitations of research
192(1)
Limitations of statistics
193(1)
Conclusions
193(1)
Questions to chapter 12
193(4)
Bias Due to Conflicts of Interests, Some Guidelines
Introduction
197(1)
The randomized controlled clinical trial as the gold standard
197(1)
Need for circumspection recognized
198(1)
The expanding commend of the pharmaceutical industry over clinical trials
198(1)
Flawed procedures jeopardizing current clinical trials
199(1)
The good news
200(1)
Further solutions to the dilemma between sponsored research and the independence of science
200(2)
References
202(1)
Statistical Tables 203(8)
Answers to Questions and Exercises 211(10)
Index 221

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