## Statistics Applied to Clinical TrialsIn 1948 the first randomized controlled trial was published by the English Medical Research Council in the British Medical Journal. Until then, observations had been uncontrolled. Initially, trials frequently did not confirm hypotheses to be tested. This phenomenon was attributed to low sensitivity due to small samples, as well as inappropriate hypotheses based on biased prior trials. Additional flaws were recognized and subsequently were better accounted for: carryover effects due to insufficient washout from previous treatments, time effects due to external factors and the natural history of the condition under study, bias due to asymmetry between treatment groups, lack of sensitivity due to a negative correlation between treatment responses, etc. Such flaws, mainly of a technical nature, have been largely corrected and led to trials after 1970 being of significantly better quality than before. The past decade has focused, in addition to technical aspects, on the need for circumspection in planning and conducting of clinical trials. As a consequence, prior to approval, clinical trial protocols are now routinely scrutinized by different circumstantial bodies, including ethics committees, institutional and federal review boards, national and international scientific organizations, and monitoring committees charged with conducting interim analyses. This book not only explains classical statistical analyses of clinical trials, but addresses relatively novel issues, including equivalence testing, interim analyses, sequential analyses, and meta-analyses, and provides a framework of the best statistical methods currently available for such purposes. The book is not only useful for investigators involved in the field of clinical trials, but also for all physicians who wish to better understand the data of trials as currently published. |

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### Contents

1 | |

2 | |

3 | |

8 | |

correlation coefficient | 11 |

Stratification issues | 13 |

Randomized versus historical controls | 14 |

Factorial designs | 15 |

Purposes of linear regression analysis | 137 |

Another real data example of multiple linear regression exploratory purpose | 138 |

Conclusions | 140 |

CONFOUNDING INTERACTION SYNERGISM 1 Introduction | 141 |

Model | 142 |

I Increased precision of efficacy | 144 |

II Confounding | 145 |

III Interaction and synergism | 146 |

References | 16 |

THE ANALYSIS OF EFFICACY DATA OF DRUG TRIALS 1 Overview | 17 |

The principle of testing statistical significance | 18 |

The TValue standardized mean result of study | 21 |

Unpaired TTest | 22 |

Nullhypothesis testing of 3 or more unpaired samples | 24 |

Three methods to test statistically a paired sample | 25 |

Nullhypothesis testing of 3 or more paired samples | 28 |

Paired data with a negative correlation | 30 |

Rank testing | 36 |

Conclusions | 39 |

THE ANALYIS OF SAFETY DATA OF DRUG TRIALS 1 Introduction summary display | 41 |

Four methods to analyze two unpaired proportions | 42 |

Chisquare to analyze more than two unpaired proportions | 48 |

McNemars test for paired proportions | 51 |

Survival analysis | 52 |

Odds ratio method for analyzing two unpaired proportions | 54 |

Odds ratios for 1 group two treatments | 57 |

CHAPTER 4EQUIVALENCE TESTING 1 Introduction | 59 |

Overview of possibilities with equivalence testing | 61 |

Calculations | 62 |

Equivalence testing a new gold standard? | 63 |

level of correlation in paired equivalence studies | 64 |

Conclusions | 65 |

STATISTICAL POWER AND SAMPLE SIZE 1 What is statistical power | 67 |

Emphasis on statistical power rather than nullhypothesis testing | 68 |

Power computations | 70 |

Example of power computation using the TTable | 71 |

Calculation of required sample size rationale | 73 |

References | 78 |

INTERIM ANALYSES 1 Introduction | 79 |

Interim analysis | 80 |

Groupsequential design of interim analysis | 83 |

Conclusions | 85 |

MULTIPLE STATISTICAL INFERENCES 1 Introduction | 87 |

variables | 92 |

Conclusions | 95 |

CONTROLLING THE RISK OF FALSE POSITIVE CLINICAL TRIALS 1 Introduction | 97 |

Bonferroni test | 99 |

Composite endpoint procedures | 100 |

Conclusions | 101 |

THE INTERPRETATION OF THE PVALUES 1 Introduction | 103 |

Standard interpretation of pvalues | 104 |

Common misunderstandings of the pvalues | 106 |

The real meaning of very large pvalues like p0 95 | 107 |

Pvalues larger than 0 95 examples Table 2 | 108 |

The real meaning of very small pvalues like p0 0001 | 109 |

Pvalues smaller than 0 0001 examples Table 3 | 110 |

Discussion | 111 |

Conclusions | 113 |

RESEARCH DATA CLOSER TO EXPECTATION THAN COMPATIBLE WITH RANDOM SAMPLING 1 Introduction | 117 |

Methods and results | 118 |

Discussion | 119 |

Conclusions | 122 |

PRINCIPLES OF LINEAR REGRESSION 1 Introduction | 125 |

More on paired observations | 126 |

Using statistical software for simple linear regression | 129 |

Multiple linear regression | 131 |

Multiple linear regression example | 133 |

Estimation and hypothesis testing | 147 |

Goodnessoffit | 148 |

Selection procedures | 149 |

Discussion | 160 |

Logistic regression | 169 |

Discussion | 175 |

the underlying mechanism 3 Regression model for parallelgroup trials with continuous efficacy data | 181 |

Conclusions | 185 |

Logistic regression equation | 190 |

INTERACTION EFFECTS IN CLINICAL TRIALS 1 Introduction 2 What exactly is interaction a hypothesized example | 193 |

How to test the presence of interaction effects statistically a real data example | 196 |

Additional real data examples of interaction effects | 198 |

Discussion 6 Conclusions | 203 |

References | 204 |

METAANALYSIS 1 Introduction | 205 |

Examples | 206 |

Clearly defined hypotheses Thorough search of trials Strict inclusion criteria | 208 |

Uniform data analysis | 209 |

Discussion where are we now? | 217 |

References | 218 |

1 Introduction | 219 |

Mathematical model | 220 |

Hypothesis testing | 221 |

Statistical power of testing | 223 |

Discussion | 226 |

Conclusion | 227 |

References | 228 |

CROSSOVER STUDIES WITH BINARY RESPONSES 1 Introduction | 229 |

Assessment of carryover and treatment effect | 230 |

Statistical model for testing treatment and carryover effects | 231 |

not have been used 4 Estimate of the size of the problem by review of hypertension | 245 |

Defining QOL in a subjective or objective way | 251 |

Results | 252 |

Discussion | 257 |

Genetics genomics proteonomics data mining | 264 |

RELATIONSHIP AMONG STATISTICAL DISTRIBUTIONS | 271 |

nullhypothesis testing with chisquare distribution 6 Examples of data where variance is more important than mean | 278 |

CLINICAL DATA WHERE VARIABILITY IS MORE | 297 |

Examples | 304 |

2 | 317 |

328 | |

Discussion | 335 |

336 | |

CHAPTER 30STATISTICS IS NO BLOODLESS ALGEBRA 1 Introduction | 337 |

Conclusions | 338 |

Statistics is not like algebra bloodless | 339 |

Statistics can turn art into science | 340 |

Statistics can help the clinician to better understand limitations and benefits of current research | 341 |

Conclusions | 342 |

343 | |

BIAS DUE TO CONFLICTS OF INTERESTS SOME GUIDELINES 1 Introduction | 345 |

Need for circumspection recognized | 346 |

Flawed procedures jeopardizing current clinical trials | 347 |

The good news | 348 |

350 | |

APPENDIX | 353 |

360 | |

364 | |

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### Common terms and phrases

ABPM angina pectoris ANOVA assessment blood pressure Bonferroni calcium channel blockers calculated carryover effect chance chapter chi-square test Cleophas TJ clinical trials compared CONCLUSIONS confidence intervals continuous data correlation coefficient covariates crossover studies curve degrees of freedom demonstrated disease drug endpoint equivalence estimate example factors Figure formula frequency distribution genes graph hypertension hypothesis interaction interim analyses linear regression logistic regression mean result medicine meta-analysis method mmol/l multiple negative correlation normal distribution null numbers of patients observed odds ratio otherwise called p-value paired placebo polynomes population positive correlation pravastatin procedure proportions randomized controlled trials regression analysis regression line regression model reject the null-hypothesis reproducibility response risk scores SEMs sensitivity significantly different square standard deviation standard error statistical power statistical tests statistically significant t-distribution t-test Table treatment comparison treatment difference treatment effect treatment groups type I error unpaired variance versus x-axis zero