Analysis of Safety Data of Drug Trials: An Update

217 Pages·2019·13.484 MB·English

by  Ton J. Cleophas, Aeilko H. Zwinderman

Ton J. Cleophas
Aeilko H. Zwinderman
Analysis of
Safety Data
of Drug Trials
An Update
Analysis of Safety Data of Drug Trials
(cid:129)
Ton J. Cleophas Aeilko H. Zwinderman
Analysis of Safety Data of
Drug Trials
An Update
TonJ.Cleophas AeilkoH.Zwinderman
AlbertSchweitzerHospital DepartmentofBiostatisticsandEpidemiology
DepartmentMedicine AcademicMedicalCenter
Sliedrecht,TheNetherlands Amsterdam,Noord-Holland,TheNetherlands
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Preface
In 2010, the fifth edition of the textbook Statistics Applied to Clinical Studies,
Springer, Heidelberg, Germany, was published by the authors, and over a million
copies have been sold. The primary objective of clinical trials of new drugs is,
generally, to demonstrate efficacy rather than safety. However, a trial in human
beings not at the same time adequately addressing safety is unethical, and the
assessmentofsafetyvariablesisanimportantelementofthetrial.
Aneffectiveapproachforthepurposeistopresentsummariesofprevalencesof
adverse effects and their 95% confidence intervals. In order to estimate the proba-
bilitythatthedifferencesbetweentreatmentandcontrolgroupdidnotoccurmerely
bychance,astatisticaltestcanbeperformed.Inthepastfewyears,thisprettycrude
method has been supplemented and, sometimes, replaced with more sophisticated
and better sensitive methodologies, based on machine learning clusters and net-
works,andmultivariateanalyses.Andso,itistimethatanupdatedversionofsafety
dataanalysiswaspublished.
For the statistical analysis of safety data, better-fit methods are, thus, available,
and this is fine. There is, however, another important topic brought forward in
connection with safety data analyses but, maybe, also relevant to the statistical
analysisofclinicaltrialsingeneral.Itincludesnovelinsightsintohypothesistesting,
favoringthealternativehypothesisoverthenullhypothesis.
Also, the issue of dependency needs to be addressed. Adverse effects may be
either dependent or independent of the main outcome. For example, an adverse
effect of alpha blockers is dizziness, and this occurs independently of the main
outcome “alleviation of Raynaud’s phenomenon.” In contrast, the adverse effect
“increasedcalorieintake”occurswith“increasedexercise,”andthisadverseeffectis
very dependent on the main outcome “weight loss.” Random heterogeneities, out-
liers, confounders, and interaction factors are common in clinical trials, and all of
themcanbeconsideredaskindsofadverseeffectsofthedependenttype.Random
regressions and analyses of variance, high dimensional clusterings, partial correla-
tions,structuralequationsmodels,andotherBayesianmethodsarehelpfulfortheir
analysis.
v
vi Preface
Thecurrenteditionwaswrittenfornon-mathematicians,particularlymedicaland
healthprofessionalsandstudents.Itprovidesexamplesofmodernanalyticmethods
so far largely unused in safety analysis. All of the 16 chapters have two core
characteristics, First, they are intended for current usage, and they are particularly
concerned with that usage. Second, they try and tell what readers need to know in
ordertounderstandandapplythemethods.Forthatpurpose,step-by-stepanalyses
of both hypothesized and real data examples will be given. Each chapter can be
studiedasastand-alone.
Sliedrecht,TheNetherlands TonJ.Cleophas
Amsterdam,TheNetherlands AeilkoH.Zwinderman
Contents
1 GeneralIntroduction. . . . . . . . .. . . . . . . .. . . . . . . . .. . . . . . . . .. 1
1 Introduction,Pharmageddon,EfficaciousTreatments. . . . . . . . . . 1
2 SomeTerminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 SignificantandInsignificantAdverseEffectsin
ClinicalTrials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 IndependentandDependentAdverseEffects. . . . . . . . . . . . . . . . 8
5 ABriefReviewofMethodsforDetectionandAssessment
ofIndependentAdverseEffects. . . . . . . . . . . . . . . . . . . . . . . . . 9
6 ABriefReviewofMethodsforDetectionandAssessment
ofDependentAdverseEffects. . . . . . . . . . . . . . . . . . . . . . . . . . 10
7 ExamplesofCausalRelationshipsBetweenDependentAdverse
EffectandOutcome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8 ExamplesofPharmacologicalMechanismsBetweenDependent
AdverseEffectandOutcome. . . . . . . . . . . . . . . . . . . . . . . . . . . 12
9 ExampleofInteractionBetweenDependentAdverse
EffectandOutcome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
10 ExampleofSubgroupMechanismBetweenDependent
AdverseEffectandOutcome. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11 ExamplesofPleiotropicDrugMechanismBetween
DependentAdverseEffectandOutcome. . . . . . . . . . . . . . . . . . . 15
12 ExampleofaCarryoverMechanismBetweenDependent
AdverseEffectandOutcome. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
13 ExampleofaCategoricalRatherthanOrdinalMechanism
BetweenDependentAdverseEffectandOutcome. . . . . . . . . . . . 17
14 ExampleofConfoundingBetweenDependentAdverse
EffectandOutcome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
15 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
16 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
vii
viii Contents
PartI TheAnalysisofIndependentAdverseEffects
2 StatisticallySignificantandInsignificantAdverseEffects. . . . . . . . 23
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 23
2 FourMethodsforTestingSignificanceofDifferenceof
TwoUnpairedProportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1 Method1,Z–Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Method2,Chi-SquareTest. . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Method3,PocketCalculatorMethod. . . . . . . . . . . . . . . . 30
2.4 Method4,FisherMethod. . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Chi-squareforAnalyzingMorethanTwoUnpairedProportions. . 31
4 McNemar’sTestforPairedProportions. . . . . . . . . . . . . . . . . . . . 34
5 MultiplePairedBinaryData(Cochran’sQTest). . . . . . . . . . . . . 35
6 SurvivalAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7 OddsRatioMethodforAnalyzingTwoUnpairedProportions. . . 39
8 OddsRatios(OR)sforOneGroup,TwoTreatments. . . . . . . . . . 42
9 LoglikelihoodRatios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
9.1 TheNormalApproximationandtheAnalysisofEvents. . . 44
9.2 LoglikelihoodRatioTestsandtheQuadratic
Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
9.3 MoreExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
10 LogisticModels. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 49
11 PoissonRegression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
12 CoxModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
13 BayesianCrosstabs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
13.1 TraditionalAnalysisfor2(cid:1)2InteractionMatrix. . . . . . . . . 59
13.2 BayesianLoglinearRegressionfor2(cid:1)2Interaction
Matrix. .. . . . .. . . . .. . . . .. . . . . .. . . . .. . . . .. . . . .. 61
14 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
15 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 IncidenceRatios,ReportingRatios,andSafetySignalsInstead
ofAdverseEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 67
2 Chi-SquareTest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3 ProportionalReportingRatios. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 StandardizedIncidenceRatios(SIR). . . . . . . . . . . . . . . . . . . . . . 73
5 ExamplesofLargerChi-SquareTablesforComparingthe
PresenceofAdverseEffectsBetweenDifferentStudies. . . . . . . . 74
6 SafetySignalsInsteadofAdverseEffects. . . . . . . . . . . . . . . . . . 76
7 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 SafetyAnalysisandtheAlternativeHypothesis. . . . . . . . . . . . . . . . 81
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 81
2 PowerandtheAlternativeHypothesis. . . . . . . . . . . . . . . . . . . . . 82
Contents ix
3 TwoMainHypothesesofClinicalResearch,Efficacy
andSafety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4 AlphasandBetas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 TheMainPurposeofHypothesisTesting. . . . . . . . . . . . . . . . . . 86
6 LimitationsofStatisticalTestinginGeneral. . . . . . . . . . . . . . . . . 86
7 FDARuleandGuidanceClassificationofAdverse
Effects2012. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8 EmphasisonTypeIErrorsIslessImportantwithSafety
Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
9 WorkingwithFlexibleAlphasandBetasforSafetyAnalyses. . . . 89
10 ComputingMinimizedBetas. . . . . . . . . . . . . . . . . . . . . . . . . . . 90
11 TheEffectofIncreasingtheTypeIErrorontheMagnitude
oftheTypeIIError. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
12 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
13 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5 ForestPlotsofAdverseEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 95
2 SystematicAssessmentofQualitativeAdverseEffects. . . . . . . . . 96
3 ForestPlotsofOddsRatios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 GraphicsofAdverseEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 103
2 VisualizationMethodsofQuantitativeAdverseEffects. . . . . . . . 104
2.1 GeneralPurpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.2 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.3 KnimeDataMiner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.4 KnimeWorkflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.5 BoxandWhiskersPlots. . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.6 LiftCharts. . .. . . . . .. . . . . . .. . . . . .. . . . . .. . . . . .. . 108
2.7 Histograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.8 LinePlots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.9 MatricesofScatterPlots. . . . . .. . . . . . . . . . . . . . . . .. . . 115
2.10 ParallelCoordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
2.11 HierarchicalClusterAnalysis. . . . . . . . . . . . . . . . . . . . . . 116
3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 AdverseEffectsinClinicalTrialswithRepeatedMeasures. . . . . . . 119
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 119
2 DataExample,MixedLinearModels. . . . . . . . . . . . . . . . . . . . . 120
3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
x Contents
8 BenefitRiskRatios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 129
2 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3 Benefit/RiskAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 131
4 ComputingtheConfidenceIntervalsoftheRatioofNormal
VariableswiththeQuadraticMethod. . . . . . . . . . . . . . . . . . . . . 132
5 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9 Equivalence,InferiorityandSuperiorityTestingofAdverse
Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 135
2 HowDoesTraditionalEquivalence,InferiorityandSuperiority
TestingWork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3 WhyEquivalence,InferiorityandSuperiorityTestingof
AdverseEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4 Example1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 140
5 Example2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 140
6 Example3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 141
7 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
PartII TheAnalysisofDependentAdverseEffects
10 IndependentandDependentAdverseEffects. . . . . .. . . . . .. . . . .. 147
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 147
2 MultiplePathAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3 PartialCorrelations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
4 HigherOrderPartialCorrelations. . . . . . . . . . . . . . . . . . . . . . . . 155
5 BayesianNetworks,PleiotropyResearch. . . . . . . . . . . . . . . . . . . 156
6 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
11 CategoricalPredictorsAssessedasDependentAdverseEffects. . . . 159
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 159
2 Example1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 160
3 Example2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 162
4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
12 AdverseEffectsoftheDependentTypeinCrossoverTrials. . . . . . 167
1 Introduction. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 167
2 AssessmentofCarryoverandTreatmentEffect. . . . . . . . . . . . . . 168
3 StatisticalModelforTestingTreatmentandCarryoverEffect. . . . 169
4 ATableofPcValuesJustYieldingaSignificantTestfor
CarryoverEffect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170