Applications of Regression Models in Epidemiology

273 Pages·2017·8.784 MB·English

by  Erick Suárez, Cynthia M. Pérez, Roberto Rivera, Melissa N. Martínez

ApplicationsofRegression
ModelsinEpidemiology

Applications of Regression
Models in Epidemiology
Erick Suárez, Cynthia M. Pérez, Roberto Rivera, and
Melissa N. Martínez
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LibraryofCongressCataloging-in-PublicationData:
Names:ErickL.Suárez,ErickL.,1953­
Title:ApplicationsofRegressionModelsinEpidemiology/ErickSuarez[andthreeothers].
Description:Hoboken,NewJersey:JohnWiley&Sons,Inc.,[2017]|Includes
index.
Identifiers:LCCN2016042829|ISBN9781119212485(cloth)|ISBN9781119212508(epub)
Subjects:LCSH:Medicalstatistics.|Regressionanalysis.|Publichealth.
Classification:LCCRA407.A672017|DDC610.2/1–dc23LCrecordavailableat
https://lccn.loc.gov/2016042829
PrintedintheUnitedStatesofAmerica
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vii
Table of Contents
Preface xv
Acknowledgments xvii
AbouttheAuthors xix
1 BasicConceptsforStatisticalModeling 1
1.1 Introduction 1
1.2 ParameterVersusStatistic 2
1.3 ProbabilityDefinition 3
1.4 ConditionalProbability 3
1.5 ConceptsofPrevalenceandIncidence 4
1.6 RandomVariables 4
1.7 ProbabilityDistributions 4
1.8 CentralityandDispersionParametersofaRandomVariable 6
1.9 IndependenceandDependenceofRandomVariables 7
1.10 SpecialProbabilityDistributions 7
1.10.1 BinomialDistribution 7
1.10.2 PoissonDistribution 8
1.10.3 NormalDistribution 9
1.11 HypothesisTesting 11
1.12 ConfidenceIntervals 14
1.13 ClinicalSignificanceVersusStatisticalSignificance 14
1.14 DataManagement 15
1.14.1 StudyDesign 15
1.14.2 DataCollection 16
1.14.3 DataEntry 17
1.14.4 DataScreening 18
1.14.5 WhattoDoWhenDetectingaDataIssue 19
1.14.6 ImpactofDataIssuesandHowtoProceed 20
1.15 ConceptofCausality 21
References 22
viii TableofContents
2 IntroductiontoSimpleLinearRegressionModels 25
2.1 Introduction 25
2.2 SpecificObjectives 26
2.3 ModelDefinition 26
2.4 ModelAssumptions 28
2.5 GraphicRepresentation 29
2.6 GeometryoftheSimpleRegressionModel 29
2.7 EstimationofParameters 30
2.8 VarianceofEstimators 31
2.9 HypothesisTestingAbouttheSlopeoftheRegressionLine 32
2.9.1 UsingtheStudent’st-Distribution 32
2.9.2 UsingANOVA 32
2.10 CoefficientofDeterminationR2 34
2.11 PearsonCorrelationCoefficient 34
2.12 EstimationofRegressionLineValuesandPrediction 35
2.12.1 ConfidenceIntervalfortheRegressionLine 35
2.12.2 PredictionIntervalofActualValuesoftheResponse 36
2.13 Example 36
2.14 Predictions 39
2.14.1 PredictionswiththeDatabaseUsedbytheModel 40
2.14.2 PredictionswithDataNotUsedtoCreatetheModel 42
2.14.3 ResidualAnalysis 44
2.15 Conclusions 46
PracticeExercise 47
References 48
3 MatrixRepresentationoftheLinearRegressionModel 49
3.1 Introduction 49
3.2 SpecificObjectives 49
3.3 Definition 50
3.3.1 Matrix 50
3.4 MatrixRepresentationofaSLRM 50
3.5 MatrixArithmetic 51
3.5.1 AdditionandSubtractionofMatrices 51
3.6 MatrixMultiplication 52
3.7 SpecialMatrices 53
3.8 LinearDependence 54
3.9 RankofaMatrix 54
3.10 InverseMatrix[A�1] 54
3.11 ApplicationofanInverseMatrixinaSLRM 56
3.12 Estimationofβ ParametersinaSLRM 56
3.13 MultipleLinearRegressionModel(MLRM) 57