Regression Models as a Tool in Medical Research

494 Pages·2012·2.781 MB·English

by  Vach, Werner

Statistics
R Regression Models
Regression Models
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Tool g Tool
as a as a
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Medical Research n
in e in Medical Research
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While regression models have become standard tools in medical research, s
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understanding how to properly apply the models and interpret the results is often
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challenging for beginners. Regression Models as a Tool in Medical Research o
presents the fundamental concepts and important aspects of regression models i
n
c
most commonly used in medical research, including the classical regression model
a
for continuous outcomes, the logistic regression model for binary outcomes,
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and the Cox proportional hazards model for survival data. The text emphasizes l
adequate use, correct interpretation of results, appropriate presentation of results, o
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and avoidance of potential pitfalls.
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After reviewing popular models and basic methods, the book focuses on advanced e
e
topics and techniques. It considers the comparison of regression coefficients, the s
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selection of covariates, the modeling of nonlinear and nonadditive effects, and the
e
s
analysis of clustered and longitudinal data, highlighting the impact of selection
a
mechanisms, measurement error, and incomplete covariate data. The text then
r a
covers the use of regression models to construct risk scores and predictors. It
s
also gives an overview of more specific regression models and their applications c
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as well as alternatives to regression modeling.
h
T
Features
• Helps readers improve their understanding of the role of regression models o
in the medical field
o
• Illustrates each technique with a concrete example, enabling readers to
l
better appreciate the properties and theory of the methods
• Uses Stata to demonstrate the practical use of the models
• Discusses how and when regression models can fail
• Describes the basic principles behind statistical computations, with more
mathematical details given in the appendices V
a
c
h
K15111 Werner Vach
K15111_Cover.indd 1 10/2/12 10:49 AM
Regression Models
Tool
as a
Medical Research
in
K15111_FM.indd 1 10/29/12 4:28 PM
K15111_FM.indd 2 10/29/12 4:28 PM
Regression Models
Tool
as a
Medical Research
in
Werner Vach
K15111_FM.indd 3 10/29/12 4:28 PM
CRC Press
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Contents
Preface xv
Acknowledgments xix
AbouttheAuthor xxi
I TheBasics 1
1 WhyUseRegressionModels? 3
1.1 WhyUseSimpleRegressionModels? 3
1.2 WhyUseMultipleRegressionModels? 4
1.3 SomeBasicNotation 6
2 AnIntroductoryExample 9
2.1 ASingleLineModel 9
2.2 FittingaSingleLineModel 11
2.3 TakingUncertaintyintoAccount 13
2.4 ATwo-LineModel 14
2.5 HowtoPerformTheseStepswithStata 17
2.6 Exercise5-HIAAandSerotonin 19
2.7 ExerciseHaemoglobin 19
2.8 ExerciseScalingofVariables 19
3 TheClassicalMultipleRegressionModel 21
4 AdjustedEffects 23
4.1 AdjustingforConfounding 23
4.2 AdjustingforImbalances 26
4.3 ExercisePhysicalActivityinSchoolchildren 27
5 InferencefortheClassicalMultipleRegressionModel 29
5.1 TheTraditionalandtheModernWayofInference 29
5.2 HowtoPerformtheModernWayofInferencewithStata 34
5.3 HowValidandGoodareLeastSquaresEstimates? 35
5.4 A Note on the Use and Interpretation of p-Values in Regression
Analyses 35
vii
viii
6 LogisticRegression 39
6.1 TheDefinitionoftheLogisticRegressionModel 39
6.2 AnalysingaDoseResponseExperimentbyLogisticRegression 40
6.3 HowtoFitaDoseResponseModelwithStata 44
6.4 EstimatingOddsRatiosandAdjustedOddsRatiosUsingLogistic
Regression 45
6.5 HowtoCompute(Adjusted)OddsRatiosUsingLogisticRegression
inStata 49
6.6 ExerciseAllergyinChildren 50
6.7 MoreonLogitScaleandOddsScale 51
7 InferencefortheLogisticRegressionModel 55
7.1 TheMaximumLikelihoodPrinciple 55
7.2 PropertiesoftheMLEstimatesforLogisticRegression 56
7.3 InferenceforaSingleRegressionParameter 57
7.4 HowtoPerformWaldTestsandLikelihoodRatioTestsinStata 58
8 CategoricalCovariates 63
8.1 IncorporatingCategoricalCovariatesinaRegressionModel 63
8.2 SomeTechnicalitiesinUsingCategoricalCovariates 65
8.3 TestingtheEffectofaCategoricalCovariate 67
8.4 TheHandlingofCategoricalCovariatesinStata 68
8.5 PresentingResultsofaRegressionAnalysisInvolvingCategorical
CovariatesinaTable 73
8.6 ExercisePhysicalOccupationandBackPain 76
8.7 ExerciseOddsRatiosandCategoricalcovariates 77
9 HandlingOrderedCategories:AFirstLessoninRegressionModelling
Strategies 79
10 TheCoxProportionalHazardsModel 85
10.1 ModellingtheRiskofDying 85
10.2 ModellingtheRiskofDyinginContinuousTime 87
10.3 UsingtheCoxProportionalHazardsModeltoQuantifytheDiffer-
enceinSurvivalBetweenGroups 90
10.4 HowtoFitaCoxProportionalHazardsModelwithStata 91
10.5 ExercisePrognosticFactorsinBreastCancerPatients—Part1 94
11 CommonPitfallsinUsingRegressionModels 97
11.1 AssociationversusCausation 97
11.2 DifferencebetweenSubjectsversusDifferencewithinSubjects 99
11.3 Real-WorldModelsversusStatisticalModels 100
11.4 RelevanceversusSignificance 102
11.5 ExercisePrognosticFactorsinBreastCancerPatients—Part2 104
ix
II AdvancedTopicsandTechniques 107
12 SomeUsefulTechnicalities 109
12.1 IllustratingModelsbyUsingModel-BasedPredictions 109
12.2 HowtoWorkwithPredictionsinStata 110
12.3 ResidualsandtheStandardDeviationoftheErrorTerm 116
12.4 WorkingwithResidualsandtheRMSEinStata 118
12.5 LinearandNonlinearFunctionsofRegressionParameters 119
12.6 TransformationsofRegressionParameters 120
12.7 CenteringofCovariateValues 121
12.8 ExercisePaternalSmokingversusMaternalSmoking 122
13 ComparingRegressionCoefficients 123
13.1 ComparingRegressionCoefficientsamongContinuousCovariates 123
13.2 ComparingRegressionCoefficientsamongBinaryCovariates 127
13.3 MeasuringtheImpactofChangingCovariateValues 128
13.4 TranslatingRegressionCoefficients 130
13.5 HowtoCompareRegressionCoefficientsinStata 131
13.6 ExerciseHealthinYoungPeople 137
14 PowerandSampleSize 139
14.1 ThePowerofaRegressionAnalysis 139
14.2 DeterminantsofPowerinRegressionModelswithaSingleCovariate 140
14.3 DeterminantsofPowerinRegressionModelswithSeveralCovari-
ates 148
14.4 Power and Sample Size Calculations When a Sample from the
CovariateDistributionIsGiven 152
14.5 Power and Sample Size Calculations Given a Sample from the
CovariateDistributionwithStata 154
14.6 TheChoiceoftheValuesoftheRegressionParametersinaSimula-
tionStudy 165
14.7 SimulatingaCovariateDistribution 166
14.8 SimulatingaCovariateDistributionwithStata 169
14.9 ChoosingtheParameterstoSimulateaCovariateDistribution 177
14.10NecessarySampleSizestoJustifyAsymptoticMethods 178
14.11ExercisePowerConsiderationsforaStudyonNeckPain 178
14.12ExerciseChoosingbetweenTwoOutcomes 179
15 SelectionoftheSample 181
15.1 SelectioninDependenceontheCovariates 181
15.2 SelectioninDependenceontheOutcome 183
15.3 SamplinginDependenceonCovariateValues 185
16 SelectionofCovariates 187
16.1 FittingRegressionModelswithCorrelatedCovariates 187
16.2 The“AdjustmentversusPower”Dilemma 189