Analysis of Correlated Data with SAS and R

514 Pages·2018·8.23 MB·English

by  Mohamed M. Shoukri

Analysis of Correlated
Data with SAS and R
Fourth Edition
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Analysis of Correlated
Data with SAS and R
Fourth Edition
Mohamed M. Shoukri
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Names:Shoukri,M.M.(MohamedM.),author.|Shoukri,M.M.(MohamedM.).
AnalysisofcorrelateddatawithSASandR.
Title:StatisticalanalysisofhealthdatausingSASandR/MohamedM.Shoukri.
Description:Fourthedition.|BocaRaton:CRCPress,2018.|Previousedition:
AnalysisofcorrelateddatawithSASandR/MohamedM.Shoukri
(BocaRaton:Chapman&Hall/CRC,2007).
Identifiers:LCCN2017050107|ISBN9781138197459(hardback)
Subjects:LCSH:Epidemiology–Statisticalmethods.|Mathematical
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To my loving wife Suhair.
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Contents
Preface.....................................................................................................................xv
1. Study Designs andMeasures ofEffect Size..............................................1
1.1 Study Designs........................................................................................1
1.1.1 Introduction..............................................................................1
1.1.2 Nonexperimental orObservational Studies........................2
1.1.3 Types of Nonexperimental Designs......................................2
1.1.3.1 Descriptive/Exploratory Survey Studies.............2
1.1.3.2 Correlational Studies(Ecological Studies)...........2
1.1.3.3 Cross-Sectional Studies...........................................3
1.1.3.4 Longitudinal Studies...............................................3
1.1.3.5 Prospective or Cohort Studies...............................3
1.1.3.6 Case-Control Studies..............................................4
1.1.3.7 Nested Case-Control Study...................................5
1.1.3.8 Case-Crossover Study.............................................6
1.1.4 Quasi-Experimental Designs..................................................7
1.1.5 Single-Subject Design (SSD)...................................................7
1.1.6 Quality ofDesigns...................................................................8
1.1.7 Confounding............................................................................8
1.1.8 Sampling...................................................................................9
1.1.9 Types of SamplingStrategies................................................9
1.1.10 Summary................................................................................10
1.2 Effect Size..............................................................................................11
1.2.1 What IsEffectSize?...............................................................11
1.2.2 Why Report Effect Sizes?......................................................11
1.2.3 Measures ofEffectSize.........................................................13
1.2.4 What IsMeant by “Small,”“Medium,”and“Large”?....13
1.2.5 Summary................................................................................15
1.2.6 American Statistical Association (ASA) Statement
about the p-value...................................................................15
Exercises..........................................................................................................17
2. ComparingGroup MeansWhen the StandardAssumptions
Are Violated...................................................................................................19
2.1 Introduction.........................................................................................19
2.2 Nonnormality.......................................................................................20
vii
viii Contents
2.3 Heterogeneity of Variances................................................................23
2.3.1 Bartlett’sTest..........................................................................24
2.3.2 Levene’sTest (1960)..............................................................27
2.4 Testing Equality ofGroup Means.....................................................27
2.4.1 Welch’sStatistic (1951).........................................................27
2.4.2 Brown and Forsythe Statistic (1974b) for Testing
Equality ofGroup Means.....................................................28
2.4.3 Cochran’s(1937) Method of Weighing forTesting
Equality ofGroup Means.....................................................29
2.5 Nonindependence...............................................................................32
2.6 Nonparametric Tests...........................................................................35
2.6.1 Nonparametric Analysis ofMilk Data Using SAS...........36
3. Analyzing Clustered Data...........................................................................43
3.1 Introduction.........................................................................................43
3.2 The Basic Feature ofCluster Data....................................................44
3.3 Effect ofOne Measured Covariate onEstimation
ofthe Intracluster Correlation...........................................................48
3.4 Samplingand Design Issues..............................................................52
3.4.1 Comparison ofMeans...........................................................52
3.5 Regression Analysis forClustered Data..........................................56
3.6 Generalized Linear Models................................................................60
3.6.1 Marginal Models (Population Average Models)..............61
3.6.2 Random Effects Models........................................................61
3.6.3 Generalized Estimating Equation (GEE)............................62
3.7 Fitting Alternative Models forClustered Data...............................64
3.7.1 Proc Mixed forClustered Data...........................................66
3.7.2 Model 1:Unconditional Means Model...............................66
3.7.3 Model 2:Including aFamily LevelCovariate..................67
3.7.4 Model 3:Including the Sib-Level Covariate......................69
3.7.5 Model 4:Including One FamilyLevel Covariate
and Two Subject Level Covariates.....................................70
Appendix.........................................................................................................72
Exercises..........................................................................................................74
4. Statistical Analysis ofCross-Classified Data...........................................79
4.1 Introduction.........................................................................................79
4.2 Measures of Association in 2×2 Tables.........................................80
4.2.1 Absolute Risk.........................................................................80
4.2.2 Risk Difference.......................................................................81
4.2.3 Attributable Risk...................................................................81
4.2.4 Relative Risk...........................................................................81
4.2.5 Odds Ratio..............................................................................81
4.2.6 Relationship between OddsRatio and Relative Risk......82
Contents ix
4.2.7 Incidence Rate and Incidence Rate Ratio AsaMeasure
of Effect Size...........................................................................82
4.2.8 What IsPerson-Time?...........................................................82
4.3 Statistical Analysis from the2 ×2Classification Data..................84
4.3.1 Cross-Sectional Sampling.....................................................84
4.3.2 Cohort and Case-Control Studies.......................................87
4.4 Statistical Inference on OddsRatio..................................................88
4.4.1 Significance Tests...................................................................90
4.4.2 Interval Estimation................................................................94
4.5 Analysis ofSeveral 2× 2Contingency Tables................................94
4.5.1 Test ofHomogeneity.............................................................97
4.5.2 Significance Testof CommonOdds Ratio.........................98
4.5.3 Confidence Interval onthe Common OddsRatio..........102
4.6 Analysis ofMatched Pairs (One Case and One Control)............103
4.6.1 Estimating the OddsRatio.................................................104
4.6.2 Testing the Equality ofMarginal Distributions..............106
4.7 Statistical Analysis ofClustered Binary Data...............................108
4.7.1 Approaches toAdjust the Pearson’s Chi-Square............110
4.7.2 Donner andDonald Adjustment......................................110
4.7.3 Procedures Basedon Ratio EstimateTheory..................110
4.7.4 Confidence Interval Construction.....................................111
4.7.5 Adjusted Chi-Square forStudies Involving More
than Two Groups................................................................114
4.8 Inference onthe Common OddsRatio..........................................121
4.8.1 Donald and Donner’sAdjustment....................................121
4.8.2 Rao andScott’sAdjustment...............................................123
4.9 Calculations ofRelative andAttributable Risks
from Clustered Binary Data............................................................130
4.10 Sample Size Requirements forClustered BinaryData................131
4.10.1 Paired-Sample Design.........................................................131
4.10.2 Comparative Studiesfor Cluster Sizes Greater
or Equalto Two...................................................................132
4.11 Discussion...........................................................................................133
Exercises........................................................................................................134
5. Modeling BinaryOutcome Data..............................................................141
5.1 Introduction.......................................................................................141
5.2 The Logistic Regression Model.......................................................143
5.3 Coding Categorical Explanatory Variables and Interpretation
ofCoefficients....................................................................................146
5.4 Interaction andConfounding inLogistic Regression..................150
5.5 The Goodness of Fit andModel Comparisons.............................155
5.5.1 The Pearson’sc2Statistic...................................................155
5.5.2 The Likelihood RatioCriterion (Deviance)......................155