# Applied Surrogate Endpoint Evaluation Methods with SAS and R

PrefaceIntroductionOverview of Surrogate Endpoint EvaluationIndividual-Level versus Trial-Level SurrogacyEarly Successes with SurrogatesEarly Failures with SurrogatesWhy Surrogate Endpoints Are Important TodayThe Need for Statistical Evaluation of SurrogatesSurrogate Evaluation and Data TransparencyTypical Uses of Surrogate EndpointsEarlier Clinical EndpointsMultiple Rating ScalesMore Sensitive Clinical EndpointsBiomarker-Based SurrogatesRegulatory Use for Accelerated ApprovalHealth Technology AssessmentStructure of This BookNotation and Example DatasetsNotationExample DatasetsThe Age-Related Macular Degeneration (ARMD) TrialFive Clinical Trials in SchizophreniaAdvanced Ovarian Cancer: A Meta-Analysis of Four Clinical TrialsAdvanced Colorectal Cancer: A Meta-Analysis of 25 TrialsAdvanced Colorectal Cancer: A Meta-Analysis of 13 TrialsAdvanced Gastric Cancer: A Meta-Analysis of 20 TrialsAdvanced Prostate Cancer: A Meta-Analysis of Two TrialsAcknowledgments for Use of DataThe History of Surrogate Endpoint Evaluation: Single-Trial MethodsIntroductionPrentice’s ApproachDefinitionAnalysis of Case Studies: The Age-Related Macular Degeneration TrialAn Appraisal of Prentice’s ApproachThe Proportion of Treatment Effect ExplainedDefinitionAnalysis of Case Studies: The Age-Related Macular Degeneration TrialAn Appraisal of the Proportion ExplainedThe Relative Effect and Adjusted AssociationDefinitionAnalysis of Case Studies: The Age-Related Macular Degeneration TrialAn Appraisal of the Adjusted Association and the Relative EffectIssues with the Adjusted AssociationIssues with the Relative EffectShould the Single-Trial Methods Be Used in Practice?II Contemporary Surrogate Endpoint Evaluation Methods: Multiple-Trial MethodsTwo Continuous OutcomesIntroductionThe Meta-Analytic FrameworkTrial-Level SurrogacyIndividual-Level SurrogacySimplified Model-Fitting StrategiesThe Trial Dimension: Fixed- versus Random-Effects ModelsThe Model Dimension: Full versus Reduced ModelsThe Endpoint Dimension: Univariate versus Bivariate ModelsThe Measurement Error Dimension: Weighted versus Unweighted ModelsGeneral Considerations in the Multiple-Trial SettingThe choice of trial-level unitsThe coding of the treatment effectA “good” surrogatePrediction of Treatment Effect: Surrogate Threshold Effect (STE)Case Study: The Age-Related Macular Degeneration TrialTrial-level surrogacyIndividual-level surrogacyTwo Failure-Time EndpointsIntroductionTheoretical BackgroundIndividual-level surrogacyTrial-level surrogacyAnalysis of Case StudiesUsing SASCopula-Based ModelsMarginal ModelsUsing RConcluding RemarksA Categorical (Ordinal) and a Failure- Time EndpointIntroductionTheoretical BackgroundAnalysis of a Case StudyUsing SASFour-Category Tumor ResponseBinary Tumor ResponseUsing RConcluding RemarksAppendixA Continuous (Normally-Distributed) and a Failure-Time EndpointIntroductionTheoretical BackgroundAnalysis of a Case StudyUsing SASCopula-Based ModelsMarginal ModelsUsing RConcluding RemarksAppendixA Longitudinal (Normally Distributed) and a Failure-Time EndpointIntroductionTheoretical BackgroundAnalysis of a Case StudyUsing SASJoint-Model-Based AnalysisMarginal ModelsUsing RConcluding RemarksEvaluation of Surrogate Endpoints from an Information-Theoretic PerspectiveIntroductionAn Information-Theoretic UnificationInformation-Theoretic Approach: Trial LevelPlausibility of Finding a Valid Surrogate: Trial LevelEstimating R21Asymptotic Confidence Interval for RhInformation-Theoretic Approach: Individual-Level SurrogacyGeneral SettingS and T Both ContinuousCase Study Analysis: The Age-Related Macular Degeneration TrialS and T LongitudinalAsymptotic Confidence Interval for RiRemarksS and T Time-to-Event VariablesEstimating Rh indCase Study Analysis: Four Ovarian Cancer TrialsS and T: Binary-Binary or Continuous-BinaryCase Study Analysis: Five Trials in SchizophreniaThe binary-binary settingTwo Categorical EndpointsIntroductionS and T: Binary-OrdinalInformation-Theoretic ApproachIndividual-Level Surrogacy: Binary-OrdinalTrial-Level Surrogacy: Binary-Ordinal SettingConfidence IntervalsComputational AspectsSeparation: Categorical VariablesSeparation: Binary VariablesSeparation: Ordinal VariablesImpact of Separation on Surrogate EvaluationSolution to Separation IssuesSeparation: Final ConsiderationsSurrogate Package: Binary-Ordinal SettingCase Study Analysis: Five Trials in SchizophreniaSummary: Binary-Ordinal SettingS and T: Ordinal-Binary or Ordinal-OrdinalInformation-Theoretic ApproachIndividual-Level Surrogacy: Ordinal-Binary or Ordinal- Ordinal SettingsTrial-Level Surrogacy: Ordinal-Binary or Ordinal-Ordinal SettingsComputational AspectsSeparation: Ordinal-Binary/Ordinal SettingSummary: Ordinal-Binary or Ordinal-Ordinal SettingConcluding RemarksIII Software Tools SAS SoftwareIntroductionGeneral Structure of the SAS Macros Available for the Analysis of Surrogate EndpointsValidation of Surrogacy Using a Joint Modeling Approach for Two Normally Distributed EndpointsThe Full Fixed-Effects ModelModel FormulationSensitivity Analysis: Leave-One-Out EvaluationThe SAS Macro %CONTCONTFULLData Analysis and OutputSAS Code for the First StepSAS Code for the Second StepThe Reduced Fixed-Effects ModelModel FormulationThe SAS Macro %CONTCONTREDData Analysis and OutputSAS Code for the First StepThe Full Mixed-Effects ModelThe SAS Macro %CONTRANFULLData Analysis and OutputSAS Code for the Full Mixed-Effects ModelReduced Mixed-Effects ModelThe SAS Macro %CONTRANREDData Analysis and OutputSAS Code for the Reduced Mixed-Effects ModelAnalysis for a Surrogacy Setting with Two Survival EndpointsA Two-Stage Approach (I)The SAS Macro %TWOSTAGECOXData Analysis and OutputSAS Code for the First-Stage ModelA Two-Stage Approach (II)The SAS Macro %TWOSTAGEKMSAS Code for Trial-Specific KM Estimates (at a Given Time Point)A Joint Model for Survival EndpointsThe SAS Macro '/.COPULAValidation Using Joint Modeling of a Time-to- Event and a Binary EndpointData StructureThe SAS Macro %SURVBINData Analysis and OutputThe SAS Macro °/„SURVCATA Continuous (Normally Distributed) and a Survival EndpointModel FormulationData StructureThe SAS Macro °/„NORMSURVData Analysis and OutputValidation Using a Joint Model for Continuous and Binary EndpointsData StructureThe SAS Macro %NORMALBINData Analysis and OutputSAS Code for the First-Stage ModelValidation Using a Joint Model for Two Binary EndpointsData StructureThe SAS Macro %BINBINData Analysis and OutputSAS Code for the First-Stage ModelValidation Using the Information-Theory ApproachIndividual-Level SurrogacyTrial-Level SurrogacyEvaluation of Surrogate Endpoint for Two Continuous EndpointsThe SAS Macro %NORMNORMINFOData Analysis and OutputEvaluation of Surrogacy for Survival and Binary EndpointsThe SAS Macro %SURVBININFOOther Surrogacy SettingsThe R Package SurrogateIntroductionTwo Normally Distributed EndpointsThe Meta-Analytic FrameworkAnalyzing the Age-Related Macular Degeneration DatasetThe Information-Theoretic FrameworkAnalyzing the Age-Related Macular Degeneration DatasetTwo Time-to-Event EndpointsAnalyzing the Ovarian Cancer DatasetTwo Binary EndpointsAnalyzing the Data of Five Clinical Trials in SchizophreniaA Binary and a Normally Distributed EndpointAnalyzing the Data of Five Clinical Trials in SchizophreniaEstimation of Trial-Level Surrogacy When Only Trial-Level Data Are AvailableAnalyzing Ten Hypothetical TrialsCloud ComputingThe Surrogate Shiny AppTwo Continuous Endpoints: The Reduced Fixed- Effects ModelTwo Time-to-Event Endpoints: A Two-Stage ApproachInformation-Theoretic ApproachIndividual- and Trial-Level SurrogacyInformation-Theoretic Approach for Two Continuous EndpointsInformation-Theoretic Approach for Two Binary EndpointsIV Additional Considerations and Further Topics Surrogate Endpoints in Rare DiseasesIntroductionConvergence Problems in Fitting Linear Mixed- Effects ModelsA Simulation StudySimulation scenariosBalance in cluster sizeOutcomes of interestResultsModel Convergence Issues and Multiple ImputationA Simulation StudyCase StudiesThe Age-Related Macular Degeneration TrialFive Clinical Trials in SchizophreniaA Formal Basis for the Two-Stage ApproachHigh-Dimensional Biomarkers in Drug Discovery: The QSTAR FrameworkIntroduction: From a Single Trial to a HighDimensional SettingThe QSTAR Framework and SurrogacyDataThe ROS1 ProjectThe EGFR ProjectGraphical Interpretation (I): The Association between a Gene and Bioactivity Accounting for the Effect of a Fingerprint FeatureModeling ApproachThe Joint ModelInferenceGraphical Interpretation (II): Adjusted Association and Conditional IndependenceAnalysis of the EGFR and the ROS1 ProjectsApplication to the EGFR Pro jectApplication to the ROS1 ProjectThe R Package IntegratedJMIdentification of BiomarkersAnalysis of One Gene Using the gls FunctionThe IntegratedJM Shiny AppConcluding RemarksEvaluation of Magnetic Resonance Imaging as a Biomarker in Alzheimer’s DiseaseIntroductionAlzheimer’s DiseaseMagnetic Resonance Imaging and Histology ParametersThe AD Mouse Model for MRI and Histology DataTwo Levels of SurrogacyEvaluation of MRI Parameters as a Biomarker for Histology FeaturesA Joint Model for MRI and HistologyGenotype-Specific Individual-Level SurrogacyDisease-Level Surrogacythe MRI Project Data: Examples of Region- Specific ModelsThe Motor Cortex: GFAP Staining and MRI-AKThe Caudate-Putamen: GFAP Staining and MRI-AKThe Surrogacy Map of the BrainImplementation in SASData StructureAge-Specific Parameters for Histology in the Wildtype ModelImplementation in RCommon Parameter for Histology in the Wildtype GroupAge-Specific Parameters for Histology in the Wild- type GroupConcluding Remarks