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Applied Surrogate Endpoint Evaluation Methods with SAS and R
Preface
Introduction
Overview of Surrogate Endpoint Evaluation
Individual-Level versus Trial-Level Surrogacy
Early Successes with Surrogates
Early Failures with Surrogates
Why Surrogate Endpoints Are Important Today
The Need for Statistical Evaluation of Surrogates
Surrogate Evaluation and Data Transparency
Typical Uses of Surrogate Endpoints
Earlier Clinical Endpoints
Multiple Rating Scales
More Sensitive Clinical Endpoints
Biomarker-Based Surrogates
Regulatory Use for Accelerated Approval
Health Technology Assessment
Structure of This Book
Notation and Example Datasets
Notation
Example Datasets
The Age-Related Macular Degeneration (ARMD) Trial
Five Clinical Trials in Schizophrenia
Advanced Ovarian Cancer: A Meta-Analysis of Four Clinical Trials
Advanced Colorectal Cancer: A Meta-Analysis of 25 Trials
Advanced Colorectal Cancer: A Meta-Analysis of 13 Trials
Advanced Gastric Cancer: A Meta-Analysis of 20 Trials
Advanced Prostate Cancer: A Meta-Analysis of Two Trials
Acknowledgments for Use of Data
The History of Surrogate Endpoint Evaluation: Single-Trial Methods
Introduction
Prentice’s Approach
Definition
Analysis of Case Studies: The Age-Related Macular Degeneration Trial
An Appraisal of Prentice’s Approach
The Proportion of Treatment Effect Explained
Definition
Analysis of Case Studies: The Age-Related Macular Degeneration Trial
An Appraisal of the Proportion Explained
The Relative Effect and Adjusted Association
Definition
Analysis of Case Studies: The Age-Related Macular Degeneration Trial
An Appraisal of the Adjusted Association and the Relative Effect
Issues with the Adjusted Association
Issues with the Relative Effect
Should the Single-Trial Methods Be Used in Practice?
II Contemporary Surrogate Endpoint Evaluation Methods: Multiple-Trial Methods
Two Continuous Outcomes
Introduction
The Meta-Analytic Framework
Trial-Level Surrogacy
Individual-Level Surrogacy
Simplified Model-Fitting Strategies
The Trial Dimension: Fixed- versus Random-Effects Models
The Model Dimension: Full versus Reduced Models
The Endpoint Dimension: Univariate versus Bivariate Models
The Measurement Error Dimension: Weighted versus Unweighted Models
General Considerations in the Multiple-Trial Setting
The choice of trial-level units
The coding of the treatment effect
A “good” surrogate
Prediction of Treatment Effect: Surrogate Threshold Effect (STE)
Case Study: The Age-Related Macular Degeneration Trial
Trial-level surrogacy
Individual-level surrogacy
Two Failure-Time Endpoints
Introduction
Theoretical Background
Individual-level surrogacy
Trial-level surrogacy
Analysis of Case Studies
Using SAS
Copula-Based Models
Marginal Models
Using R
Concluding Remarks
A Categorical (Ordinal) and a Failure- Time Endpoint
Introduction
Theoretical Background
Analysis of a Case Study
Using SAS
Four-Category Tumor Response
Binary Tumor Response
Using R
Concluding Remarks
Appendix
A Continuous (Normally-Distributed) and a Failure-Time Endpoint
Introduction
Theoretical Background
Analysis of a Case Study
Using SAS
Copula-Based Models
Marginal Models
Using R
Concluding Remarks
Appendix
A Longitudinal (Normally Distributed) and a Failure-Time Endpoint
Introduction
Theoretical Background
Analysis of a Case Study
Using SAS
Joint-Model-Based Analysis
Marginal Models
Using R
Concluding Remarks
Evaluation of Surrogate Endpoints from an Information-Theoretic Perspective
Introduction
An Information-Theoretic Unification
Information-Theoretic Approach: Trial Level
Plausibility of Finding a Valid Surrogate: Trial Level
Estimating R21
Asymptotic Confidence Interval for Rh
Information-Theoretic Approach: Individual-Level Surrogacy
General Setting
S and T Both Continuous
Case Study Analysis: The Age-Related Macular Degeneration Trial
S and T Longitudinal
Asymptotic Confidence Interval for Ri
Remarks
S and T Time-to-Event Variables
Estimating Rh ind
Case Study Analysis: Four Ovarian Cancer Trials
S and T: Binary-Binary or Continuous-Binary
Case Study Analysis: Five Trials in Schizophrenia
The binary-binary setting
Two Categorical Endpoints
Introduction
S and T: Binary-Ordinal
Information-Theoretic Approach
Individual-Level Surrogacy: Binary-Ordinal
Trial-Level Surrogacy: Binary-Ordinal Setting
Confidence Intervals
Computational Aspects
Separation: Categorical Variables
Separation: Binary Variables
Separation: Ordinal Variables
Impact of Separation on Surrogate Evaluation
Solution to Separation Issues
Separation: Final Considerations
Surrogate Package: Binary-Ordinal Setting
Case Study Analysis: Five Trials in Schizophrenia
Summary: Binary-Ordinal Setting
S and T: Ordinal-Binary or Ordinal-Ordinal
Information-Theoretic Approach
Individual-Level Surrogacy: Ordinal-Binary or Ordinal- Ordinal Settings
Trial-Level Surrogacy: Ordinal-Binary or Ordinal-Ordinal Settings
Computational Aspects
Separation: Ordinal-Binary/Ordinal Setting
Summary: Ordinal-Binary or Ordinal-Ordinal Setting
Concluding Remarks
III Software Tools
SAS Software
Introduction
General Structure of the SAS Macros Available for the Analysis of Surrogate Endpoints
Validation of Surrogacy Using a Joint Modeling Approach for Two Normally Distributed Endpoints
The Full Fixed-Effects Model
Model Formulation
Sensitivity Analysis: Leave-One-Out Evaluation
The SAS Macro %CONTCONTFULL
Data Analysis and Output
SAS Code for the First Step
SAS Code for the Second Step
The Reduced Fixed-Effects Model
Model Formulation
The SAS Macro %CONTCONTRED
Data Analysis and Output
SAS Code for the First Step
The Full Mixed-Effects Model
The SAS Macro %CONTRANFULL
Data Analysis and Output
SAS Code for the Full Mixed-Effects Model
Reduced Mixed-Effects Model
The SAS Macro %CONTRANRED
Data Analysis and Output
SAS Code for the Reduced Mixed-Effects Model
Analysis for a Surrogacy Setting with Two Survival Endpoints
A Two-Stage Approach (I)
The SAS Macro %TWOSTAGECOX
Data Analysis and Output
SAS Code for the First-Stage Model
A Two-Stage Approach (II)
The SAS Macro %TWOSTAGEKM
SAS Code for Trial-Specific KM Estimates (at a Given Time Point)
A Joint Model for Survival Endpoints
The SAS Macro '/.COPULA
Validation Using Joint Modeling of a Time-to- Event and a Binary Endpoint
Data Structure
The SAS Macro %SURVBIN
Data Analysis and Output
The SAS Macro °/„SURVCAT
A Continuous (Normally Distributed) and a Survival Endpoint
Model Formulation
Data Structure
The SAS Macro °/„NORMSURV
Data Analysis and Output
Validation Using a Joint Model for Continuous and Binary Endpoints
Data Structure
The SAS Macro %NORMALBIN
Data Analysis and Output
SAS Code for the First-Stage Model
Validation Using a Joint Model for Two Binary Endpoints
Data Structure
The SAS Macro %BINBIN
Data Analysis and Output
SAS Code for the First-Stage Model
Validation Using the Information-Theory Approach
Individual-Level Surrogacy
Trial-Level Surrogacy
Evaluation of Surrogate Endpoint for Two Continuous Endpoints
The SAS Macro %NORMNORMINFO
Data Analysis and Output
Evaluation of Surrogacy for Survival and Binary Endpoints
The SAS Macro %SURVBININFO
Other Surrogacy Settings
The R Package Surrogate
Introduction
Two Normally Distributed Endpoints
The Meta-Analytic Framework
Analyzing the Age-Related Macular Degeneration Dataset
The Information-Theoretic Framework
Analyzing the Age-Related Macular Degeneration Dataset
Two Time-to-Event Endpoints
Analyzing the Ovarian Cancer Dataset
Two Binary Endpoints
Analyzing the Data of Five Clinical Trials in Schizophrenia
A Binary and a Normally Distributed Endpoint
Analyzing the Data of Five Clinical Trials in Schizophrenia
Estimation of Trial-Level Surrogacy When Only Trial-Level Data Are Available
Analyzing Ten Hypothetical Trials
Cloud Computing
The Surrogate Shiny App
Two Continuous Endpoints: The Reduced Fixed- Effects Model
Two Time-to-Event Endpoints: A Two-Stage Approach
Information-Theoretic Approach
Individual- and Trial-Level Surrogacy
Information-Theoretic Approach for Two Continuous Endpoints
Information-Theoretic Approach for Two Binary Endpoints
IV Additional Considerations and Further Topics
Surrogate Endpoints in Rare Diseases
Introduction
Convergence Problems in Fitting Linear Mixed- Effects Models
A Simulation Study
Simulation scenarios
Balance in cluster size
Outcomes of interest
Results
Model Convergence Issues and Multiple Imputation
A Simulation Study
Case Studies
The Age-Related Macular Degeneration Trial
Five Clinical Trials in Schizophrenia
A Formal Basis for the Two-Stage Approach
High-Dimensional Biomarkers in Drug Discovery: The QSTAR Framework
Introduction: From a Single Trial to a HighDimensional Setting
The QSTAR Framework and Surrogacy
Data
The ROS1 Project
The EGFR Project
Graphical Interpretation (I): The Association between a Gene and Bioactivity Accounting for the Effect of a Fingerprint Feature
Modeling Approach
The Joint Model
Inference
Graphical Interpretation (II): Adjusted Association and Conditional Independence
Analysis of the EGFR and the ROS1 Projects
Application to the EGFR Pro ject
Application to the ROS1 Project
The R Package IntegratedJM
Identification of Biomarkers
Analysis of One Gene Using the gls Function
The IntegratedJM Shiny App
Concluding Remarks
Evaluation of Magnetic Resonance Imaging as a Biomarker in Alzheimer’s Disease
Introduction
Alzheimer’s Disease
Magnetic Resonance Imaging and Histology Parameters
The AD Mouse Model for MRI and Histology Data
Two Levels of Surrogacy
Evaluation of MRI Parameters as a Biomarker for Histology Features
A Joint Model for MRI and Histology
Genotype-Specific Individual-Level Surrogacy
Disease-Level Surrogacy
the MRI Project Data: Examples of Region- Specific Models
The Motor Cortex: GFAP Staining and MRI-AK
The Caudate-Putamen: GFAP Staining and MRI-AK
The Surrogacy Map of the Brain
Implementation in SAS
Data Structure
Age-Specific Parameters for Histology in the Wildtype Model
Implementation in R
Common Parameter for Histology in the Wildtype Group
Age-Specific Parameters for Histology in the Wild- type Group
Concluding Remarks
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