Quantitative Methods in Pharmaceutical Research and Development: Concepts and Applications

Preface
Contents
Chapter 1: Biostatistics in Clinical Trials
	1.1 Introduction
		1.1.1 What Is Biostatistics
		1.1.2 Basic Biostatistics Principals for Clinical Trials
			1.1.2.1 Population and Sample
			1.1.2.2 Sampling Error and Bias
			1.1.2.3 Choice of Control
			1.1.2.4 Randomization and Allocation
			1.1.2.5 Blinding
			1.1.2.6 Sample Size
			1.1.2.7 Statistical Significance and Clinical Significance
			1.1.2.8 Role of Biostatistics and Biostatisticians in Clinical Development
	1.2 Phases of Clinical Development and Design Types
		1.2.1 Phases of Clinical Development
		1.2.2 Clinical Trial Designs
			1.2.2.1 Parallel Group Designs
			1.2.2.2 Factorial Designs
			1.2.2.3 Crossover Designs
			1.2.2.4 Enrichment Designs
			1.2.2.5 Group Sequential and Adaptive Designs
	1.3 Statistical Methods
		1.3.1 Basic Principals of Probability and Inference
			1.3.1.1 Probability Distributions
				Normal Distribution
				Binomial Distribution
				Multinomial Distribution
				Poisson and Negative Binomial Distribution
			1.3.1.2 Statistical Estimation
			1.3.1.3 Statistical Inference
		1.3.2 Linear Regression and Generalized Linear Models
			1.3.2.1 Linear Regression Model
			1.3.2.2 Generalized Linear Models
				Logistic Regression for Binary Responses
				Log-Linear Regression for Counts
				Overdispersion
				Model Selection
		1.3.3 Applied Longitudinal Analysis
			1.3.3.1 Mean Response Profiles for Continuous Longitudinal Data
			1.3.3.2 Parametric Curve Models for Continuous Response
			1.3.3.3 Modeling the Covariance
			1.3.3.4 Linear Mixed Effects Models
		1.3.4 Analysis of Time-to-Event Outcome
			1.3.4.1 Kaplan-Meier Survival Curves and the Log-Rank Test
			1.3.4.2 The Cox Proportional Hazards Model and Its Characteristics
	1.4 Important Considerations in Clinical Trials
		1.4.1 Missing Data and Patient Retention
		1.4.2 Multiple Objectives and Multiplicity Adjustments
		1.4.3 Subgroup Analysis
		1.4.4 Multiregional Trials
		1.4.5 Safety Evaluation
	1.5 Concluding Remarks
	References
Chapter 2: Pharmacometrics: A Quantitative Decision-Making Tool in Drug Development
	2.1 Background
		2.1.1 What Is Pharmacometrics
		2.1.2 Evolution of Pharmacometrics
		2.1.3 Role of Pharmacometrics in Drug Development
	2.2 Pharmacometric Analysis Approaches
		2.2.1 PK Models
		2.2.2 PK/PD Models
			2.2.2.1 Basic Concentration-Effect Relationships
			2.2.2.2 Direct Effect
			2.2.2.3 Link/Effect Compartment Model
			2.2.2.4 Indirect Response/Turnover Model
		2.2.3 Emerging Approaches
			2.2.3.1 Physiologically Based PK Modeling
			2.2.3.2 Quantitative Systems Pharmacology
			2.2.3.3 Model-Based Meta-analysis
	2.3 Pharmacometric Analysis Methodology
		2.3.1 Software
		2.3.2 Pharmacometric Analysis Work Flow
		2.3.3 Model Development
			2.3.3.1 Structural Model
			2.3.3.2 Statistical Model
			2.3.3.3 Covariate Model
		2.3.4 Model Evaluation and Qualification
		2.3.5 Simulation
			2.3.5.1 Stochastic Simulation
			2.3.5.2 Parameter Uncertainty
			2.3.5.3 Simulation Approach Selection
	2.4 Case Studies
		2.4.1 Translational Development
		2.4.2 Early Clinical Development
		2.4.3 Late Clinical Development
		2.4.4 Pediatric Development
	2.5 Concluding Remark
	References
Chapter 3: Genomics and Bioinformatics in Biological Discovery and Pharmaceutical Development
	3.1 Introduction: Bioinformatics-A Confluence of Molecular Biology, Genetics, Statistics, and Computing
		3.1.1 What Is Bioinformatics
		3.1.2 Two Sides of the Same Coin: Genomics and Proteomics
		3.1.3 Important Concepts
	3.2 Pharmaceutical Analytics
		3.2.1 Bioinformatics in Clinical Practice
		3.2.2 General Motivation and Need for Bioinformatics
	3.3 Bioinformatic Methods
		3.3.1 Introduction
		3.3.2 Important Genomic Characteristics and Concepts Related to Bioinformatics
		3.3.3 Genomic Assays and Technologies
			3.3.3.1 PCR (Polymerase Chain Reaction)
			3.3.3.2 Microarrays and Other Hybridization-Based Platforms
			3.3.3.3 Sequencing
			3.3.3.4 Platform Combinations
		3.3.4 Bioinformatic Algorithms, Pipelines, and Methods
			3.3.4.1 Algorithms
			3.3.4.2 Bioinformatic Pipelines
			3.3.4.3 Bioinformatic Methods
				Filtering
				Clustering and Correlated Genes
				Linking Multiple Sources of Information
				Importance of Annotation
		3.3.5 Statistics in Bioinformatics
			3.3.5.1 Mathematical and Statistical Methods
		3.3.6 Informative Graphics
	3.4 Case Studies in Genomic Bioinformatics with Associated Impacts to Treatment and Therapy
		3.4.1 BRAF and NF1 Somatic Mutations Across Traditional Indications
		3.4.2 Breast Cancer Subtypes
		3.4.3 Characterizing Multiple Biological Systems Using Gene Expression Data
	3.5 Current Challenges and Developments in Bioinformatics
		3.5.1 RNA Versus DNA Biomarkers: Advantages and Disadvantages in the Clinical Space
		3.5.2 Emerging Methods in Immuno-oncology
	3.6 Concluding Remarks
	References
Chapter 4: Biostatistical Methods in Pharmacoepidemiology
	4.1 Introduction
		4.1.1 Experiment vs. Observation
		4.1.2 Observational Studies
			4.1.2.1 Descriptive and Etiologic Studies
			4.1.2.2 Designs in Etiologic Studies
	4.2 Measures in Pharmacoepidemiology
		4.2.1 Frequency Measures
			4.2.1.1 Measures of Disease Frequency in Epidemiology (Incidence and Prevalence)
			4.2.1.2 Other Commonly Used Measures of Disease Frequency in Epidemiology
		4.2.2 Association Measures
		4.2.3 Measures of Potential Impact
	4.3 Sources of Variability and Errors in Pharmacoepidemiology
		4.3.1 Errors (Random or Systematic)
		4.3.2 Confounding
			4.3.2.1 How to Identify Confounding
			4.3.2.2 How to Deal with Confounding
		4.3.3 Interaction (Effect Modification)
			4.3.3.1 How to Identify an Interaction
			4.3.3.2 How to Deal with an Interaction
			4.3.3.3 Stratification
			4.3.3.4 Three-Way, Four-Way, and More-Way Interactions
	4.4 Addressing Confounding/Interaction Analytically
		4.4.1 Multivariate Analysis (OLS, Logistic, Cox, Others)
			4.4.1.1 What It Is, When and Why to Use It
				Ordinary Least Squares (OLS) Regression for Single and Multiple Predictors
				Logistic Regression
				Other Types of Regression
					Poisson Regression
					Negative Binomial Regression
					Hierarchical Linear Modeling
					Stepwise Regression
					Residuals
					P-Values, Confidence Intervals, and Error
				Survival Analysis
					Survival and Hazard
					Kaplan-Meier (Product Limit): Survival Estimate
					Cox Regression: Hazard Estimates
					Comparing Survival Curves and Hazards
				Adjustment
		4.4.2 Advanced Methods of Adjustment
			4.4.2.1 Propensity Score
				Propensity Score Estimation
				Variables Selection
				Matching
				Stratification
				Weighting Strategies
			4.4.2.2 Instrumental Variables
				Assessing IV Validity and Strength
				Estimation of Treatment Effect Using an IV
			4.4.2.3 Mediator and Moderator Variables
				Structural Equation Modeling, Path Analysis, and the Assessment of Direct and Indirect Effects
	References
Chapter 5: Causal Inference in Pharmacoepidemiology
	5.1 Introduction
		5.1.1 Challenges in Big Health Data
		5.1.2 Causal Inference and Potential Outcomes
		5.1.3 Definition of a Causal Effect
		5.1.4 A Short Introduction to Causal Directed Acyclic Graphs
		5.1.5 Randomized Experiments
		5.1.6 Observational Studies
		5.1.7 Using Big Data to Emulate a Target Trial
		5.1.8 Effect Modification and Interaction
	5.2 Important Sources of Bias in Pharmacoepidemiology
		5.2.1 Confounding
		5.2.2 Selection Bias
		5.2.3 Measurement Error
	5.3 Causal Modeling in Pharmacoepidemiology
		5.3.1 Random Variability
		5.3.2 Motivation for Modeling
		5.3.3 Marginal Structural Models
	5.4 Advanced Topics
		5.4.1 Causal Survival Analysis
		5.4.2 Time-Varying Exposures
		5.4.3 Instrumental Variables
	5.5 Concluding Remarks
	References
Chapter 6: Statistical Data Mining of Clinical Data
	6.1 Introduction
		6.1.1 What Is Data Mining?
		6.1.2 Machine Learning and Data Mining Framework
		6.1.3 Machine Learning Tasks for Solving Clinical Problems
			6.1.3.1 Supervised Learning
			6.1.3.2 Unsupervised Learning
			6.1.3.3 Semi-supervised Learning
			6.1.3.4 Feature Selection and Dimensionality Reduction
	6.2 Overview of Key Concepts
		6.2.1 Bias-Variance Trade-Off
		6.2.2 Model Selection
		6.2.3 Variable Importance
		6.2.4 Multiple Testing
		6.2.5 Cross-Validation
		6.2.6 Bootstrap
		6.2.7 Ensemble Learning
	6.3 Overview of Selected Methods
		6.3.1 Supervised Learning
			6.3.1.1 Penalized Regression
			6.3.1.2 Classification and Regression Trees
			6.3.1.3 Bagging
			6.3.1.4 Random Forests
			6.3.1.5 Boosting
			6.3.1.6 Support Vector Machines
			6.3.1.7 Artificial Neural Networks
		6.3.2 Unsupervised Learning
			6.3.2.1 Clustering
			6.3.2.2 Principal Components and Related Methods
		6.3.3 Semi-supervised Learning
			6.3.3.1 Methods for Biomarker and Subgroup Identification from Clinical Trial Data
			6.3.3.2 Q-Learning for Dynamic Treatment Regimes
	6.4 Principles of Data Mining with Clinical Data
		6.4.1 Documenting Business Need and Scientific Rationale for Data Mining
		6.4.2 Developing a Data Mining Analytic Plan
		6.4.3 Ensuring Data Integrity
	6.5 Case Studies
		6.5.1 Evaluation of Subpopulations Using SIDES Methodology
			6.5.1.1 SIDES Methodology
			6.5.1.2 Analysis Data
			6.5.1.3 Results
		6.5.2 Evaluating Optimal Dynamic Treatment Regimes via Q-Learning
			6.5.2.1 The STEP-BD Trial, Analysis Objectives, and Available Data
			6.5.2.2 Q-Learning Methodology for the RAD Trial
			6.5.2.3 Results of Q-Learning
		6.5.3 Estimating Treatment Effect in an Oncology Trial Using Inverse Probability of Censoring Weights
			6.5.3.1 Introduction
			6.5.3.2 Example Data Set in Prostate Cancer
			6.5.3.3 IPCW Methodology
			6.5.3.4 Estimating Stabilized Weights with Logistic Regression
			6.5.3.5 Estimating Stabilized Weights Using Random Forests
			6.5.3.6 Results
			6.5.3.7 Discussion
	6.6 Discussion and Conclusions
	References
Chapter 7: Segmentation and Choice Models
	7.1 Online Data Collection: The Current Standard
		7.1.1 The Role of ``Pre-launch´´ Qualitative Research
		7.1.2 Survey Complexity and Length Considerations
		7.1.3 ``Soft-Launch´´ and In-Field Data Monitoring
			7.1.3.1 Excluding Cases and Why
				Rapid Response
				``Flat Liners´´
				``Contradictors´´
	7.2 Market Segmentation
		7.2.1 What Is Segmentation and What Are the Goals of Such Research?
		7.2.2 Pre-launch vs. Post-Launch Segmentation
		7.2.3 Art vs. Science
		7.2.4 Top-Down vs. Bottom-Up
		7.2.5 Instrument (Survey) Development
			7.2.5.1 Considerations for Online Data Collection
			7.2.5.2 Item Development
			7.2.5.3 Data Collection Approaches
				Likert: Type Items
				Ranking Items
				Forced-Choice Approaches
				Other Approaches
		7.2.6 Defining the Sample
			7.2.6.1 HCP Research
			7.2.6.2 Patient/Caregiver Research
		7.2.7 Data Preparation
			7.2.7.1 Identification of Foundation Variables: Selecting the Right Subset
				Key Driver/Regression Analyses
				Factor Analytic Models
				Distributional Analyses
		7.2.8 Segment Estimation
			7.2.8.1 K-Means
			7.2.8.2 CHAID
			7.2.8.3 Latent Class Models
		7.2.9 Solution Selection Criteria
			7.2.9.1 Statistical Indices (Where Applicable)
			7.2.9.2 Managerial Implications
			7.2.9.3 Attitudinal Algorithms
			7.2.9.4 Behavioral Algorithms
	7.3 Choice-Based Conjoint Model/DCM
	7.4 Choice Models
		7.4.1 Goals of Such Research
			7.4.1.1 TPP Development
			7.4.1.2 Patient Profiles/Drivers
			7.4.1.3 Other Applications
		7.4.2 Choice Model Form
			7.4.2.1 Mathematical Foundation
			7.4.2.2 Logit and Multinomial Logit Models
			7.4.2.3 Probit Models
			7.4.2.4 Nested Logit Models
			7.4.2.5 Random Effects MNL Models
			7.4.2.6 Mixture MNL Models
			7.4.2.7 Ordered Logit and Probit Models
		7.4.3 Sample Considerations
			7.4.3.1 Stakeholders
			7.4.3.2 Sample Size
			7.4.3.3 Subpopulations
			7.4.3.4 Design Complexity
		7.4.4 Data Collection/Survey Design Considerations
			7.4.4.1 Conjoint
				Max-Diff
			7.4.4.2 Discrete Choice
				Allocations
			7.4.4.3 Hybrid Methods
			7.4.4.4 Number of Choice Tasks
		7.4.5 Efficient Designs
			7.4.5.1 Attribute and Levels
			7.4.5.2 Measures of Design Efficiency
			7.4.5.3 Design Optimization
			7.4.5.4 Blocking
		7.4.6 Estimation
			7.4.6.1 Maximum Likelihood and Gradient Descent
			7.4.6.2 Expectation-Maximization (EM) Algorithm
			7.4.6.3 Hierarchical Bayesian Approaches
		7.4.7 Model Selection
			7.4.7.1 Statistical Criteria
			7.4.7.2 Iteration and Estimation Constraints
		7.4.8 Sensitivity Analysis and Attribute Importance
	7.5 Summary and Conclusion
	References
Chapter 8: Modern Analytic Techniques for Predictive Modeling of Clinical Trial Operations
	8.1 Introduction
	8.2 Predictive Patient Enrollment Modeling
		8.2.1 Poisson-Gamma Enrollment Model
		8.2.2 Trial Start-Up Stage
			8.2.2.1 Enrollment Prediction at Trial Start-Up Stage
			8.2.2.2 Enrollment Prediction at Trial Start-Up Stage in Any Region
		8.2.3 Enrollment Reforecasting at Interim Stage
		8.2.4 Interim Assessment of Enrollment Performance and Risk-Based Monitoring
			8.2.4.1 Interim Assessment of Center´s Enrollment Performance
			8.2.4.2 Interim Assessment of Country´s Enrollment Performance
	8.3 Optimal Trial Design
		8.3.1 Optimal Enrollment Design at Start-Up Stage
		8.3.2 Optimal Adaptive Enrollment Adjustment at Interim Stage
	8.4 Modeling Event´s Counts in Event-Driven Trials
		8.4.1 Design of the Event-Driven Trial at Start-Up Stage
		8.4.2 Risk-Based Monitoring in Event-Driven Trials at Interim Stage
		8.4.3 Forecasting in Event-Driven Trials at Interim Stage
	8.5 Modeling Trial Operational Characteristics
	8.6 Discussion
	Appendix
		Appendix 8.1: Proof of Lemma 8.8
		Appendix 8.2: Proof of Lemma 8.11
		Appendix 8.3: Proof of Theorem 8.2
	References
Chapter 9: Better Together: Examples of Biostatisticians Collaborating in Drug Development
	9.1 Introduction
	9.2 Clinical
		9.2.1 Biosimilar Sample Size for Equivalence Studies
		9.2.2 Trial Design via Simulation
	9.3 Nonclinical Research and Chemistry, Manufacturing, and Controls (CMC)
		9.3.1 Bioanalytical Assay Development
		9.3.2 Bioanalytical Assay Acceptance Criteria
		9.3.3 Formulation Development
		9.3.4 Software as a Medical Device (SaMD)
	9.4 Conclusion
	References