Statistical Modeling for Biological Systems

Preface
Cancer Cell Vulnerabilities: Finding Needles in a Haystack with Andrei Yakovlev: A Personal Observation
	References
Contents
Contributors
Part I Research Articles
	Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes
		1 Introduction
		2 Subsequent Generations of Cells Induced to Proliferation and Some Characteristics of Cell Cycle Temporal Organization
		3 Distributions of Pulse-Labeled Discrete Marks in Branching Populations of Cells
		4 Continuous Label Distributions in Proliferating Cell Populations
		5 Limiting Age and Residual Lifetime Distributions for Continuous-Time Branching Processes
		6 Limit Theorems and Estimation Theory for Multitype Branching Populations and Relative Frequencies with a Large Numberof Ancestors
		7 Age-Dependent Branching Populations with Randomly Chosen Paths of Evolution
		8 Concluding Remarks
		References
	Age-Dependent Branching Processes with Non-homogeneous Poisson Immigration as Models of Cell Kinetics
		1 Introduction
		2 A Biological Motivation
		3 Model, Notation, and Basic Equations
		4 Asymptotics for First- and Second-Order Moments
		5 Statistical Inference
		6 Examples and Applications
			6.1 An Age-Dependent Branching Process with Homogeneous Poisson Immigration
			6.2 A Simulation Study
		7 Dedication
		References
	A Study of the Correlation Structure of Microarray Gene Expression Data Based on Mechanistic Modeling of Cell Population Kinetics
		1 Introduction
		2 The Effect of Cell Mixtures on Observed Correlations
		3 A Comprehensive Study of Correlation Based on Mechanistic Modeling of Cell Population Kinetics
			3.1 Gene Expression Levels During the Cell Cycles
			3.2 Simulation Study
		4 Heterogeneity of Subjects
		5 Discussion
		References
	Correlation Between the True and False Discoveries in a Positively Dependent Multiple Comparison Problem
		1 Background and Introduction
		2 Methods
			2.1 A Parametric Model with Two t-Tests
			2.2 Correlation Between the Two t-Statistics
			2.3 Correlation Between the True and False Positives
			2.4 A General Multiple Testing Design Motivated by Microarray Analysis
		3 Simulation Results
		4 Discussion
		Appendix: Proof of Proposition 2.1
		References
	Multiple Testing Procedures: Monotonicity and Someof Its Implications
		1 Introduction
		2 Basic Notions
			2.1 Uninformed MTPs
			2.2 Monotonicity
			2.3 Step-Down and Step-Up Procedures
			2.4 Threshold Step-Up-Down Procedures
			2.5 Generalized Family-Wise Error Rates
			2.6 Per-Family Error Rate
			2.7 Comparison of Procedures
		3 Some Implications of Monotonicity
			3.1 Optimality of the Holm Procedure
			3.2 Extensions of the Holm Procedure
			3.3 Extensions of the Bonferroni Procedure
			3.4 Quasi-Thresholds
			3.5 Some Sharp Inequalities
			3.6 Bounds on Generalized Family-Wise Error Rates
			3.7 An ``All-or-Nothing\'\' Theorem
		References
	Applications of Sequential Methods in Multiple Hypothesis Testing
		1 Introduction
		2 The Empirical Hypothesis Test as Stopped Binary Process
			2.1 Monte Carlo Hypothesis Tests as SBPs
			2.2 Estimation of Significance Level
			2.3 Fixed Level Tests
			2.4 Hybrid Test
		3 Overview of the Sequential Probability Ratio Test
		4 Application of the SPRT to Hypothesis Tests Based on Simulated Replications of an Accept–Reject Rule
			4.1 Single Hypothesis Test
			4.2 Multiple Hypothesis Tests
		5 Optimal Design of Stopping Times Based on SPRTs
			5.1 Constrained Optimization
			5.2 Solution Method
			5.3 Numerical Example
		6 Examples
			6.1 Gene Set Analysis
			6.2 Confidence Sets in Statistical Genetics
		7 Conclusion
		References
	Multistage Carcinogenesis: A Unified Framework for Cancer Data Analysis
		1 Introduction
		2 Brief Review of Mathematical Issues
		3 Construction of Likelihoods
		4 Number and Size Distribution of Intermediate (Premalignant) Lesions
		5 Model for Colon Cancer
			5.1 Applications of the Model
				5.1.1 Screening for Colon Cancer
				5.1.2 Impact of Folate Fortification on Colon Cancer Risk
		6 Discussion
		References
	A Machine-Learning Algorithm for Estimating and Ranking the Impact of Environmental Risk Factors in Exploratory Epidemiological Studies
		1 Introduction
		2 Background
		3 Data Structure and Parameters of Interest
		4 CHAMACOS Data Description
		5 Methods
			5.1 Estimation: DR-IPW Estimation of the Population Intervention Model
			5.2 Single Exposure Inference: A Modified Conditional Permutation Test
			5.3 Joint Inference: Quantile Transformation Method
		6 Results
		7 Discussion
		References
	A Latent Time Distribution Model for the Analysis of Tumor Recurrence Data: Application to the Role of Age in Breast Cancer
		1 Introduction
		2 Material and Methods
			2.1 Cox Model
			2.2 Cox Model with Time-Dependent Covariates
			2.3 Yakovlev Models
			2.4 Breast Cancer Data
		3 Results
			3.1 Dataset
			3.2 Cox Models
			3.3 Yakovlev Model
		4 Discussion
		References
	Estimation of Mean Residual Life
		1 Introduction and Summary
		2 Convergence on R+: Covariance Function of the Limiting Process
		3 Alternative Sufficient Conditions: Var[Z(x)] as x →∞
		4 Examples
		5 Confidence Bands for e
		6 Illustration of the Confidence Bands
		7 Further Developments
			7.1 Confidence Bands and Inference
			7.2 Censored Data
			7.3 Median and Quantile Residual Life Functions
			7.4 Semiparametric Models for Mean and Median Residual Life
			7.5 Monotone and Ordered Mean Residual Life Functions
			7.6 Bivariate Residual Life
		References
	Likelihood Transformations and Artificial Mixtures
		1 Artificial Mixtures
		2 The Quasi-Expectation Operator and the Quasi-EM (QEM) Algorithm
		3 Multinomial Regression
		4 Nonlinear Transformation Models (NTM)
		5 Copula Models
		6 Example
			6.1 A Composition of Gamma and Positive Stable Shared Frailty Models
			6.2 Retinopathy Application
			6.3 Numerical Experiments and Simulations
		7 Discussion
		References
	On the Application of Flexible Designs When Searching for the Better of Two Anticancer Treatments
		1  Introduction
		2   Flexible Two-Stage Designs in Survival Trials
			2.1  Two-Stage Group Sequential Survival Trials
				2.1.1 Cox Proportional Hazards Model to Describe Survival Times and Score Statistics
				2.1.2 Statistical Decision in Interim and Final Analysis of Survival Trials
			2.2  Adaptive Design Approaches for Two-Stage Survival Trials
				2.2.1  P-value Combination Rules to Combine Results from Both Study Stages
				2.2.2  The Adaptive CRP Principle to Extend Group Sequential Trials
				2.2.3  Sample Size Determination
		3 Simulation Studies
			3.1 Design of Simulation Studies
			3.2 Simulation Results
			3.3 Evaluation of Simulation Results
			3.4 Application of Simulation Results
		4 Discussion
		Appendix: Numerical Results
		References
	Parameter Estimation for Multivariate Nonlinear Stochastic Differential Equation Models: A Comparison Study
		1 Introduction
		2 Estimation Methods for Nonlinear SDEs
			2.1 Euler Method
			2.2 Simulated Maximum Likelihood Method
		3 Improved Local Linearization (ILL) Method
		4 Numerical Example: HIV Dynamic Model
		5 Conclusion
		References
	On Frailties, Archimedean Copulas and Semi-Invariance Under Truncation
		1 Introduction
		2 Basics
		3 Uniqueness
		4 Some Examples
			4.1 Clayton\'s Model—Gamma Distributed Frailties
			4.2 Inverse Gaussian Model
			4.3 Logarithmic Series Distribution: Frank\'s Model
			4.4 Poisson Model
			4.5 Positive Stable Model
			4.6 Exterior Power Families
			4.7 Interior Power Families
		5 The Kendall Distribution and Kendall\'s Tau
		6 Truncation Invariance and Semi-Invariance
		7 The Kendall Distribution Under Truncation
		8 Higher Dimensions
		References
Part II Short Communications
	The Generalized ANOVA: A Classic Song Sung with Modern Lyrics
		1 Introduction
		2 Generalized ANOVA for Mean and Variance
		3 Inference for Generalized ANOVA
		4 Extension to a Longitudinal Data Setting with Missing Data
		5 Simulation
		6 Discussion
		References
	Analyzing Gene Pathways from Microarrays to Sequencing Platforms
		1 Introduction
		2 Pathway Methods for Microarrays
			2.1 The GSA Method
				2.1.1 The Maxmean Statistic
				2.1.2 Determining the Univariate p-Value
		3 Case Study
		4 Next Generation Sequencing Tests
		5 Discussion and Conclusions
		References
	A New Approach for Quantifying Uncertainty in Epidemiology
		1 Preamble
		2 Uncertainty and Epidemiology
			2.1 Quantification of Randomness
			2.2 Quantification of Ignorance
		3 Ambiguity of Epidemiological Results
			3.1 Statistics and Ambiguity
			3.2 Epidemiological Measurements
		4 A Stochastic Model of Uncertainty
			4.1 The Bernoulli Space
			4.2 Estimating Probabilities
				4.2.1 Bernoulli Space
				4.2.2 The Stochastic Measurement Procedure
		References
	Branching Processes: A Personal Historical Perspective
		1 Introduction and Summary
		References
	Principles of Mathematical Modeling in Biomedical Sciences: An Unwritten Gospel of Andrei Yakovlev
		1 Mathematics and Biology: A Tough Marriage
		2 Mathematical Models as Axiomatic Systems
		3 A Mathematical Modeler\'s Dilemma: Deterministic or Stochastic?
		4 A Devil in the Corner: Model Non-identifiability
		5 Mathematical Models and Biological Reality
		References
Appendix: Publications of Andrei Yakovlev
	Appendix: Publications of Andrei Yakovlev
		Books
		Peer-Reviewed Papers Published in English
		Peer-Reviewed Papers Translated into English
		Peer-Reviewed Papers Translated into English
		Book Chapters
		Selected Inventions
Index