Decision Analytics and Optimization in Disease Prevention and Treatment

NAN KONG, PhD, is Associate Professor in the Weldon School of Biomedical Engineering at Purdue University. Dr. Kong is a member of INFORMS and SMDM, and his research interests include healthcare resource allocation, medical decision–making, and hospital operations management. SHENGFAN ZHANG, PhD, is Assistant Professor in the Department of Industrial Engineering at the University of Arkansas. Dr. Zhang is a member of INFORMS and IISE, and her research interests include mathematical modeling of stochastic systems, medical decision–making, and health analytics.

CONTRIBUTORS xiii


PREFACE xvii


PART 1 INFECTIOUS DISEASE CONTROL AND MANAGEMENT 1


1 Optimization in Infectious Disease Control and Prevention: Tuberculosis Modeling Using Microsimulation 3
Sze?–chuan Suen


1.1 Tuberculosis Epidemiology and Background 4


1.1.1 TB in India 5


1.2 Microsimulations for Disease Control 6


1.3 A Microsimulation for Tuberculosis Control in India 8


1.3.1 Population Dynamics 9


1.3.2 Dynamics of TB in India 9


1.3.3 Activation 10


1.3.4 TB Treatment 11


1.3.5 Probability Conversions 13


1.3.6 Calibration and Validation 14


1.3.7 Intervention Policies and Analysis 16


1.3.8 Time Horizons and Discounting 18


1.3.9 Incremental Cost?–Effectiveness Ratios and Net Monetary Benefits 19


1.3.10 Sensitivity Analysis 22


1.4 Conclusion 22


References 23


2 Saving Lives with Operations Research: Models to Improve HIV Resource Allocation 25
Sabina S. Alistar and Margaret L. Brandeau


2.1 Introduction 25


2.1.1 Background 25


2.1.2 Modeling Approaches 27


2.1.3 Chapter Overview 31


2.2 HIV Resource Allocation: Theoretical Analyses 31


2.2.1 Defining the Resource Allocation Problem 31


2.2.2 Production Functions for Prevention and Treatment Programs 35


2.2.3 Allocating Resources among Prevention and Treatment Programs 37


2.3 HIV Resource Allocation: Portfolio Analyses 39


2.3.1 Portfolio Analysis 39


2.3.2 O piate Substitution Therapy and ART in Ukraine 40


2.3.3 Pre?–exposure Prophylaxis and ART 42


2.4 HIV Resource Allocation: A Tool for Decision Makers 44


2.4.1 REACH Model Overview 44


2.4.2 Example Analysis: Brazil 45


2.4.3 Example Analysis: Thailand 48


2.5 Discussion and Further Research 50


Acknowledgment 53


References 53


3 Adaptive Decision?–Making During Epidemics 59
Reza Yaesoubi and Ted Cohen


3.1 Introduction 59


3.2 Problem Formulation 61


3.3 Methods 63


3.3.1 The 1918 Influenza Pandemic in San Francisco, CA 63


3.3.2 Stochastic Transmission Dynamic Models 64


3.3.3 Calibration 66


3.3.4 O ptimizing Dynamic Health Policies 69


3.4 Numerical Results 73


3.5 Conclusion 75


Acknowledgments 76


References 76


4 Assessing Register?–Based Chlamydia Infection Screening Strategies: A Cost?–Effectiveness Analysis on Screening Start/End Age and Frequency 81
Yu Teng, Nan Kong, and Wanzhu Tu


4.1 Introduction 81


4.2 Background Literature Review 83


4.2.1 Clinical Background on CT Infection and Control 83


4.2.2 CT Screening Programs 85


4.2.3 Computational Modeling on CT Transmission and Control 85


4.3 Mathematical Modeling 89


4.3.1 An Age?–Structured Compartmental Model 89


4.3.2 Model Parameterization and Validation 93


4.4 Strategy Assessment 98


4.4.1 Base?–Case Assessment 98


4.4.2 Sensitivity Analysis 100


4.5 Conclusions and Future Research 101


References 102


5 Optimal Selection of Assays for Detecting Infectious Agents in Donated Blood 109
Ebru K. Bish, Hadi El?–Amine, Douglas R. Bish, Susan L. Stramer, and Anthony D. Slonim


5.1 Introduction and Challenges 109


5.1.1 Introduction 109


5.1.2 The Challenges 111


5.2 The Notation and Decision Problem 113


5.2.1 Notation 114


5.2.2 Measures of Interest 115


5.2.3 Model Formulation 117


5.2.4 Relationship of the Proposed Mathematical Models to Cost?–Effectiveness Analysis 118


5.3 The Case Study of the Sub?–Saharan Africa Region and the United States 119


5.3.1 Uncertainty in Prevalence Rates 122


5.4 Contributions and Future Research Directions 123


Acknowledgments 123


References 124


6 Modeling Chronic Hepatitis C During Rapid Therapeutic Advance: Cost?–Effective Screening, Monitoring, and Treatment Strategies 129
Shan Liu


6.1 Introduction 129


6.2 Method 131


6.2.1 Modeling Disease Natural History and Intervention 132


6.2.2 Estimating Parameters for Disease Progression and Death 134


6.3 Four Research Areas in Designing Effective HCV Interventions 139


6.3.1 Cost?–Effective Screening and Treatment Strategies 139


6.3.2 Cost?–Effective Monitoring Guidelines 141


6.3.3 O ptimal Treatment Adoption Decisions 141


6.3.4 O ptimal Treatment Delivery in Integrated Healthcare Systems 145


6.4 Concluding Remarks 148


References 148


PART 2 NONCOMMUNICABLE DISEASE PREVENTION 153


7 Modeling Disease Progression and Risk?–Differentiated Screening for Cervical Cancer Prevention 155
Adriana Ley?–Chavez and Julia L. Higle


7.1 Introduction 155


7.2 Literature Review 157


7.3 Modeling Cervical Cancer Screening 159


7.3.1 Model Components 160


7.3.2 Parameter Selection 166


7.3.3 Implementation 169


7.4 Model?–Based Analyses 171


7.4.1 Cost?–Effectiveness Analysis 171


7.4.2 Sensitivity Analysis 172


7.5 Concluding Remarks 174


References 175


8 Using Finite?–Horizon Markov Decision Processes for Optimizing Post?–Mammography Diagnostic Decisions 183
Sait Tunc, Oguzhan Alagoz, Jagpreet Chhatwal, and Elizabeth S. Burnside


8.1 Introduction 183


8.2 Model Formulations 185


8.3 Structural Properties 188


8.4 Numerical Results 193


8.5 Summary 196


Acknowledgments 196


References 197


9 Partially Observable Markov Decision Processes for Prostate Cancer Screening, Surveillance, and Treatment: A Budgeted Sampling Approximation Method 201
Jingyu Zhang and Brian T. Denton


9.1 Introduction 201


9.2 Review of POMDP Models and Benchmark Algorithms 204


9.3 A POMDP Model for Prostate Cancer Screening, Surveillance, and Treatment 206


9.4 Budgeted Sampling Approximation 209


9.4.1 Lower and Upper Bounds 209


9.4.2 Summary of the Algorithm 211


9.5 Computational Experiments 213


9.5.1 Finite?–Horizon Test Instances 213


9.5.2 Computational Experiments 214


9.6 Conclusions 217


References 219


10 Cost?–Effectiveness Analysis of Breast Cancer Mammography Screening Policies Considering Uncertainty in Women’s Adherence 223
Mahboubeh Madadi and Shengfan Zhang


10.1 Introduction 223


10.2 Model Formulation 225


10.3 Numerical Studies 231


10.4 Results 233


10.4.1 Perfect Adherence Case 233


10.4.2 General Population Adherence Case 234


10.5 Summary 236


References 237


11 An Agent?–Based Model for Ideal Cardiovascular Health 241
Yan Li, Nan Kong, Mark A. Lawley, and José A. Pagán


11.1 Introduction 241


11.2 Methodology 243


11.2.1 Agent?–Based Modeling 243


11.2.2 Model Structure 244


11.2.3 Parameter Estimation 246


11.2.4 User Interface 248


11.2.5 Model Validation 249


11.3 Results 250


11.3.1 Simulating American Adults 250


11.4 Simulating the Medicare?–Age Population and the Disease?–Specific Subpopulations 252


11.5 Future Research 254


11.6 Summary 255


References 255


PART 3 TREATMENT TECHNOLOGY AND SYSTEM 259


12 Biological Planning Optimization for High?–Dose?–Rate Brachytherapy and its Application to Cervical Cancer Treatment 261
Eva K. Lee, Fan Yuan, Alistair Templeton, Rui Yao, Krystyna Kiel, and James C.H. Chu


12.1 Introduction 261


12.2 Challenges and Objectives 263


12.3 Materials and Methods 265


12.3.1 High?–Dose?–Rate Brachytherapy 265


12.3.2 PET Image 266


12.3.3 Novel OR?–Based Treatment?–Planning Model 266


12.3.4 Computational Challenges and Solution Strategies 271


12.4 Validation and Results 273


12.5 Findings, Implementation, and Challenges 276


12.6 Impact and Significance 279


12.6.1 Quality of Care and Quality of Life for Patients 279


12.6.2 Advancing the Cancer Treatment Frontier 279


12.6.3 Advances in Operations Research Methodologies 280


Acknowledgment 281


References 281


13 Fluence Map Optimization in Intensity?–Modulated Radiation Therapy Treatment Planning 285
Dionne M. Aleman


13.1 Introduction 285


13.2 Treatment Plan Evaluation 288


13.2.1 Physical Dose Measures 289


13.2.2 Biological Dose Measures 291


13.3 FMO Optimization Models 292


13.3.1 O bjective Functions 293


13.3.2 Constraints 295


13.3.3 Robust Formulation 297


13.4 O ptimization Approaches 299


13.5 Conclusions 300


References 301


14 Sliding Window IMRT and VMAT Optimization 307
David Craft and Tarek Halabi


14.1 Introduction 307


14.2 Two?–Step IMRT Planning 309


14.3 O ne?–Step IMRT Planning 310


14.3.1 O ne?–Step Sliding Window Optimization 310


14.4 Volumetric Modulated ARC Therapy 313


14.5 Future Work for Radiotherapy Optimization 315


14.5.1 Custom Solver for Radiotherapy 315


14.5.2 Incorporating Additional Hardware Considerations into Sliding Window VMAT Planning 315


14.5.3 Trade?–Off between Delivery Time and Plan Quality 316


14.5.4 What Do We Optimize? 316


14.6 Concluding Thoughts 317


References 318


15 Modeling the Cardiovascular Disease Prevention–Treatment Trade?–Off 323
George Miller


15.1 Introduction 323


15.2 Methods 325


15.2.1 Model Overview 325


15.2.2 Model Structure 327


15.2.3 Model Inputs 331


15.3 Results 334


15.3.1 Base Case 334


15.3.2 Interaction between Prevention and Treatment Spending 335


15.3.3 Impact of Discount Rate on Cost?–Effectiveness 336


15.3.4 O ptimal Spending Mix 337


15.3.5 Impact of Prevention Lag on Optimal Mix 338


15.3.6 Impact of Discount Rate on Optimal Mix 340


15.3.7 Impact of Time Horizon on Optimal Mix 340


15.3.8 Impacts of Research 341


15.4 Discussion 344


Acknowledgment 346


References 346


16 Treatment Optimization for Patients with Type 2 Diabetes 349
Jennifer Mason Lobo


16.1 Introduction 349


16.2 Literature Review 350


16.3 Model Formulation 353


16.3.1 Decision Epochs 354


16.3.2 States 354


16.3.3 Actions 355


16.3.4 Probabilities 355


16.3.5 Rewards 356


16.3.6 Value Function 356


16.4 Numerical Results 357


16.4.1 Model Inputs 357


16.4.2 Optimal Treatment Policies to Reduce Polypharmacy 358


16.5 Conclusions 362


References 363


17 Machine Learning for Early Detection and Treatment Outcome Prediction 367
Eva K. Lee


17.1 Introduction 367


17.2 Background 369


17.3 Machine Learning with Discrete Support Vector Machine Predictive Models 372


17.3.1 Modeling of Reserved?–Judgment Region for General Groups 373


17.3.2 Discriminant Analysis via Mixed?–Integer Programming 374


17.3.3 Model Variations 376


17.3.4 Theoretical Properties and Computational Strategies 379


17.4 Applying Damip to Real?–World Applications 380


17.4.1 Validation of Model and Computational Effort 381


17.4.2 Applications to Biological and Medical Problems 381


17.4.3 Applying DAMIP to UCI Repository of Machine Learning Databases 389


17.5 Summary and Conclusion 393


Acknowledgment 394


References 394


INDEX 401