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Estimation of adjusted relative risks in log-binomial regression using the Bekhit–Schöpe–Wagenpfeil algorithm

  • Stefan Wagenpfeil , Jakob Schöpe and Adam Bekhit
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BIOKYBERNETIKA
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Abstract

Classical log-binomial regression is a prominent statistical model for adjusted relative risk estimation in the framework of prospective, observational studies. However, there was and still is an already long-lasting debate on workarounds due to problems and sometimes failed convergence of respective maximum likelihood estimation (MLE) of model parameters, i. e., regression constant as well as covariate effects. We describe two areas of problems that can be seen as essential sources for nonconvergence issues in the specific class of regression models. In order to overcome the problems, a new and direct approach for MLE in log-binomial regression, called BSW, is presented. The implementation of BSW can either be seen as generalization of the classical Newton method for nonlinear programming without constraints to the further case of linear inequalities. On the other hand, one can simplify a classical sequential quadratic programming (SQP) algorithm allowing for nonlinear equalities and inequalities to the specific case of linear inequality constraints analogously, and obtain the same algorithmic approach, which we call BSW. Furthermore, convergence issues considering local and global convergence as well as convergence speed are discussed and referenced also. For algorithmic application, we present essential results summarizing large simulation studies on the one hand, and give reference to a real data example on the other. Exemplary visualization of the iterative steps of BSW is also given, and implementation of BSW can be found as an R package on CRAN.

Abstract

Classical log-binomial regression is a prominent statistical model for adjusted relative risk estimation in the framework of prospective, observational studies. However, there was and still is an already long-lasting debate on workarounds due to problems and sometimes failed convergence of respective maximum likelihood estimation (MLE) of model parameters, i. e., regression constant as well as covariate effects. We describe two areas of problems that can be seen as essential sources for nonconvergence issues in the specific class of regression models. In order to overcome the problems, a new and direct approach for MLE in log-binomial regression, called BSW, is presented. The implementation of BSW can either be seen as generalization of the classical Newton method for nonlinear programming without constraints to the further case of linear inequalities. On the other hand, one can simplify a classical sequential quadratic programming (SQP) algorithm allowing for nonlinear equalities and inequalities to the specific case of linear inequality constraints analogously, and obtain the same algorithmic approach, which we call BSW. Furthermore, convergence issues considering local and global convergence as well as convergence speed are discussed and referenced also. For algorithmic application, we present essential results summarizing large simulation studies on the one hand, and give reference to a real data example on the other. Exemplary visualization of the iterative steps of BSW is also given, and implementation of BSW can be found as an R package on CRAN.

Chapters in this book

  1. Frontmatter I
  2. Prologue I VII
  3. Prologue II XI
  4. Prologue III XIII
  5. Preface XVII
  6. Overview XIX
  7. Contents XXXIII
  8. Part I: Theories
  9. Part I-A: Overarching theory
  10. Introduction 1
  11. Universal axioms in classical Chinese philosophy 5
  12. Category theory for structural characterization 15
  13. Axiomatic bipolar dynamics and their control 45
  14. Part I-B: Systems theories
  15. Introduction 75
  16. Stochastic formalization of agent-oriented systems 79
  17. Simplification of high-dimensional multitempo dynamic models 109
  18. Ideas of symmetry as a biophysical basis of system biomedicine 123
  19. Disorder of multiscale control 149
  20. Part II: Person’s life-sphere
  21. Part II-A: Person’s biosphere
  22. Introduction 185
  23. Mutations as activators of biological evolutionary processes at population levels 189
  24. Immunometabolism of T-cells in COVID-19 209
  25. Part II-A.2: Body’s vital functions
  26. Introduction 245
  27. Structural modeling of vascular networks 249
  28. Mathematical modeling of AI application for the diagnosis of blood flow disorders 283
  29. Modeling of glucose and insulin regulation within the framework of a self-consistent model of the cardiovascular system 303
  30. Hemodynamics in residual myocardial ischemia 319
  31. The quasi-one-dimensional model of the lymph flow in the human lymphatic system 335
  32. An integrate-and-fire mechanism for modeling rhythmicity in the neuroendocrine system 365
  33. Kinetic network modeling of the neuroendocrine hypothalamic-pituitary-adrenal axis dynamics with particular attention on the role of alcohol as a digestif 377
  34. Inflammation and immune response in atherosclerosis 393
  35. Part II-A.3: Body’s motor functions
  36. Introduction 423
  37. A magnetic resonance spectroscopy approach to quantitatively measure GABA and phosphorus level changes in the primary motor cortex elicited by transcranial direct current stimulation 427
  38. Part II-A.4: Body’s operational functions
  39. Introduction 441
  40. The fermionic mind hypothesis–a category-theoretic verification of consciousness 445
  41. Cross-task cognitive workload measurement based on the sample selection of the EEG data 459
  42. Part II-B: Person’s eco-sphere exposures
  43. Introduction 475
  44. The spread of SARS-CoV-2 in Russia and the evolution of the properties of the pathogen 479
  45. Agent-based modeling of epidemic spread via kinetic Monte Carlo method 491
  46. Control of SARS-nCoV outbreaks in China 2020 513
  47. Part II-B.2: Civilization
  48. Introduction 531
  49. Pesticide exposure: Toward holistic environmental modeling 535
  50. Part II-C: Person’s sociosphere exposures
  51. Introduction 559
  52. Evolution of the health system in Shanghai, China, 2016–2020 563
  53. Part III: Technologies
  54. Introduction 577
  55. Design-process automation using functional process blocks 581
  56. Slow/fast dynamic models with applications to engineering problems 601
  57. Part III-B: Information sciences
  58. Introduction 613
  59. Numerical modeling of medical ultrasound using the grid-characteristic method 617
  60. The direct and the inverse magnetic encephalography problem 635
  61. Part III-C: Data-analytic sciences
  62. Introduction 653
  63. Assessing the bioequivalence of two different drugs with the same active ingredient 655
  64. Estimation of adjusted relative risks in log-binomial regression using the Bekhit–Schöpe–Wagenpfeil algorithm 665
  65. Part IV: Clinical medicine
  66. Introduction 679
  67. Finding optimal two-stage combined treatment protocols for a blood cancer model 681
  68. Unraveling the mysteries: Mathematical perspectives on traditional Chinese medicine meridians 697
  69. Epilogue 721
  70. Index 723
https://doi.org/10.1515/9783111341996-043

Chapters in this book

  1. Frontmatter I
  2. Prologue I VII
  3. Prologue II XI
  4. Prologue III XIII
  5. Preface XVII
  6. Overview XIX
  7. Contents XXXIII
  8. Part I: Theories
  9. Part I-A: Overarching theory
  10. Introduction 1
  11. Universal axioms in classical Chinese philosophy 5
  12. Category theory for structural characterization 15
  13. Axiomatic bipolar dynamics and their control 45
  14. Part I-B: Systems theories
  15. Introduction 75
  16. Stochastic formalization of agent-oriented systems 79
  17. Simplification of high-dimensional multitempo dynamic models 109
  18. Ideas of symmetry as a biophysical basis of system biomedicine 123
  19. Disorder of multiscale control 149
  20. Part II: Person’s life-sphere
  21. Part II-A: Person’s biosphere
  22. Introduction 185
  23. Mutations as activators of biological evolutionary processes at population levels 189
  24. Immunometabolism of T-cells in COVID-19 209
  25. Part II-A.2: Body’s vital functions
  26. Introduction 245
  27. Structural modeling of vascular networks 249
  28. Mathematical modeling of AI application for the diagnosis of blood flow disorders 283
  29. Modeling of glucose and insulin regulation within the framework of a self-consistent model of the cardiovascular system 303
  30. Hemodynamics in residual myocardial ischemia 319
  31. The quasi-one-dimensional model of the lymph flow in the human lymphatic system 335
  32. An integrate-and-fire mechanism for modeling rhythmicity in the neuroendocrine system 365
  33. Kinetic network modeling of the neuroendocrine hypothalamic-pituitary-adrenal axis dynamics with particular attention on the role of alcohol as a digestif 377
  34. Inflammation and immune response in atherosclerosis 393
  35. Part II-A.3: Body’s motor functions
  36. Introduction 423
  37. A magnetic resonance spectroscopy approach to quantitatively measure GABA and phosphorus level changes in the primary motor cortex elicited by transcranial direct current stimulation 427
  38. Part II-A.4: Body’s operational functions
  39. Introduction 441
  40. The fermionic mind hypothesis–a category-theoretic verification of consciousness 445
  41. Cross-task cognitive workload measurement based on the sample selection of the EEG data 459
  42. Part II-B: Person’s eco-sphere exposures
  43. Introduction 475
  44. The spread of SARS-CoV-2 in Russia and the evolution of the properties of the pathogen 479
  45. Agent-based modeling of epidemic spread via kinetic Monte Carlo method 491
  46. Control of SARS-nCoV outbreaks in China 2020 513
  47. Part II-B.2: Civilization
  48. Introduction 531
  49. Pesticide exposure: Toward holistic environmental modeling 535
  50. Part II-C: Person’s sociosphere exposures
  51. Introduction 559
  52. Evolution of the health system in Shanghai, China, 2016–2020 563
  53. Part III: Technologies
  54. Introduction 577
  55. Design-process automation using functional process blocks 581
  56. Slow/fast dynamic models with applications to engineering problems 601
  57. Part III-B: Information sciences
  58. Introduction 613
  59. Numerical modeling of medical ultrasound using the grid-characteristic method 617
  60. The direct and the inverse magnetic encephalography problem 635
  61. Part III-C: Data-analytic sciences
  62. Introduction 653
  63. Assessing the bioequivalence of two different drugs with the same active ingredient 655
  64. Estimation of adjusted relative risks in log-binomial regression using the Bekhit–Schöpe–Wagenpfeil algorithm 665
  65. Part IV: Clinical medicine
  66. Introduction 679
  67. Finding optimal two-stage combined treatment protocols for a blood cancer model 681
  68. Unraveling the mysteries: Mathematical perspectives on traditional Chinese medicine meridians 697
  69. Epilogue 721
  70. Index 723
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