Exploration of Causal and Correlational Modelling in Cancer : Glioblastoma Case Study
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EXPLORATION OF CAUSAL AND CORRELATIONAL MODELLING IN CANCER : GLIOBLASTOMA CASE STUDY by SOMPOP SAENGPHUENG Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Advisor: Dr. Sree N. Sreenath Department of Electrical Engineering & Computer Science CASE WESTERN RESERVE UNIVERSITY May 2015 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of SOMPOP SAENGPHUENG candidate for the Doctor of Philosophy degree * Dr. Sree N. Sreenath Dissertation Advisor Professor, Dr. James W. Jacobberger Professor, Dr. Mihajlo Mesarovic Professor, Dr. Vira Chankong Associate Professor, Dr. Evren Cavusoglu Assistant Professor, July 8th, 2014 *We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents Table of Contents ............................. iii List of Tables ............................... vii List of Figures ............................... viii Acknowledgement ............................. x Abstract .................................. xi 1 Introduction 1 1.1 Objective and Challenge ......................... 1 1.2 Biological Problem ............................ 4 1.3 Hallmark of Cancer and Angiogenesis .................. 7 1.4 Cause and Correlation of Angiogenesis in Glioblastoma ........ 8 1.5 Computer-aid analysis of causal structure ................ 9 1.6 Glioblastoma ............................... 9 1.7 Summary ................................. 9 2 Background 11 2.1 Glioblastoma or Glioblastoma multiforme (GBM) ........... 11 2.1.1 Glioblastoma ........................... 11 2.1.2 Causes of glioblastoma ...................... 12 2.1.3 Treatment ............................. 12 2.1.4 Glioblastoma, angiogenesis, and VEGF ............. 14 iii 2.1.5 Activation of VEGF pathway in glioblastoma ......... 16 2.1.6 Influence of VEGF on glioblastoma microvasculature ..... 16 2.1.7 Summary of VEGF in glioblastoma ............... 17 2.2 Understanding Angiogenesis and the VEGF Ligand ......... 17 2.2.1 Angiogenesis is regulated by the VEGF ligand ......... 17 2.2.2 The VEGF ligand is continuously expressed .......... 18 2.2.3 VEGF expression during tumor development .......... 20 2.2.4 Strategies for inhibiting the VEGF pathway .......... 21 2.2.5 Extracellular targeting of the VEGF ligand ........... 22 2.2.6 Intracellular targeting of the VEGF receptor .......... 23 2.2.7 Inhibition of new and recurrent tumor vessel growth ...... 23 2.2.8 Regression of existing tumor vasculature ............ 23 2.2.9 Regrowth of tumor vasculature ................. 24 2.2.10 The rationale for continuing VEGF inhibition ......... 25 2.2.11 An evolving understanding of tumor biology .......... 25 2.3 Cancer stem cells ............................. 27 2.4 Observational Model ........................... 28 2.5 Causal Model ............................... 30 2.6 Translating from causal to statistical model .............. 32 2.7 d-separation ................................ 33 2.8 Summary ................................. 34 3 Model Selection : Glioblastoma model 35 3.1 Glioblastoma model ............................ 35 3.1.1 Glucose .............................. 38 3.1.2 Oxygen .............................. 39 3.1.3 Transforming Growth Factor alpha ............... 41 iv 3.1.4 Vascular Endothelial Growth Factor (VEGF) ......... 41 3.1.5 Fibronectin ............................ 43 3.2 Other published works of brain cancer, angiogenesis, and cancer cell . 47 3.3 Summary ................................. 47 4 Methodology 50 4.1 Translating from causal to statistical model .............. 50 4.2 Statistical control and physical control ................. 51 4.3 Path analysis and d-separation ...................... 53 4.3.1 d-separation test ......................... 55 4.3.2 Independence of d-separation statements ............ 56 4.3.3 Testing for probabilistic independence .............. 58 4.4 Structural Equation Modeling (SEM) .................. 59 4.4.1 Steps to perform SEM analysis ................. 59 4.4.2 Path analysis and maximum likelihood ............. 62 4.4.3 Nested models and multilevel model ............... 63 4.5 The causal expression of SEM ...................... 65 4.5.1 Assumptions and representations ................ 65 4.5.2 Causal assumptions in nonparametric models ......... 67 4.5.3 Intervention and causal effects .................. 68 4.6 Exploration, discovery and equivalents of causal graph ........ 70 4.6.1 Exploring hypothesis space .................... 70 4.6.2 The shadow cause revisited ................... 71 4.6.3 Obtaining the undirected dependency graph .......... 71 4.6.4 Hypothesis setting ........................ 73 4.6.5 Causal inference for brain cancer ................ 73 4.7 Analysis of randomized experiment through SEM ........... 74 v 4.8 Develop a randomized experiment to address causal issues ...... 75 4.9 Advantages, Disadvantages, and Limitation ............... 76 4.10 Summary ................................. 77 5 Results 78 5.1 Part 1: Glioblastoma without TKI treatment .............. 79 5.2 Part 2: Glioblastoma with TKI treatment ............... 86 5.3 Estimation of path coefficient ...................... 90 6 Conclusion 96 6.1 Interpretation of the result ........................ 96 6.2 Suggestion for future research ...................... 98 6.3 Contribution ................................ 98 6.4 Summary ................................. 98 Appendix A The first Appendix 100 A.1 SEM and causality ............................ 100 A.2 Search algorithms using TETRAD ................... 103 A.2.1 PC algorithm ........................... 103 A.2.2 FCI algorithm ........................... 106 A.2.3 SEM parametric models ..................... 106 A.2.4 SEM instantiated model ..................... 107 A.3 Multilevelness of Angiogenesis ...................... 108 Bibliography 109 vi List of Tables 2.1 The effects of the VEGF ligand ..................... 19 3.1 Initial values and parameter values ................... 42 3.2 Other published works of brain cancer ................. 47 4.1 A basis set for the DAG ......................... 57 5.1 Mean coefficient and fit statistics of models without TKI ....... 85 5.2 Mean coefficient and fit statistics of models with TKI ......... 91 vii List of Figures 2.1 VEGF is known to express throughout the tumor life cycle ...... 20 2.2 Strategies for inhibiting the VEGF pathway .............. 21 2.3 Observational Relationships and Causal Relationships ......... 28 2.4 Statistical Model ............................. 29 2.5 A directed graph describing the causal relationships ......... 30 2.6 A directed graph used to illustrate the notion of d-separation .... 33 3.1 Multilevel phenotype switch functioning in the brain cancer ..... 37 3.2 Probability for endothelial tip cells migration .............. 49 4.1 The translation from a causal model to an observational model .... 50 4.2 Alternative causal model ......................... 52 4.3 A directed acyclic graph (DAG) involving six variables ........ 58 4.4 Nesting model: Model B is nested within A .............. 64 4.5 A simple SEM, and its associated diagrams ............... 66 4.6 The diagrams associated with model .................. 67 4.7 Path diagram vs Undirected graph ................... 72 5.1 Causal Model: Without TKI treatment ................. 80 5.2 Alternative Models: Without TKI treatment .............. 82 5.3 Causal Model: With TKI treatment ................... 86 viii 5.4 Alternative Models 1,2: With TKI treatment .............. 87 5.5 Alternative Models 3,4: With TKI treatment .............. 88 5.6 Estimation of path coefficient in causal model: With TKI treatment . 92 5.7 Implied correlation matrix of causal model: With TKI treatment ... 93 5.8 Estimation of path coefficient in alternative model: With TKI treatment 93 5.9 Implied correlation matrix of alternative model: With TKI treatment 94 A.1 SEM methodology depicted as an inference engine ........... 102 A.2 Causal Structure using PC algorithm .................. 104 ix ACKNOWLEDGEMENTS My dissertation would have not been finished without my professor, Dr. Mihajlo Mesarovic, who gives me guidance and inspires me in every possible way.He not only has given me knowledge, but he has also inspired and shaped my life. I have learned many things from him, and I am forever grateful for our relationship both inside and outside the classroom.It has been four years of being his visitor at home and it was the four years of enjoying conversation about my dissertation. I would like to thank you him for supporting me and devoting himself to my study since the beginning. I would like to thank you Dr. Sree N. Sreenath for his kind effort to support me and to provide an indispensable advice, information, and support on different aspects of my dissertation.Thank you for your patience with me over the last four years of my study. Your support was essential for my success here. Additionally, I would like to thank you Dr.Vira Chankhong who gives me an opportunity to pursuit my dream. I cannot imagine where am I going to be if he was not there at the first place.Without him I could not have a chance to see another successful steps of my life. Finally, I would like to thank you the committee,Dr. James W. Jacobberger and Dr. Evren Cavusoglu, whose work demonstrated to me that concern for cancer treat- ment requires another approach that can help solve the problems and it is required diversity of knowledge. Thank you. x Exploration of Causal and Correlational Modelling