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Table Of Integrals Series And Products

On robust estimation of the location parameter

This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

/pdf/bayesian-experimental-design-a-review-1z4pqf25ac.pdf

Bayesian Experimental Design: A Review

Matrix Differential Calculus with Applications in Statistics and Econometrics

Generalized Linear Models (2nd ed.)

This article summarizes recent work in optimal experimental design in nonlinear problems, in which the major difficulty in obtaining good or optimal designs is their dependence on the true value of the parameters. This difficulty arises in problems with nonlinear models or with linear models in which interest lies in a nonlinear function of the parameters. Most approaches use a static design based on “prior” information about the parameters or a sequential procedure that takes advantage of the inflow of new information about them. The various versions of these methods are discussed, as are some of the consequent problems of inference. Some selected procedures are compared using simulation studies.

https://www.jstor.org/stable/pdfplus/1270364.pdf

Recent Advances in Nonlinear Experimental Design

A trigonometric regression model is assumed for a problem involving circadian rhythm exhibited by peak expiratory flow. Experimental designs are sought with a view to estimating a particular nonlinear function of the parameters. Both optimal and nonoptimal, but more practicable, designs are derived and their relative efficiencies are established.

An optimal design problem in rhythmometry.

Contributors. Preface. Introduction. I CANCER AND HUMAN HEALTH RISK ASSESSMENT. Introductory remarks. 1. Principles of Cancer Risk Assessment: The Risk Assessment Paradigm (Vincent J. Cogliano). 1.1 The risk assessment paradigm. 1.2 Hazard identification. 1.3 Dose-response assessment. II BIOLOGICAL ASPECTS OF CARCINOGENESIS. Introductory remarks. 2. Molecular Epidemiology in Cancer Research (Gerassimos Voutsinas, Anastasia Apostolidou and Natalia Spyrou). 2.1 Introduction. 2.2 From carcinogen exposure to cancer. 2.3 Biomarkers. 2.4 Validation of biomarkers. 2.5 Factors influencing cancer risk. 2.6 New tools in molecular epidemiology. 2.7 Conclusions. 3. Genetic Polymorphisms in Metabolising Enzymes as Lung Cancer Risk Factors (Angela Risch, Heike Dally and Lutz Edler). 3.1 Introduction. 3.2 Methodological aspects. 3.3 Examples. 3.4 Discussion. Acknowledgements. 4. Biological Carcinogenesis: Theories and Models (Sylvia Solakidi, Constantinos E. Vorgias and Constantine E. Sekeris). 4.1 Introduction. 4.2 Models of human carcinogenesis. 4.3 The multistage mouse skin carcinogenesis model. 4.4 Epilogue. 5. Biological and Mathematical Aspects of Multistage Carcinogenesis (E. Georg Luebeck and Suresh H. Moolgavkar). 5.1 Introduction. 5.2 Features of multistage carcinogenesis. 5.3 Generalized TSCE model. 5.4 Modeling cancer incidence. 5.5 Summary. 6. Risk Assessment and Chemical and Radiation Hormesis: A Short Commentary and Bibliographic Review (Jose J. Amaral Mendes and Eric Pluygers). 6.1 Introduction. 6.2 The concept of hormesis. 6.3 Chemical hormesis. 6.4 Radiation hormesis. 6.5 Concluding remarks. III MODELING FOR CANCER RISK ASSESSMENT. Introductory remarks. 7. Modeling Exposure and Target Organ Concentrations (Karen H. Watanabe). 7.1 Introduction. 7.2 Data from molecular biology. 7.3 The next generation of physiological models. 7.4 Discussion and conclusions. Acknowledgements. 8. Stochastic Carcinogenesis Models (Annette Kopp-Schneider, Iris Burkholder and Jutta Groos). 8.1 Introduction. 8.2 Stochastic models for hepatocarcinogenesis. 8.3 Model-based evaluation of liver focal lesion data. 8.4 Conclusions. 9. A Unified Modeling Approach: From Exposure to Disease Endpoints (Chao W. Chen). 9.1 Background. 9.2 Conventional approach to modeling carcinogenesis. 9.3 State space modeling using sampling techniques. 9.4 Self-organizing algorithm for state space modeling. 9.5 Some examples of state space models. 9.6 A computing procedure for the three-stage model. 9.7 Discussion. Appendix: Simulation programs. 10. Modeling Lung Cancer Screening (Marek Kimmel, Olga Y. Gorlova and Claudia I. Henschke). 10.1 Introduction. 10.2 Screening and Other Relevant Studies. 10.3 Principles of modeling of lung cancer screening. 10.4 Review of modeling approaches. 10.5 Modeling the impact of new screening modalities on reduction of mortality from lung cancer. 10.6 Comparison of models and concluding remarks. 11. Optimal Regimens of Cancer Screening (Leonid G. Hanin and Lyudmila V. Pavlova). 11.2 Optimal screening. 11.3 Formula for the screening efficiency functional. 11.4 The data and parameter estimation. 11.5 Numerical experiments. 11.6 Discussion. Acknowledgement. IV STATISTICAL APPROACHES FOR CARCINOGENESIS STUDIES. Introductory remarks 12. Analysis of Survival Data with Non-proportional Hazards and Crossings of Survival Functions (Vilijandas B. Bagdonavic ius and Mikhail S. Nikuline). 12.1 Introduction. 12.2 Models. 12.3 Parametric and semiparametric estimation. 12.4 Goodness-of-fit for the Cox model against the cross-effects models. 12.5 Examples. 12.6 Concluding remarks. Appendix: Proof of Theorem 12.1. 13. Dose-response Modeling (Lutz Edler, Annette Kopp-Schneider and Harald Heinzl). 13.1 Introduction. 13.2 Elements of the dose-response assessment. 13.3 Dose-response models. 13.4 Dose-response models in risk assessment. 13.5 Dose-Response modeling of 2,3,7,8-tetrachlorodibenzo-p-dioxin. 13.6 Concluding remarks. 14 Benchmark Dose Approach (Fred Parham and Christopher Portier). 14.1 Introduction. 14.2 Use by regulatory agencies. 14.3 Calculation methods. 14.4 Literature survey. 14.5 Software and calculation example. 15. Uncertainty Analysis: The Bayesian Approach (Frederic Y. Bois and Cheikh T. Diack 15.1 Introduction. 15.2 Representations of uncertainty. 15.3 Causes of uncertainty. 15.4 Types of uncertainty. 15.5 Quantifying uncertainty. 15.6 Reducing uncertainty. 15.7 Conclusion. Acknowledgements. 16. Optimal Designs for Bioassays in Carcinogenesis (Christos P. Kitsos). 16.1 Introduction. 16.2 On the optimal design theory. 16.3 The Michaelis-Menten model. 16.4 Dose extrapolation designs. 16.4.1 The Weibull model. 16.5 Discussion. Acknowledgements. V SPECIFIC MODELING APPROACHES FOR HEALTH RISK ASSESSMENT. Introductory remarks 17. Cancer Risk Assessment for Mixtures (Christos P. Kitsos and Lutz Edler). 17.1 Introduction. 17.2 Basic principles. 17.3 Design of mixture experiments. 17.4 Discussion. 18. Designs and Models for Mixtures: Assessing Cumulative Risk (James J. Chen, Ralph L. Kodell and Yi-Ju Chen). 18.1 Introduction. 18.2 Experimental designs and models for whole mixture. 18.3 Dose-response modeling for component-based approach. 18.4 Component-based risk assessment for quantitative response data. 18.5 Discussion. 19 Estimating the Natural History of Breast Cancer from Bivariate Data on Age and Tumor Size at Diagnosis (Alexander V. Zorin, Lutz Edler, Leonid G. Hanin and Andrej Y. Yakovlev). 19.1 Introduction. 19.2 The model. 19.3 Estimation of model parameters. 19.4 Data analysis. Acknowledgements. VI CASE STUDIES. Introductory remarks. 20. Statistical Issues in the Search for Biomarkers of Colorectal Cancer Using Microarray Experiments (Byung-Soo Kim, Sunho Lee, Inyoung Kim, Sangcheol Kim, Sun Young Rha and Hyun Cheol Chung). 20.1 Introduction. 20.2 Experiments, data and statistical issues. 20.3 Results. 20.4 Discussion. Acknowledgements. 21. Optimal Experimental Designs for Prediction of Morbidity after Lung Resection (Jesus F. Lopez Fidalgo, Sandra A. Garcet-Rodr& acute guez and Gonzalo Varela). 21.1 Medical problem. 21.2 Prediction model and advantage of designing the experiment. 21.3 Optimal experimental design approach. 21.4 Solution. 22. Logistic Regression Methods and their Implementation (Vassiliki K. Kotti and Alexandros G. Rigas). 22.1 Introduction. 22.2 Neurophysiological example. 22.3 Logistic regression. 22.4 Neurophysiological example revisited. 22.5 Discussion. 23. The use of Logistic Regression, Discriminant Analysis and Classification Trees in Predicting Persisting Remission in Childhood Leukemia (Malgorzata Cwiklinska-Jurkowska, Piotr Jurkowski and Andrzej Koltan). 23.1 Introduction. 23.2 Patients. 23.3 Methods. 23.4 Results. 23.5 Discussion. 23.6 Concluding remarks. 24. Non-melanoma Skin and Lung Cancer Incidence in Relation to Arsenic Exposure: 20 Years of Observation (Vladim& acute r Bencko, Petr Franek, Jir& acute Rames, Elenora Fabianova and Miloslav Gotzl). 24.1 Introduction. 24.2 Material and methods. 24.3 Results. 24.4 Discussion. 24.5 Conclusion. Acknowledgements. 25. Thyroid Cancer Incidence Rates in Zaragoza (Milagros Bernal). 25.1 Introduction. 25.2 Materials and methods. 25.3 Results. 25.4 Discussion. References. Index.

Recent advances in quantitative methods in cancer and human health risk assessment

Evaluation of the optimal design “cosinor model” for enhancing the potential of robotic theodolite kinematic observations

We introduce a three-parameter generalized normal distribution, which belongs to the Kotz type distribution family, to study the generalized entropy type measures of information. For this generalized normal, the Kullback-Leibler information is evaluated, which extends the well known result for the normal distribution, and plays an important role for the introduced generalized information measure. These generalized entropy type measures of information are also evaluated and presented.

Christos P. Kitsos

Papers

Recent Advances in Nonlinear Experimental Design

An optimal design problem in rhythmometry.

Recent advances in quantitative methods in cancer and human health risk assessment

Evaluation of the optimal design “cosinor model” for enhancing the potential of robotic theodolite kinematic observations

New Information Measures for the Generalized Normal Distribution