Assessing By Model Fitting Criteria and Comparing Between Stirling and Aitken Interpolation Formulas to Determine the Preferred Treatment of Choice, (Surgery) Or (Surgery with Chemotherapy), For Lung Cancer, In Kurdistan
DOI:
https://doi.org/10.21271/zjhs.28.3.15Keywords:
Stirling's interpolation formula and Aitken interpolation formula, (surgery) or (surgery with chemotherapy) treatments, Model Fitting Criteria.Abstract
Numerical analysis is a branch of mathematical science; Interpolation is a method in Numerical analysis used for creating a model for group of discrete data points. This paper focused on two interpolations methods [Stirling's and Aitken] in numerical analysis can use the applied mathematics, to identify the mathematical model which it is bio statistical model refers to the equation about the effect of the best type of treatment for the Lung cancer, where the Lung cancer is a dangers disease either starts in the lungs then extend to the lymphatic system or from cancer in the other part of body to the Lung.to determine the preferred treatment of lung cancer, by surgery, or surgery with chemotherapy. for this analysis data obtained from the doctor specialist in Lung cancer through ratio percentages success of treatment , and by [Stirling's and Aitken interpolation formula] we formulated, firstly two(equations) or models for (surgery with chemotherapy treatments) with the fourth and third degrees , and Secondly, another two equations for (surgery treatments ) with second degree , this confirms that surgery with chemotherapy is preferred treatment of lung cancer patients, and since the Stirling interpolation equation in the fourth degree emphasize that it is the most appropriate formula for bio-statistical analyses. by Cox and Snell R-Square in both treatments refer to good ratio and in the statistical analysis, the model fitting criteria in both analyzes the p-values emphasize the best fit of the models indicates perfect prediction. Improvement.
References
-Anita Pal (2017) Numerical Analysis. Aitken's and Hermite's Interpolation Methods Department of Mathematics National Institute of Technology Durgapur Durgapur-713209 august 2017
-BARZNJI, N. S, (2018). Using Logistic Regression Analysis and Linear Discriminate Analysis to identify the risk factors of diabetes, Vol.22, No.6, (pp 248-268), ID No.2115).
-Collins LG, Haines C, Perkel R, Enck RE (2007). "Lung cancer: diagnosis and management". American Family Physician. 75 (1):56–63
-David Kincaid and Ward Cheney,"(2002) Numerical Analysis - Mathematics of Scientific Computing", American Mathematical Society, Providence, Rhode Island
-Endre S¨uli and David F. Mayers (2003) "An Introduction to Numerical Analysis"
Published in the United States of America by Cambridge University Press, New Yorkwww.cambridge.org
- Goldstein SD, Yang SC (2011). "Role of surgery in small cell lung cancer". Surgical Oncology Clinics of North America. 20 (4): 769-–. doi:10.1016/j.soc.2011.08.001. PMID 21986271
-Hecht SS (2012). "Lung carcinogenesis by tobacco smoke". International Journal of Cancer. 131 (12):2724-32. doi:10.1002/ijc.27816. PMC 3479369. PMID 22945513
-Humpherys, Jeffrey; Jarvis, Tyler J. (2020). "9.2 - Interpolation". Foundations of Applied Mathematics Volume 2: Algorithms, Approximation, Optimization. Society for Industrial and Applied Mathematics. p. 418. ISBN 978-1-611976-05-2.
-Islam, S., Y. Khan, N. Faraz and F. Austin, 2010. "Interpolation and approximation, Numerical solution of logistic differential equations "Second edition, Dover, New York, NY, 1975. by using the Laplace decomposition method, World Appl. Sci. J., 8: 1100-1105.
-Kahaner, David, Cleve Moler, and Stephen Nash.( 1989) Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall.
-Karl, L. W. and P (2016), Binary Logistic Regression with SPSS, published in the Journal of Social Behavior and Personality, 13, P.P139-150.
-Kendall E. Atkinson, (2012) "An Introduction to Numerical Analysis", Wiley India.
-Kumar, Rakesh (2020) “Interpolation” (Deptt. Of Mathematics), P.G.G.C.G, Sec-11, Chandigarh.
-Meijering, Erik(2002). “A Chronology of Interpolation: From Ancient Astronomy to Modern Signal and Image Processing.” Proceedings of the IEEE. vol. 90, no. 3, pp. 319-42. March
-Menard, S. (2022). Applied Logistic Regression Analysis. SAGE. p. 91.
-Mertler, C.A., & Vannatta, R.A. (2015). Advanced and multivariate statistical methods: practical application and interpretation (3rd. edition). Glendale, CA: Pyrczak Publishing
-Milne-Thomson, Louis Melville (2000). "The Calculus of Finite Differences" AMS Chelsea Publishing. pp. 67–68. ISBN 9780821821077.
-Miller AB, Fox W, Tall R (2019). "Five-year follow-up of the Medical Research Council comparative trial of surgery and radiotherapy for the primary treatment of small-celled or oat-celled carcinoma of the bronchus". Lancet. 2 (7619): 501–5. doi:10.1016/S0140-6736(69)90212-8. PMID 4184834
-Pal. Dr. Anita (2007)” Numerical Analysis” Department of Mathematics National Institute of Technology Durgapur Durgapur-713209 email: anita.buie@gmail.com
-Pletzer, Alexander; Hayek, Wolfgang (2019-01-01). "Mimetic Interpolation of Vector Fields on Arakawa C/D Grids". Monthly Weather Review. 147 (1): 3–16. Bibcode:2019MWRv..147....3P. doi:10.1175/MWR-D-18-0146.1. ISSN 1520-0493. S2CID 125214770.
-P.J. Davis, (1975) "Interpolation and approximation" , Dover, reprint pp. 108–F.B.
-P. Sam Johnson (2020) Newton’s Interpolation Methods"(NITK) February 7, 2020 .1 / 47
-Richard L. Burden and J. Douglas Faires (2015)," Numerical Analysis - Theory and Applications", Cengage Learning, Singapore.
-Robbins, Herbert (1955), "A Remark on Stirling's Formula", The American Mathematical Monthly, 62 (1):26–29, doi:10.2307/2308012, JSTOR 2308012
- Romik, Dan (2000), "Stirling's approximation for : the ultimate short proof?", The American Mathematical Monthly, 107 (6): 556–557, doi:10.2307/2589351, JSTOR 2589351, MR 1767064
-Steffensen, J. F. (2006). Interpolation (Second ed.). Mineola, N.Y. ISBN 978-0-486-15483-1. OCLC 867770894
-Whittaker, E. T. & Watson, G. N. (1996), A Course in Modern Analysis (4th ed.), Newwork
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