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Computer program of nonlinear, curved regression for ‘probacent’-probability equation in biomedicine

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DOI: 10.4236/jbise.2011.49078    4,289 Downloads   8,140 Views   Citations
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ABSTRACT

On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘probacent’-probability equation, Equation (1) and death rate (mortality probability) equation, Equation (2) derivable from Equation (1) that may be applica-ble as a general approximation method to make use-ful predictions of probable outcomes in a variety of biomedical phenomena [1-4]. Equations (1) and (2) contain a constant, γ and c, respectively. In the pre-vious studies, the author used the least maximum- difference principle to determine these constants that were expected to best fit reported data, minimizing the deviation. In this study, the author uses the method of computer-assisted least sum of squares to determine the constants, γ and c in constructing the ‘probacent’-related formulas best fitting the NCHS- reported data on survival probabilities and death rates in the US total adult population for 2001. The results of this study reveal that the method of com-puter-assisted mathematical analysis with the least sum of squares seems to be simple, more accurate, convenient and preferable than the previously used least maximum-difference principle, and better fit-ting the NCHS-reported data on survival probabili-ties and death rates in the US total adult population. The computer program of curved regression for the ‘probacent’-probability and death rate equations may be helpful in research in biomedicine.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Chung, S. (2011) Computer program of nonlinear, curved regression for ‘probacent’-probability equation in biomedicine. Journal of Biomedical Science and Engineering, 4, 620-630. doi: 10.4236/jbise.2011.49078.

References

[1] Chung, S.J. (1960) Studies on a mathematical relationship between stress and response in biological phenomena. Republic of Korea Journal of the National Academy of Sciences, 2, 115-162.
[2] Chung, S.J. (1986) Computer-assisted predictive math- ematical relationship among metrazol dose and time and mortality in mice. Computer Methods and Programs in Biomedicine, 22, 275-284. doi:org/10.1016/0169-2607(86)90004-0
[3] Chung, S.J. (2007) Computer-assisted predictive formulas expressing survival probability and life expectancy in US adults, men and women, 2001. Computer Methods and Programs in Biomedicine, 86, 197-209. doi:org/10.1016/j.cmpb.2007.02.009
[4] Chung, S.J. (2011) Predictive formulas expressing dose rate, duration of exposure and mortality probability in total body irradiation in humans. Journal of Biomedical Science and Engineering, 4, 497-505. doi:org/10.4236/jbise.2011.47063
[5] Chung, S.J. (1959) Studies of positive radial acceleration on mice. Journal of Applied Physiology, 14, 52-54.
[6] Boak, H. and Chung, S.J. (1962) Studies on a relationship between dose, time and percentage of occurrence of response and a method of evaluation of combined action in drugs. The New Medical Journal, 5, 35-82.
[7] Kim, C.C. and Chung, S.J. (1962) Studies on a relationship between stress, duration of exposure and percentage of response in goldfish to single, double and triple stresses of acceleration, electroshock, heat, chemical and osmotic stimuli. Republic of Korea Theses of Catholic Medical College, 5, 257-336.
[8] Cho, D.W. and Chung, S.J. (1961) Studies of tolerance of Paramecium caudatum to hydrogen and hydroxyl ions. Bulletin of Yamaguchi Medical School, 8, 151-160.
[9] Chung, S.J. (1989) Computer-assisted mathematical relationship among electroshock voltage and duration and occurrence of convulsion in mice. Computer Methods and Programs in Biomedicine, 28, 23-30. doi:org/10.1016/0169-2607(89)90177-6
[10] Cerveny, T.J., MacVittie, T.J. and Young, R.W. (1989) Acute radiation syndrome in humans. Medical Consequences of Nuclear Warfare, TMM Publishers, Office of the Surgeon General, Falls Church, Virginia, 1989, 15-36.
[11] Forbes, W.H., Sergent, F. and Roughton, F.J.W. (1988) The risk of carbon monoxide uptake by normal men. American Journal of Physiology, 143, 594-608.
[12] Chung, S.J. (1988) Formula predicting carboxyhemoglobin resulting from carbon monoxide exposure. Veterinary and Human Toxicology, 30, 528-532.
[13] Prescott, L.F., Roscoe, P., Wright, N. and Brown, S.S. (1991) Plasma paracetamol half-life and hepatic necrosis in patients with paracetamol overdosage. Lancet, I, 519-522.
[14] Chung, S.J. (1989) Computer-assisted predictive math- ematical relationship among plasma acetaminophen concentration, time after ingestion and occurrence of hepatotoxicity in man. Computer Methods and Programs in Biomedicine, 28, 37-43. doi:org/10.1016/0169-2607(89)90179-X
[15] Popescu, N.A., Beard, C.M., Winkelman, P.J., O’Brien, P.C. and Kurland, L.T. (1990) Cutaneous malignant melanoma in Rochester, Minnesota: Trends in incidence and survivorship, 1950 through 1985. Clinical Proceedings, 65, 1293-1302.
[16] Chung, S.J. (1991) Formula predicting survival in patients with invasive cutaneous malignant melanoma. International Journal of Biomedical Computing, 28, 151-159.
[17] Chung, S.J. (1994) Formulas expressing relationship among lesion thickness, time after diagnosis and survival probability in patients with malignant melanoma.
[18] Chung, S.J. (1994) Formula expressing a relationshipp among lesion thickness and time after diagnosis and survival probability in patients with malignant melanoma. International Journal of Biomedical Computing, 37, 171- 180. doi:org/10.1016/0020-7101(94)90139-2
[19] Kirklin, J.R., Naftel, D.C., Kirklin, J.W., Blackstone, E.H., White-Williams, C. and Bourge, R.C. (1988) Pulmonary vascular resistance and the risk of heart transplantation. Journal of Heart Transplantation, 7, 331-336.
[20] Chung, S.J. (1993) Formula predicting survival probability in patients with heart transplantation. International Journal of Biomedical Computing, 32, 211-221. doi:org/10.1016/0020-7101(93)90015-X
[21] Magbool, G., Kaul, K.K., Corea, J.R., Osman, M. and Arfaj, A. (1993) Weight and height of Saudi children six to 16 years from the Eastern Province. Annal of Saudi Medicine, 13, 344-349.
[22] Vaughan, V. C. and Litt, I. F. (1987) Growth and development. Textbook of Pediatrics, Philadelphia, 6-35.
[23] Chung, S. J. (1994) Formulas expressing relationship among age height and weight, and percentile in Saudi and US children of ages 6-16 years. International Journal of Biomedical Computing, 37, 259-272. doi:org/10.1016/0020-7101(94)90124-4
[24] Sholz, D.C., Kitzman, D.W., Hagen, P.T., Ilstrup, D.H. and Edwards, W.D. (1988) Age-related changes in normal human hearts during the first 10 decades of life. Part. I. (Growth): A quantitative anatomic study of 200 specimens from subjects from birth to 19 years old. Mayo Clinic Proceedings, 13, 126-136, 637.
[25] Chung, S.J. (1990) Formulas predicting the percentiles of heart weight by body weight in subjects from birth to 19 years of age. International Journal of Biomedical Computing, 26, 257-269. doi:org/10.1016/0020-7101(90)90049-Z
[26] Feinleib, M. (1986) Total serum cholesterol levels of adults 20-70 years of age; United States, 1976-1980. US Department of Health and Human Services publication (PHS). The National Health Survey, 11, 86-1686.
[27] Chung, S.J. (1990) Formulas predicting the percentile of serum cholesterol levels by age in adults. Archives of Pathology and Laboratory Medicine, 114, 869-895.
[28] Chung, S.J. (1992) Relationship among age, serum cholesterol level and population percentile in adults. International Journal of Biomedical Computing, 31, 99-1116.
[29] The National Center for Health Statistics (1993) Annual survey of births, deaths, marriages and divorces, United States, 1992. Monthly Vital Statistics Report, 41, 1-36.
[30] Arias, E. (2004) United States life tables, 2001. National Vital Statistics Report, 52, 1-40.
[31] Chung, S.J. (1995) Formulas expressing life expectancy, survival probability and death rate in life tables at various ages in US adults. International Journal of Biomedical Computing, 39, 209-217. doi:org/10.1016/0020-7101(94)01068-C
[32] Chung, S.J. (1997) Comprehensive life tables of computer-assisted predictive mathematical relationship among age and life expectancy, survival probability or death rate in US adults. Computer Methods and Programs, 52, 67-73. doi:org/10.1016/S0169-2607(96)01778-6
[33] Lee, E.T. and Wang, J.W. (2003) Statistical Methods for Survival Data, John Wiley & Sons, Hoboken, New Jersey, 8-197. doi:org/10.1002/0471458546.ch2
[34] Chung, S.J. (2011) Predictive formulas expressing mathematical relationship between dose rate of total body irradiation and survival time in mice, (unpublished).
[35] Mehta, S.C. and Joshi, H.C. (2004) Model based point estimates of survival/death rate: An input for radiation risk evaluation in Indian context. Indian Journal of Nuclear Medicine, 19, 16-18.
[36] Dixon, W.J. and Massey J.F.J. (1957) Introduction to Statistical Analysis, McGraw-Hill, New York, 191-204, 226-227.
[37] Fogiel, M. (2004) The Statistics Problem Solver, Research and Education Associates, Piscataway, New Jersey. Simpson, D.G. (2010) All about linear regression. http://www.pgccphy.net/Linreg/linreg.html.pdf
[38] Department of Statistics, University of Florida, Multiple linear regression model, (2006). http://www.stat-ufl.edu/CouseINFO/STA6167/Linear%20Regression%202.pdf
[39] Atkins, G. (1971) A versatile digital computer program for non-linear regression analysis. Biochimica et Biophysica Acta, 252, 405-420.
[40] Buys, J.D. and Gadow, K.V. (1987) A PASCAL program for fitting nonlinear regression models on a microcomputer. Medicine and Biology (Medizin und Biologie), 18, 105-107.
[41] Boomer, D.W.A. (2001) Phar 7633 Chapter 22, Nonlinear regression analysis of pharmacokinetic data, individual data and population analysis. http://boomer.org/c/p4/c22/c2201.html.
[42] Laub, P.B. and Gallo, J.M. (1996) NCOMP-A windows- based computer program for noncompartmental analysis of pharmacokinetic data. Journal of Pharmacokinetical Science, 85, 393-395. doi:org/10.1021/js9503744
[43] Hastings J.C. (1955) Approximation for Digital Computer, Princeton University Press, Princeton, New Jersey, 185.
[44] Presley, B. (1982) A Guide to Programming-the IBM Personal Computer, Lawrenceville Press, Inc., New York.
[45] Gottfried, B. (1993) Shaum’s Outline of Theory and Problems of Programming with Standard BASIC, McGraw-Hill, Inc., New York.
[46] Chung, S.J. (2009) Seeking a New World: A New Philosophy of Confucius and Kim Hang, iUniverse, Bloomington, Indiana, 68-76, 153.
[47] Hawking, S.W. (1988) A Brief History of Time, Bantam Books, New York, 31-32, 53-61.
[48] Suplee, C. (1999) Physics in the 20th Century, Hany N. Abrams, Inc., New York, 82.
[49] Chung, S.J. (2010) The Book of Right Change, Jeong Yeok: A New Philosophy of Asia, iUniverse, Bloomington, Indiana, 10.

  
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