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.
Highlights
The results of this study reveal that the method of computer-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 fitting the National Center for Health Statistics (NCHS)-reported data on survival probabilities and death rates in the US total adult population
The above results suggest that regression curves of the least sum of squares are closer to the NCHS-data-connecting line than those of the least maximum-difference
A computer program of nonlinear, curved regression of the least sum of squares is designed to determine the constant values of γ in Eq.1 and c in Eq.2 that seems better fitting and more accurate than those obtained by the least maximum-difference principle as suggested by the data shown in Tables 3 and 4
Summary
The model of the “probacent”-probability equation was constructed from experimental studies on animals to express survival probability in mice exposed to g-force in terms of magnitude of acceleration and exposure time [1,5]; and to express a relationship among intensity of stimulus or environmental agent (such as drug [1,2,6], heat [7], pH [8], electroshock [7,9] and radiation [4,10]), duration of exposure and biological response in animals. The model was applied to the United States life tables, 1992 and 2001 reported by the National Center for Health Statistics (NCHS) to construct formulas expressing age-specific survival probability, death rate and life expectancy in US adults, men and women [3,28,29,30,31].
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