This paper is concerned with the estimation of parameters when mathematical models are fitted to data. Two new algorithms are presented. The first is fast (economical in computation time), requires no initial estimates, but is not so accurate. The second requires more computation time, and fairly accurate initial estimates, but achieves high accuracy. The models discussed consist of sets of coupled, non-linear differential equations, but the second algorithm is applicable to wider classes of models as well.The accuracy of the computed values of the parameters depends on the number of data points, and the errors in the data. The sensitivity of the different parameters to errors may differ by orders of magnitude. A method of calculating the expected errors in the parameters is described, and the results of some applications of the method are presented.

Study The aim of this study was to use a mathematical model to predict the trend in the smoking induced cancer rate for white males in the USA over a recent 15 year period. This is a matter of substantial public health importance, as there has been a major increase in the lung cancer rate for white males, as well as for all other sectors of the US population during this period. One proposed explanation is that this is the delayed effect of males taking up smoking during the period starting at the beginning of the 20th century and ending in about 1960. A second explanation is that the lung cancer increase is due to other environmental factors, such as exposure to synthetic organic carcinogens, the production and use of which rose exponentially during the postwar period. Proponents of the latter explanation point out that the relative risk of lung cancer declines sharply after a person stops smoking. Rises in smoking prevalence 25 or more years ago, which were followed by steady declines in prevalence, could not therefore be responsible for the current increase in lung cancer rate.This initial study was confined to white males in the USA because of the relatively large amount and accuracy of appropriate data, and because of the long period of decline in smoking prevalence for this group. The model can easily be extended to other groups in the population. In this paper, lung cancer rate will always mean mortality rate, although the difference between the mortality and incidence rate for lung cancer is small. BACKGROUND ON CARCINOGENESIS MODELS

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