Survival Curve for Cancer Patients Following Treatment

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Abstract
On the basis of experience with calculated survivorships of patients following treatment for cancer, a simple function, in terms of two physically meaningful parameters, has been evolved, which fits such survivorship data very well. These two parameters can be used to compare succinctly the mortality of two groups, different in respect of treatment, type of cancer, or other characteristics. The parameters are c (“cured”), which represents the proportion of the population which is subject only to “normal” death rates, and β, which is the death rate from the cancer, to which the rest of the population [not “cured,” (1–c)] is subject. Thus if one treatment is characterized by c 1 = 0.30, β 1 = 0.25, another by c 2 = 0.20, β 2 = 0.15, this could be interpreted as meaning that while the first treatment “cured” a larger proportion of the population than did the second treatment, it did not ameliorate the deaths attributable to cancer in the patients not cured as much as did the second treatment. If l T is the proportion of the total population surviving to time t, then the function is l T = cl 0+ (1 – c)l 0e −-βt where l 0 is the net survivorship corresponding to “normal” deaths, obtained from standard life tables. A graphic method and also a “least squares” method of estimating c and β are presented with an example, and the evaluated parameters are given for several series of treated cancer patients. Expectation of life and other functions of the life table also have been calculated from the evaluated parameters, for the same series.

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