Using a Mathematical Model in the Evaluation of Human Tumor Response to Chemotherapy23

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Abstract
The paper presents a method for analyzing short-term response of human tumors to cancer chemotherapy. The method was applied on data furnished through the courtesy of the Clinical Drug Evaluation Program, Eastern Region, a cooperative chemotherapy program of the National Institutes of Health. A mathematical model describing the progress of tumor size during a period of chemotherapy was used. During intervals between doses of the drug the tumor was assumed to follow an exponential growth process. The proportion of tumor cells killed by the drug was assumed to be a logistic function of the logarithm of the cumulative dosage of the drug. From fitting the model, estimates of tumor growth rate and drug effect were obtained for each tumor. The respective averages of these parameters across tumors in a patient provided summary values of drug effect and tumor growth rate for the patient. Two drugs, 5-fluorouracil and 6-mercaptopurine, were studied in patients whose primary lesion site was the lung, breast, the colon or rectum, or the mouth, larynx, or pharynx. Among patients whose primary lesion site was the colon or rectum, those treated with 5-fluorouracil showed a significantly greater effect than those treated with 6-mercaptopurine. For the other three primary sites, no significant differences between the drugs were found. In addition, tumors within a patient resembled one another more than they resembled tumors of other patients, both with regard to their growth rates and to their response to the drug.

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