How do the various models help us to address the questions posed in the first two paragraphs? What are the implications of the various cytokinetic models for treatment? To illustrate how mathematical models have been used to design clinical trials, two clinical trials for the adjuvant treatment of breast cancer are briefly discussed.
One of the relatively early clinical trials for women with node-positive breast cancer compared the Norton-Simon model (four courses of adriamycin followed by eight courses of CMF ['sequential']) with the Goldie-Coldman model (two courses of CMF alternated with one course adriamycin for a total of 12 courses ['alternating']) [42]. The 5-year relapse-free survival for the sequential administration arm was 61% and for the alternating administration was 38% (P = 0.001). The corresponding figures for 5-year overall survival were 78 and 62%, respectively. The benefit of sequential therapy was observed in all patient subsets.
A clinical trial was designed by the International Breast Cancer Study Group, trial VI, in order to try to examine the possibility that chemotherapy reintroduced at times after the completion of an early postoperative course would be able to treat those cells that have emerged from dormancy [43]. Premenopausal women with node-positive breast cancer (n = 1554) were randomly assigned in a 2 × 2 factorial design to receive the following: CMF for six consecutive courses on months 1-6 (CMF ×6); CMF × 6 plus three single courses of reintroduction CMF on months 9, 12 and 15; CMF for 3 consecutive courses on months 1-3 (CMF × 3); or CMF × 3 plus three single courses of reintroduction CMF given on months 6, 9 and 12.
Patients who were treated with reintroduction chemotherapy had a 5-year disease-free survival rate of 58 ± 2%, compared with 55% ± 2% for those who did not receive reintroduction (hazards ratio 0.86, 95% confidence interval 0.73-1.01; P = 0.07). The overall survival figures were 76% ± 2% and 75% ± 2%, respectively. Although reintroduction showed a trend toward a therapeutic effect, this difference was not statistically significant. Patients randomized to receive reintroduction had an estimated reduction of relapse of 14% whether the initial chemotherapy consisted of three cycles or six cycles.
Although this study does not definitively support the Retsky-Demicheli model, it could be due to the design of the study. Women who were eligible for the International Breast Cancer Study Group trial VI ranged across the staging spectrum from IIA to IIIA. The benefit of reintroduction may have accrued disproportionately to those women who had primary tumors that were less than or equal to 2.0 cm (T1) with one to three positive nodes, and it may be enlightening to re-examine this subset of patients specifically. Also to be considered when examining the results of the trial are the consequences of prolonged chemotherapy. Compliance with chemotherapy trials is inversely associated with toxicity and duration of treatment. Among the patients assigned to receive reintroduction after six initial courses, 85% started and 75% completed the reintroduction as scheduled in months 9, 12, and 15. This decreased compliance may have diluted the therapeutic effect of the reintroduction regimen in practice. This suggests the possibility that a cytostatic agent, such as an angiogenesis inhibitor, which could be administered chronically with less toxicity, might be better tolerated than an intermittent cytotoxic agent.
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