Abstract
Based on the data available through published trial results, we build a mixed integer nonlinear programming (MINLP) model in order to find an optimal treatment plan for a given HR+ early stage breast cancer patient who is postmenopausal. The objective is to maximize the disease-free survival percentage at the end of the treatment period subject to the constraints on the risk of contralateral breast cancer and the risks of several side effects, including endometrial cancer, thromboembolic events, cardiovascular diseases, bone fractures, hot flushes, and vaginal bleeding. The results of numerical experiments suggest the effectiveness of some of the schedules currently used in practice, as well as suggest some attractive alternative treatment plans.
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References
American Cancer Society (2009). Cancer reference information. http://www.cancer.org.
Agur, Z., Hassin, R., & Levy, S. (2006). Optimizing chemotherapy scheduling using local search heuristics. Operations Research, 54(5), 829–846.
ATAC Trialist Group (2004). Results of the ATAC (Arimidex, Tamoxifen, Alone or in Combination) trial after completion of 5 years’ adjuvant treatment of breast cancer. Lancet, 364, 1–3.
Barbolosi, D., & Iliadis, A. (2001). Optimizing drug regimens in cancer chemotherapy: a simulation study using a pk-pd model. Computers in Biology and Medicine, 31, 157–172.
Beil, D. R., & Wein, L. M. (2001). Analysis and comparison of multimodal cancer treatments. IMA Journal of Mathematics Applied in Medicine and Biology, 18, 343–376.
Bergman, L., Beelen, M., Gallee, M. P., Hollema, H., Benraadt, J., & van Leeuwen, F. (2000). Risk and prognosis of endometrial cancer after tamoxifen for breast cancer. Lancet, 356, 881–887.
Boccardo, F., Rubagotti, A., Puntoni, M., et al. (2005). Switching to anastrozole versus continued tamoxifen treatment of early breast cancer: preliminary results of the Italian tamoxifen anastrozole trial. Lancet, 366, 455–462.
Brahme, A. (2001). Individualizing cancer treatment: biological optimization models in treatment planning and delivery. International Journal of Radiation Oncology, Biology, Physics, 49(2), 327–337.
Breast International Group (BIG) 1-98 Collaborative Group (2005). A comparison of letrozole and tamoxifen in postmenopausal women with early breast cancer. New England Journal of Medicine, 353(26), 2747–2757.
Buzdar, A. U. (2005). Aromatase inhibitors in the adjuvant treatment of breast cancer. ASBD Breast Healthcare Update.
Coombes, R. C., Hall, E., Gibson, L.J., et al. (2004). A randomized trial of exemestane after two to three years of tamoxifen therapy in postmenopausal women with primary breast cancer. New England Journal of Medicine, 350, 1081–1092.
Cuzick, J., Sasieni, P., & Howell, A. (2006). Should aromatase inhibitors be used as initial adjuvant treatment or sequenced after tamoxifen? British Journal of Cancer, 94(4), 460–464.
Duffy, S., Jackson, T., Lansdown, M., Philips, K., Wells, M., Pollard, S., Clack, G., Coibion, M., & Bianco, A. (2006). The ATAC (‘Arimidex’, Tamoxifen, Alone or in Combination) adjuvant breast cancer trial: first results of the endometrial sub-protocol following 2 years of treatment. Human Reproduction, 21(2), 545–553.
Early Breast Cancer Trialist’s Collaborative Group (1998). Tamoxifen for early breast cancer: an overview of the randomised trials. Lancet, 351, 1451–1467.
Fallowfield, L., Cella, D., Cuzick, J., Francis, S., Locker, G., & Howell, A. (2004). Quality of life of postmenopausal women in the Arimidex, Tamoxifen, Alone or in Combination (ATAC) adjuvant breast cancer trial. Journal of Clinical Oncology, 22, 4261–4271.
Fallowfield, L. J., Bliss, J. M., Porter, L. S., Price, M. H., Snowdon, C. F., Jones, S. E., Coombes, R. C., & Hall, E. (2006). Quality of life in the intergroup exemestane study: a randomized trial of exemestane versus continued tamoxifen after 2 to 3 years of tamoxifen in postmenopausal women with primary breast cancer. Journal of Clinical Oncology, 24, 910–917.
Ferris, M. C., Lim, J., & Shepard, D. M. (2003). An optimization approach for radiosurgery treatment planning. SIAM Journal on Optimization, 13(3), 921–937.
Fister, K. R., & Panetta, J. C. (2000). Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM Journal of Applied Mathematics, 60, 1059–1072.
Goss, P. E., Ingle, J. N., Martino, S., et al. (2003). A randomized trial of letrozole in postmenopausal women after five years of tamoxifen therapy for early-stage breast cancer. New England Journal of Medicine, 349, 1793–1802.
Goss, P. E., Ingle, J. N., Martino, S., et al. (2005). Randomized trial of letrozole following tamoxifen as extended adjuvant therapy in receptor-positive breast cancer: updated findings from NCIC CTG MA.17. Journal of the National Cancer Institute, 97(17), 1262–1271.
Hamacher, H., & Küfer, K. (2002). Inverse radiation therapy planning—a multiple objective optimization approach. Discrete Applied Mathematics, 118, 145–161.
Jakesz, R., & Menzel, C. (2005). Switching of postmenopausal women with endocrine-responsive early breast cancer to anastrozole after 2 years’ adjuvant tamoxifen: combined results of abcsg trial 8 and arno 95 trial. Lancet, 366, 455–462.
Jakesz, R., Jonat, W., Grant, M., et al. (2005). Switching of postmenopausal women with endocrine-responsive early breast cancer to anastrozole after 2 years’ adjuvant tamoxifen: combined results of ABCSG Trial 8 and ARNO 95 Trial. Journal of Clinical Oncology, 23(22), 5138–5147.
Lee, E. K., Fox, T., & Crocker, I. (2003). Integer programming applied to intensity-modulated radiation therapy treatment planning. Annals of Operations Research, 119, 165–181.
National Cancer Institute (2008). Aromatase inhibitors come of age. http://www.cancer.gov. Accessed January 2008.
Neos Server for Optimization (2008). http://www-neos.mcs.anl.gov/. Accessed January 2008.
Punglia, R. S., Kuntz, K. M., Winer, E. P., Weeks, J. C., & Burstein, H. J. (2005). Optimizing adjuvant endocrine therapy in postmenopausal women with early-stage breast cancer: a decision analysis. Journal of Clinical Oncology, 23, 5178–5187.
Romeijn, H. E., Ahuja, R. K., Dempsey, J. F., & Kumar, A. (2006). A new linear programming approach to radiation therapy treatment planning problems. Operations Research, 54, 201–216.
Saphner, T., Tormey, D. C., & Gray, R. (1996). Annual hazard rates of recurrence for breast cancer after primary therapy. Journal of Clinical Oncology, 14(10), 2738–2746.
Shin, K. G., & Pado, R. (1982). Design of optimal cancer chemotherapy using a continuous-time state model of cell kinetics. Mathematical Biosciences, 59, 225–248.
Thürliman, B. (2005). Letrozole vs. tamoxifen as adjuvant endocrine therapy for postmenopausal women with receptor-positive breast cancer. BIG 1-98: a prospective randomized double-blind phase III study. St. Gallen, Switzerland.
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Kahruman, S., Ulusal, E., Butenko, S. et al. Scheduling the adjuvant endocrine therapy for early stage breast cancer. Ann Oper Res 196, 683–705 (2012). https://doi.org/10.1007/s10479-010-0741-y
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DOI: https://doi.org/10.1007/s10479-010-0741-y