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Research Article

Distribution of the number of clonogens surviving fractionated radiotherapy: a long-standing problem revisited

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Pages 205-213 | Published online: 03 Jul 2009

  • ASSELAIN, B., FOURQUET, A., HOANG, T., TSODIKOV, A. D. and YAKOVLEV, A. Y., 1996, A parametric regression model of tumor recurrence: an application to the analysis of clinical data on breast cancer. Statistics and Probability Letters, 29, 271-278.
  • DEASY, J., 1996, Poisson formulas for tumor control probability with clonogen proliferation. Radiation Research, 145, 382-384.
  • HANIN, L. G., 2000, Iterated birth and death process as a model of radiation cell survival, submitted to Mathematical Biosciences.
  • HANIN, L. G., YAKOVLEV, A. Y. and PAVLOVA, L. V., 1994, Biomathcmatical Problems in Optimization of Cancer Radiotherapy (Boca Raton: CRC Press).
  • KENDAL, W. S., 1998, A closed-form description of tumour control with fractionated radiotherapy and repopulation. International Journal of Radiation Biology, 73, 207-210.
  • KLEIN, M. and BARTOSZYNSKI, R., 1991, Estimation of growth and metastatic rates of primary breast cancer. In Mathematical Population Dynamics, edited by O. Arino, D. E. Axelrod and M. Kimmel (New York: Marcel Dekker), pp. 397-412.
  • MUNRO, T. R. and GILBERT, C. W., 1961, The relation between lethal doses and radiosensitivity of tumor cells. British Journal of Radiology, 34, 246-251.
  • OKADA, S., 1970, Radiation Biochemistry, Vol. 1: Cells (New York: Academic Press).
  • PORTER, E. H., 1980a, The statistics of dose/cure relationships for irradiated tumours, Part I. British Journal of Radiology, 53, 210-227.
  • PORTER, E. H., 1980b, The statistics of dose/cure relationships for irradiated tumours, Part II. British Journal of Radiology, 53, 336-345.
  • SUIT, H. D., SEDLACEK, R., FAGUNDES, L., GOITEIN, M. and ROTHMAN, K.J., 1978, Time distributions of recurrences of immunogenic and nonimmunogenic tumors following local irradiation. Radiation Research, 73, 251-266.
  • SUIT, H. D., SHALEK, R. J. and WETTE, R., 1965, Radiation response of C3H mammary carcinoma. In Cellular Radiation Biology (Baltimore, MD: Williams & Wilkins), pp. 514-530.
  • TSIATIS, A., 1975, A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences of the United States of America, 72, 20-22.
  • TSODIKOV, A., 1998a, A proportional hazards model taking account of long-term survivors. Biometrics, 54, 138-146.
  • TSODIKOV, A., 1998b, Asymptotic efficiency of a proportional hazards model with cure. Statistics and Probability Letters, 39, 237-244.
  • TSODIKOV, A. D., ASSELAIN, B., FOURQUET, A., HOANG, T. and YAKOVLEV, A. Y., 1995, Discrete strategies of cancer post-treatment surveillance. Estimation and optimization problems. Biometrics, 51, 437-447.
  • TSODIKOV, A. D., LOEFFLER, M. and YAKOVLEV, A. Y., 1998, A cure model with time-changing risk factor: an application to the analysis of secondary leukemia. A report from the International Database on Hodgkin's disease. Statistics in Medicine, 17, 27-40.
  • TUCKER, S. L., 1999, Modeling the probability of tumor cure after fractionated radiotherapy. In Mathematical Models in Medical and Health Sciences, edited by M. A. Horn, G. Simonett and G. Webb (Nashville: Vanderbilt University Press), pp. 1-15.
  • TUCKER, S. L. and TAYLOR, J. M. G., 1996, Improved models of tumour cure. International Journal of Radiation Biology, 70, 539-553.
  • TUCKER, S. L., THAMES, H. D. and TAYLOR, J. M. G., 1990, How well is the probability of tumor cure after fractionated irradiation described by Poisson statistics? Radiation Research, 124, 273-282.
  • WEISS, B. G., 1971, Perturbations in precursor incorporation into DNA of X-irradiated HeLA S3 cells. Radiation Research, 48, 128-145.
  • WILLIAMS, T., 1965, The basic birth-death model for microbial infections. Journal of The Royal Statistical Society, Ser. B, 27, 338-360.
  • YAKOVLEV, A. Y., 1993, Comments on the distribution of clonogens in irradiated tumors [Letter to the Editor]. Radiation Research, 134, 117-120.
  • YAKOVLEV, A. Y. and TSODIKOV, A. D., 1996, Stochastic Models of Tumor Latency and their Biostatistical Applications (Singapore: World Scientific Publications).
  • YAKOVLEV, A. Y., ASSELAIN, B., BARDOU, V.-J., FOURQUET, A., HOANG, T., ROCHEFORDIERE, A. and TSODIKOV, A. D., 1993, A simple stochastic model of tumor recurrence and its application to data on premenopausal breast cancer. In B. Asselain, M. Boniface, C. Duby, C. Lopez, J. P. Masson and J. Tranchefort. Biometrie et Analyse de Donnees Spatio-Temporelles, Vol. 12 (Rennes, France: Société Française de Biométrie, ENSA), pp. 66-82.
  • YAKOVLEV, A. Y., TSODIKOV, A. D. and BOUCHER, K., 1999, The shape of the hazard function in breast carcinoma: curability of the disease revisited. Cancer, 85, 1789-1798.
  • ZAIDER, M. and MINERBO, G. N., 2000, Tumour control probability: a formulation applicable to a temporal protocol of dose delivery. Physics in Medicine and Biology, 45, 279-293.

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