Recently, an increase in the incidence of multiple primary malignant neoplasms has been observed, specifically, when two or more unrelated tumors originate from different organs and appear in the body simultaneously or sequentially, one after another. During past few years, the interval between the first and second reproductive cancer diagnosis has decreased in 6 times – from 11 to just 2 years while probability of surviving the next 3 years after 8.5 years past initial diagnosis has decreased from 0.995 to 0.562. Using performed analysis, this paper provides details of survival modelling for women with breast cancer with the aim to find the most significant factors affecting the likelihood of survival not by chance alone. The data used for research were obtained from Ukrainian National Institute of Cancer covering 1981–2017 period. The modelling was performed using Cox regression with forward effect selection method and stay in p-value boundary equal to 0.15. The forward method firstly computes the adjusted chi-square statistics for each variable. Then, it examines the largest computed statistics and if particular one is significant, the corresponding variable is added to the model. Once the variable is entered, it is never removed from the model. 3 out of 4 factors that appeared to be significant according to forward selection method were confirmed as the significant ones by stepwise selection method. The results of modelling proved the possibility of prediction the survival using certain set of disease features and subjects’ characteristics. Testing of global hypothesis for Beta resulted in rejecting of null hypothesis (Beta = 0) in favor of the alternative one (Beta ≠ 0) thus it was confirmed that the models make sense and can be used to predict survival in women with breast cancer. According to obtained results, the most significant disease features and subjects characteristics appeared to be: type of multiple processes (synchronous or metachronous), presence of relapse and/or metastasis, type and combination of treatment, stage of disease. Cancer with synchronous processes is characterized by greater aggressiveness and it reduces survival by almost 13 times compared with cancer where metachronous processes take place. Even though chemotherapy significantly increases the survival rate of patients, it also impacts the probability of relapses and metastasis occurrence, which are 16 times more likely to occur if chemotherapy was a part of treatment. This gives grounds for assumption that it has an indirect effect on survival and hence needs to be analyzed considering its negative impact on the relapses and metastasis occurrence probability, which, in turn, reduces survival by 10 times. This fact, in our opinion, introduces the need for further in-depth analysis. The significant difference between survival rates in patients with the first and third stages of cancer has been proved – the chances to survive with the disease at the first stage are almost 12 times higher than with disease at the third stage. At the same time, the difference in the survival rates in women with the disease at the second and the third stages is not so big and it is only 1.6 times. The modern method of conducting surgery compared with the standard one appeared to be capable to reduce the risk of relapses and metastases by 2.6 times, while breast conservative surgery in multiple oncological processes – by 3 times compared with mastectomy, which allows to state that both factors have a positive effect on the survival probability and reduce the risk of mortality. Regarding subgroup models built for patients having synchronous process and patients with metachronous processes separately, an increase in the sample size is needed to assess assumed difference in factors affecting survival and to improve predictive abilities of models. This, in turn, requires additional studies during which the necessary amount of data can be collected.

Breast cancer is most common tumour diagnosis for women worldwide. Over the last almost 40 years widespread adoption of mammographic screening has established Breast Conserving Surgery (BCS) followed by irradiation as the most practised treatment of choice. However, in absence of tools to determine the optimal quantum of tissue to be excised the debate continues for achieving a balance between the effectiveness of surgical intervention and the later stage personalisation of treatment, and so, a wide variation in practice is a common phenomenon globally. We attempt to introduce a definite measure that determines efficacy of BCS while protecting aesthetic value of life for Women affected with breast cancer. 74 mammography examinations and the surgical interventions of those women underwent for the management of breast cancer were used to compute the coefficient of lesion. In first step the lesion and the mammary gland proper are measured applying geometry. In the second step volume of tissue mass to be removed was calculated taking into account the measures from the 1st step and we present the coefficient of lesion mathematically. We empirically illustrated our methodological approach for determining the tissue mass to be excised. Conventionally, it is assumed that if the volume of tissues to be removed does not exceed 25% of the volume of the mammary gland, a Breast Conserving Surgery, is performed, however, our empirical illustration demonstrated that the established decision making parameter is not tenable for determining the extent / type of surgery undertaken. We have developed a coefficient aligned with the stage of the carcinoma and founded the base for developing a statistical (mathematical) model. Application of such a model accommodating tumour biology and patient characteristics shall not only provide intraoperative real time information to surgeons but also predict the prognosis of optimal surgical intervention of breast cancer. The next step is to develop a model using the data of the mammographic examination and the coefficient of breast lesion as covariates for determining the potentially effective volumes of surgical intervention needed, and plan reconstructive measures considering the effect of time on such intervention.

Breast cancer is the most common tumour diagnosis for women worldwide. Over the last 40 years widespread adoption of mammographic screening has established Breast Conserving Surgery (BCS) followed by irradiation as the most practised treatment of choice. However, given the absence of tools to determine the optimal volume of tissue to be excised, the debate continues for achieving a balance between the effectiveness of surgical intervention and the later stage personalization of treatment, and so, a wide variation in practice is a common phenomenon globally. This study is devoted to modeling and analysis of factors which affect the choice of type and volume of surgical intervention for patients with breast cancer in not at random manner. Given the problems of treating patients with breast cancer, it is extremely important to determine the criteria for an objective choice of the type of surgical intervention at the diagnostic stage. These criteria should ensure both the radical nature of the surgical intervention and the preservation of aesthetically acceptable forms and sizes of the mammary glands. The study included 73 patients with breast cancer who underwent a mammographic examination and surgery planned according to this examination. The planned type and volume of interventions were compared with the type and volume of the performed ones. Based on the simulation results, the leading mammographic factors were determined. A statistical model allowing one to quite effectively determine optimal type and volume of surgical intervention based on the data of a mammographic examination and the lesion coefficient as the covariates was built. The proposed model considers the characteristics of the tumor and the anatomical features of patients which, in addition to providing real-time information, enables for predicting the optimal type and amount of surgical intervention. An adequate choice of type of the intervention allows one to plan short-term reconstructive measures in advance, to ensure an adequate quality of life for patients after treatment.

Breast cancer is most common tumour diagnosis for women worldwide. Over the last almost 40 years widespread adoption of mammographic screening has established Breast Conserving Surgery (BCS) followed by irradiation as the most practised treatment of choice. However, in absence of tools to determine the optimal quantum of tissue to be excised the debate continues for achieving a balance between the effectiveness of surgical intervention and the later stage personalisation of treatment, and so, a wide variation in practice is a common phenomena globally. We attempt to introduce a definite measure that determines efficacy of BCS while protecting aesthetic value of life for women affected with breast cancer. 74 mammography examinations and the surgical interventions of those women underwent for the management of breast cancer were used to compute the coefficient of lesion. In first step the lesion and the mammary gland proper are measured applying geometry. In the second step volume of tissue mass to be removed was calculated taking into account the measures from the 1st step and we present the coefficient of lesion mathematically. We empirically illustrated our methodological approach for determining the tissue mass to be excised. Conventionally, it is assumed that if the volume of tissues to be removed does not exceed 25 % of the volume of the mammary gland, a Breast-conserving surgery (BCS), is performed, however, our empirical illustration demonstrated that the established decision making parameter is not tenable for determining the extent / type of surgery undertaken. We have developed a coefficient aligned with the stage of the carcinoma and founded the base for developing a statistical (mathematical) model. Application of such a model accommodating tumor biology and patient characteristics shall not only provide intraoperative real time information to surgeons but also predict the prognosis of optimal surgical intervention of breast cancer. Key words: coefficient of lesion for mammary gland, optimum surgical intervention, breast cancer, survival, probit regression model.