A Statistical Modelling Approach for Guiding the Optimum Surgical Intervention of Breast Cancer. Part I

N. V. Kovtun, DSc in Economics, Professor, Department of Statistics and Demography, Taras Shevchenko National University of Kyiv, E-mail: kovtun_natali@ukr.net Researcher ID: M-6596-2017, ORCID: https://orcid.org/0000-0002-2935-8597; I. M. Motuziuk, PhD in Medicine, Associate Professor, Department of oncology, O. O. Bogomolets National Medical University, E-mail: 180978igor@gmail.com ORCID: https://orcid.org/0000-0002-8332-3280; R. O. Ganzha, Postgraduate Student, Taras Shevchenko National University of Kyiv, E-mail: ganzha.roman.alex@gmail.com ORCID: https://orcid.org/0000-0002-3418-7593 Doi: 10.31767/su. 2(85)2019.02.05

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.
Key words: coefficient of lesion for mammary gland, optimum surgical intervention, breast cancer, Breast Conserving Surgery, mastectomy, two-dimensional mammography.

Background
Globally, breast cancer is the most frequently diagnosed cancer in women. Incidence rates vary greatly worldwide from 19.3 per 100,000 women in Eastern Africa to 89.7 per 100,000 women in Western Europe (WHO, 2017). There are about half a million deaths per year from breast cancer worldwide making it the most common cause of female cancer death in both the developed and developing world [1].
While substantial advances have been made in breast cancer research and treatment in the last decade, there remain significant gaps in translating this newly acquired knowledge into the survivorship experience. Surgery remains the primary choice of treatment for most women, with breast conservation (plus whole breast radiotherapy) providing similar outcomes to mastectomy [2]. Clinical decisionmaking tools to support individualised treatment can influence treatment choices and experiences [3]. A significant number of patients are overtreated to achieve the improved overall survival in early breast cancer, since individual risk of disease recurrence and sensitivity to intervention remains elusive. A review study has found that excising a wider margin of tissue around an invasive malignant tumour does not result lower rates of local recurrence [4]. Morrow et al. have echoed similar views that available evidences do not support that wider cancer-free surgical margins reduce the risk of local recurrence after lumpectomy for invasive breast cancer [5].
Despite strong evidence supporting the use of Breast Conserving Surgery (BCS), the majority of women are continued to be treated with mastectomy [6]. With the widespread adoption of sentinel node biopsy (SNB) limiting surgery to the axilla has substantially reduced arm morbidity [7]. Swanson and Rynearson established that removal of additional tissue worsens the cosmetic result while finding of the positive margin is not necessarily a precise indicator of the quantum of disease left in the breast [8].
Adequacy of the excision margin is well acknowledged guide for the success of BCS [8]. The threshold that surgeon accepts as an adequate for surgical margin varies widely [9][10][11]. Diagnostic pathology does not find any consensus on this long standing and extensive debate and that results a considerable variations in clinical practice [12]. A detailed understanding of tumour is required to support decisions around surgical management and to define optimal treatment strategies for an individual patient.
Personalisation of treatment avoids radiationinduced toxicity in later stage [13]. Using a sample of 16,643 patients of stage 1 and stage II breast tumour treated, Morrow et al. (2001) demonstrated that the predictors of BCS often do not correspond to those suggested in case management protocol and guidelines [6]. Abandoning practice of conventional surgical margins or some other arbitrary width has the potential to dramatically decrease healthcare costs but also simultaneously to improve the cosmetic outcome of BCS [14].
The need for an objective and patient specific decision-making information is well documented [15; 16]. This paper presents a "theragnostic" tool [17], an approach, never explored earlier, that enables surgeons to determine an optimal extent of breast tissue excision.

Data and methods
Data for this study comes from retrospective review of 74 mammography reports. Mammographic screening has been shown to be effective in reducing the mortality from breast cancer [18][19][20][21][22][23]. Following the guidelines of American Joint Committee on Cancer, the stages of breast tumour classified were 6 in the sample that we used.
A two-dimensional mammography was performed on 74 women of different age groups and having different stages of breast cancer. The mammography captured breast tissue images on different planes (cross-sectional -Cranial and Caudal, and Sagittal). We assessed: 1. Tumour localization by quadrants (upperouter, upper-inner, lower-outer, lower-inner, at the proximity of two quadrants and tumour in dispersed location all over the mammary gland).
7. Presence of edema. 8. Presence of nipple retraction. 9. Presence of "path" to the nipple. 10. Presence of tumour invasion to the large mammary (pectoralis major) muscle.
12. Coefficient of mammary gland (breast) lesion -size of tumour relative to mammary gland (breast) volume.
Above characteristics (attributes) were considered as the deciding factors for determining the size of affected mammary gland (breast) parenchyma to be removed during surgical intervention.
We calculated the coefficient of lesion from the data of mammographic examination as detailed here. For tumour: Calculation of tissues mass to be removed: during mammography examination two imaginary lines were drawn -one connecting nipple-areolar region to pectoralis major muscle along the lateral and medial "visible" edge of the tumour (cranio-caudal projection -СС) and other, between upper and lower edge of the tumour (sagittal projection -S).
For mammary gland: Calculation of volume followed three-dimensional measurements -СС, S and H where H is the "height" of mammary gland (breast tissue proper).
1st step: the volume of the mammary gland was computed using the ellipsoid formula divided by two yielding the volume of semi-ellipsoid: The use of these two approaches is for reasons: if coefficient of the lesion computed using greater semiaxis (a) is bigger than 100%, and then it has to be re-derived using smaller semi-axis (b). In case both coefficients calculated according to approaches a) and b) give more than 100% of affliction with lesion, the coefficient of the lesion has to be set to cut-off value equal to 100%.
The coefficient of lesion for mammary gland is calculated as: (Eq. 4)

Empirical illustration
In order to assess the adequacy of the proposed approach the variance of coefficient of lesion was checked across different stages (Table 1). We found that the coefficient of lesion increased with the increase in the severity of the disease (stage) (p-value = 0.06) (Table 1, Figure 1, based on data from retrospective review of 74 mammography reports). Table 2 presents the stage of the disease and the type of surgery. Test of independence was significant at p-value equal to 0.03. Therefore, with advancement of tumour stage, the chance for mastectomy increases as well. At the Stage 1 of the tumour, accounted for only 20% mastectomy of all types of surgeries, the share of Stage 2A was 57%, and Stages 2B and 2C, equal to 75%. The lower percentage (more than half) of mastectomy in Stage 3 (groups four and five) compared to the Stage 2 can be explained by relatively substantial a smaller number of observations in Stage 3.  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 BCS is performed, and if necessary, the correction of the form or size of the contralateral mammary gland breast is done to achieve symmetry. Alternately, if volume of the mammary gland tissue to be removed exceeds 25%, then a mastectomy is performed with a one-stage breast reconstruction by autologous or allograft materials upon patient's choice.
In our data, the decision border of 25% was not justified (p-value = 0.1226). The results of the test showed that the differences between groups in the coefficient of lesion are random (Table 3) translating the fact that the established decision-making parameter is not tenable for determining the extent / type of surgical intervention. Further, we also examined possible effect of the tumour attributes on the decision of surgical intervention. Table 4 presents our findings on this dimension. Therefore, only two attributes are (except for the stage, Table 2), having the significant effect to determine the type of surgical intervention that was not at random: а) nipple retraction (p-value = 0.004), Table 5. The ODDS Ratio (OR) was being computes as follows: It means the BCS was indicated with 10.7 times more often than mastectomy in the absence of nipple retraction. b) "path" to the nipple (p-value = 0.001), Table 6.  Reciprocally, the presence of the "path" determined the need for mastectomy 4.3 times more often compared to another variant, ceteris paribas.

Discussion
The ongoing debate on the optimal treatment strategies and individual risk of recurrence of breast cancer demands an objective decision-making criterion. We have attempted to develop an approach that defines an optimal extent of surgical intervention with an effective cut-off for the surgical margin in BCS. We have used data from 74 mammography examinations and the surgical interventions of those women underwent for the management of breast cancer. We have developed a coefficient aligned with the stage of the carcinoma. Thus, our index can act as a tool to determine the extent of surgical excision and simultaneous choice of options for reconstructive surgery in the management of breast cancer. The confirmation of the tissue mass to be removed was subjected to the validation by the approach of worstcase scenario. Given Cranio-Caudal and Sagittal measurements, the tissue mass to be removed was maximized with Eq. 2 and Eq. 3 which in turn effectively penalized the model. Alternately, we have overcome the variability and instability in subset selection with a computationally efficient fashion establishing robustness in our approach. Our empirical illustration could not establish the rationale of conventional decision-making process where breast conserving surgery is performed when the volume of tissues removed from the breast does not exceed 25% of the gland tissue proper, and a mastectomy, when the volume of tissues removed from the breast exceeds 25% of the gland tissue proper.
Our findings and the techniques developed thus sets the foundation for developing a statistical model to realise the goal of an optimal balance between good cosmetic results and defining the optimal tissue excision. Such a model shall predict the intraoperative margin assessment and thus the prognosis of optimal surgical intervention of breast cancer. We shall integrate in our model biological knowledge of tumour and patient characteristics to accommodate risk factors. Application of statistical model in breast cancer management shall not only make surgical intervention more efficient and effective but also would ensure survival with enhanced quality of life and substantially reduced risk of recurrence for women with breast cancer.
To conclude, our approach shall bring the consensus on the contentious issue of margin status in BCS by defining the cut-off for the margin width. 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. Such an objective approach would not only improve the efficiency of breast cancer treatment, but also would ensure supposedly a better quality of life for patients after treatment. Arguably, such a model would contribute for reduction of the risk of recurrence and increase survival of women with breast cancer.