Generalized linear model (GLM) analysis: Multivariables of microcalcification specimens obtained via X-ray guided by stereotactic wire localization biopsy

Abstract

OBJECTIVE:

To retrospectively explore correlation of the resected specimen volume of breast microcalcification lesions and endogenous and exogenous factors of stereotactic needle localization biopsy (SNLB).

MATERIALS AND METHODS:

Totally 214 patients underwent SNLB for non-palpable breast lesion with microcalcification lesions. Of 211 patients, 198 patients underwent single needle localization and 13 patients underwent multi-needle localization (26 lesions). Lesion sizes, distribution characteristics, lesion localization accuracy and resected specimen volumes were recorded and analyzed using a generalized linear model (GLM).

RESULTS:

The average lesion diameter is 2.63±1.73 cm. The localization accuracy of 187 lesions were moderate, 26 were too deep and 11 were too superficial. The mean resected specimen volume (V) was 17.51±5.14 cm³. One-way ANOVA analysis showed that 3 factors, including lesion sizes, distribution characteristics and the localization accuracy were associated with resected specimen volume (F = 67.56–112.78, P < 0.001). GLM revealed that lesion sizes, single clustered distribution and accurate localization were significant factors for resected specimen volume (F = –4.82–11.36, P < 0.05). The ratio (%) of the resected specimen volume to the involved breast volume (V0) was defined as the degree of breast defect. The mean breast defect of 125 benign patients (V/V0) was 27.5% ranging from 10.1% to 42.3%.

CONCLUSION:

Average lesion diameter and localization accuracy are highly significant variables for the resected specimen volume. Localization accuracy as a subjective controllable variable is one of the important factors that determine the volume of lesion resection. Single clustered distribution was more susceptible localization accuracy than other characteristic distributions. Improving localization accuracy can reduce resected specimen volume, which can reduce breast defect to a certain extent.

Keywords

Generalized linear model stereotactic wire localization biopsy non-palpable breast lesions breast cancer microcalcifications

1. Introduction

With the spread of breast cancer screening population every year and the extensive use of high resolution X-ray digital mammography and other imaging screening modalities [1, 2], a large number of non-palpable breast lesions (NPLBs) is found in clinical, of which microcalcifications are the main feature in early stage of breast diseases, especially breast cancer [3 –6]. For NPLBs of Breast Imaging Reporting and Data System (BI-RADS) category 4 and above, lesion biopsy and further surgical resection are recommended. Core needle biopsy (CNB), vacuum-assisted biopsy (VAB) and needle localization biopsy (NLB) are the main lesion biopsy for histological confirmation methods [7 –9], of which stereotactic needle localization biopsy (SNLB) can cover the shortage of histological underestimation due to insufficient specimen of stereotactic core needle biopsy (SCNB), and avoid the possible needle metastases of breast cancer cells during stereotactic vacuum-assisted biopsy (SVAB) [10 –12].

SNLB can maintain the morphological integrity as far as possible by oriented resection and obtain enough reliable pathological specimen for qualitative diagnosis of NPLB at the same time. Previous researches [13, 14] showed that 52–60% of the SNLB histological diagnosis are benign. Of these patients, the biopsy resected specimen volume directly decides the breast defect degree after surgical biopsy, and affects the psychological health status and quality of life of females to a certain extent, especially for Asian young women because of insufficient glands and small volume. Meanwhile, most of the affected women who are under 40 years and still in the reproductive age with breastfeeding needs. It is important for them to maximize breast shape and function after SNLB.

The resected specimen volume achieved by SNLB directly determines the extent of breast defects. SNLB is performed under x-ray guidance. Patient position, the site and depth of needle insertion are dependent on microcalcification sizes D (defined as maximum diameter + minimum diameter/2) and distribution characteristics as D*. Microcalcification distribution characteristics above 3 grades by BI-RADS are extremely complex and broadly resulted into single-clustered, multi-and regional distribution. And these variables are due to the endogenous characteristics of microcalcification. Localization accuracy as L (defined as the distance between the wire tip and microcalcification center) of SNLB is based on the guide wire passing through the center of microcalcification. And the degree of localization accuracy is one of the exogenous factors, which can be controlled and improved. Endogenous and exogenous factors were together determine the size of the specimen and directly impact breast shape and function after SNLB. GLM can better explain the determinative effect of multiple conditional independent variables on outcome dependent variables. Hence, GLM is constructed to explore the correlation of the resected specimen volume and endogenous and exogenous factors of SNLB.

This study retrospectively analyzed the data of 211 patients with NPLBs who underwent SNLB biopsy in our hospital to find out the variables which are related with the resected specimen volume by analyzing variables of lesion size, distribution characteristic and localization accuracy.

2. Materials and methods

2.1. Study population

The data of 214 patients who were diagnosed with NPLBs and underwent stereotactic wire localization SNLBs biopsy from April 2015 to December 2017 in our hospital were enrolled. And three patients were excluded because of intraoperative vagus nerve response.

211 patients were female, age of 26 to 63 years old (Median, 39 years old). Mammography examination showed 224 lesions with single-clustered, mulit-sand-like, scattered or regional distributed microcalcifications, of which, 208 patients were BI-RADS category 4 to 5 and 3 patients were BI-RADS category 3 with severe anxiety. All patients underwent SNLB biopsy after mammography diagnosis in a week. This research was approved by medical ethics committee and all patients signed informed consent.

2.2. X-ray guided by stereotactic wire localization biopsy

We used MAMMO DS digital high resolution breast X-ray equipment of GE Company. Matched three-dimensional positioning system and fishhook-shaped single hook locating pin of 20G (hook90/80/70, Promex Company) was applied. Conventional and orientation photographing applied Stand mode exposure. Previewing conventional images before orientation to choose orientation calcification. Patients were asked to sit, soft rolls were put behind their back for support to reduce displacement. CC or ML, LM oppression were chosen, according to lesion size, position and distribution to put target calcification in the center of posting, taking the shortest distance of locating pin passing through breast. Oppressed breast and extended glands at the same time to reduce the skin surface apophysis after oppressing the breast. Pressure was 15–24dan till there was no breast morphological change. Applied each film of 0° and±15° photography for bulb tube, system automatically calculated the three-dimensional coordinate value. Chose locating pin of appropriate length, adjusted rack to preselection spot, sterilized skin surface, insert the needle through needle holder groove and made sure whether the ubiety between the needle tip and the target calcification is right or not, and then relieved oppression and pulled out epitheca. Took a film perpendicular to the needle inserting direction, verified whether the back stitch is open or not, evaluated the distance from needle tip to lesion and fixed the end of the guide wire. Delineated the excision extent on the last localization film to guide surgery.

2.3. GLM related parameters

Microcalcification distribution (D*) as rank variable, was grouped into single-clustered, multi-and regional distribution by two mammography radiologists with more than 5 years of diagnosis experience. Classification criterion of D* was as follows: single-clustered, single microcalcification center with distributing in clusters in related region; multi-clustered, multiple microcalcification centers with distributing in clusters in related region; regional distribution, no decentralized and relatively sparse distribution. The average maximum diameter of microcalcifications (D/cm) was performed as maximum diameter + minimum diameter/2 on the conventional cranio-caudal mammography. The distance (L/cm) as localization accuracy was measured from the needle tip to the target calcification on the last localization film. L≤± 1.5 cm was taken as moderate, L > 1.5 cm as too deep and L < – 1.5 cm as too superficiall [15]. After specimen surgery, mammography affirmed that whether the microcalcification is excised completely, comparing with the lesion on the original film. The excised integrity was estimated and the excision sample volume (V/cm³) was measured and calculated as maximum diameter×minimum diameter×oppression thickness. Not completely excised microcalcifications through evaluation would underwent secondary resection. And histopathological diagnosis was performed. The estimation of the whole breast volume refers to the two figure methods [16], combing the thickness, the longest diameter and the widest diameter after mammography oppression, the whole breast estimated volume (V0/cm³) was calculated as maximum diameter×minimum diameter×oppression thickness. V/V0 was used to represent the defect degree after SNLB. And the estimated diameter () of resected specimen volume was calculated as ³√ maximum diameter×minimum diameter×oppression thickness.

2.4. Statistical data analysis

SAS 9.5 software was used for recording data and statistical analysis. Quantitative data was represented as $\bar{x} \pm s$ . Qualitative data was represented as Rank data. One-way analysis of variance was used for lesion average diameter (D), distribution characteristics (D*), location accuracy (L) and resected specimen volume (V). Independent variables with statistical significance were chosen to establish general linear regression model (GLM) with dependent variable V [17]. Viewing to D* as Rank variable and L as subjective and conditional variable, if assuming the generalized Bernoulli distribution of V, the function was constructed as Function 1, and the maximum likelihood estimate was obtained. Pearson correlation analysis was done between and D. Kappa test was performed between two observers. P < 0.05 was statistically significant. $\begin{matrix} ℓ (θ) & = & \sum_{i = 1}^{m} log p (y^{(i)} | x^{(i)}; θ) \\ = & \sum_{i = 1}^{m} log \prod_{l = 1}^{k} {(\frac{e^{θ_{l}^{T} x^{(i)}}}{\sum_{j = 1}^{k} e^{θ_{j}^{T} x^{(i)}}})}^{1 {y^{(i)} = 1}} \\ . . . . . . . . . . . . . Function 1 \end{matrix}$

3. Results

211 patients (224 lesions) with microcalcifications was studied, including 127 of single clustered, 53 of multiple clustered and 44 of regional distribution as D* (Kappa = 0.859). The average lesion diameter (D) is 2.63±1.73 cm. 198 patients (198 lesions) went through single needle localization and 12 patients (26 lesions) went through bilateral breast multiple needle localization. After localization mammography evaluation, 187 lesions were localization moderate (L≤±1.5 cm), 27 lesions were localization too deep (L > 1.5 cm) and 11 lesions were localization to superficial (L < – 1.5 cm). The specimen mammography showed that 215 microcalcifications were completely excised, 9 lesions underwent secondary resection. The average volume estimation of specimen (V) was 17.51±5.14 cm³.The average estimated diameter of resected specimen (³ √ V) was 2.21±3.28 cm³.The whole breast volume estimation of specimen (V0) was 78.64±13.55 cm³

According to the pathological diagnosis (Table 1), 135 (60.3%, 135/224) lesions were benign, 27 microcalcifications were cystic hyperplasia, 26 lesions were hyperplasia with calcification, 32 lesions were hyperplasia accompanied with intraductal papilloma, 39 lesions were mammary adenosis, 7 lesions were cyst with latex calcification, 4 lesions were inflammation and 21 lesions (9.4%, 21/224) were atypical ductal hyperplasia (ADH). 68 lesions (30.4%, 68/224) were pathologically diagnosed as breast cancer, among which 37 lesions were invasive ductal carcinoma, 11 were lobular carcinoma, 8 lesions were mucinous adenocarcinoma and 12 lesions were carcinoma in situ or intraductal carcinoma (Fig. 1).

Table 1
Comparison of breast mammography BI-RADS category with pathological results

BI-RADS Benign ADH Malignant Total

DCIS IDC LC MAC

3 3 (1.3%) 0 (–) 0 (–) 0 (–) 0 (–) 0 (–) 3 (1.3%)

4 132 (58.9%) 21 (9.4%) 12 (5.4%) 15 (6.7%) 6 (2.7%) 8 (3.6%) 194 (86.6%)

5 0 (–) 0 (–) 0 (–) 22 (9.8%) 5 (2.2%) 0 (–) 27 (12.1%)

Total 135 (60.3%) 21 (9.4%) 12 (5.4%) 37 (16.5%) 11 (4.9%) 8 (3.6%) 224 (100%)

BI-RADS	Benign	ADH	Malignant	Total
3	3 (1.3%)	0 (–)	0 (–)	0 (–)	0 (–)	0 (–)	3 (1.3%)
4	132 (58.9%)	21 (9.4%)	12 (5.4%)	15 (6.7%)	6 (2.7%)	8 (3.6%)	194 (86.6%)
5	0 (–)	0 (–)	0 (–)	22 (9.8%)	5 (2.2%)	0 (–)	27 (12.1%)
Total	135 (60.3%)	21 (9.4%)	12 (5.4%)	37 (16.5%)	11 (4.9%)	8 (3.6%)	224 (100%)

DCIS: ductal carcinoma in situ, IDC: invasive ductal carcinoma, LC: lobular carcinoma, MAC: mucinous adenocarcinoma.

Fig.1

Patient, female, 42 years old. Right breast of non-palpable breast lesions with microcalcifications (1.1×1.5 cm²) on the superior lateral quadrant, the needle was inserted vertically. Localization moderate. Histologic result was shown as intraductal carcinoma in situ with small focal ductal carcinoma infiltration.

Lesion average diameter (D), distribution characteristic (D*) and localization accuracy (L) were all independent variables affecting resected specimen volume. (F = 13.21–112.78, P < 0.05) (Table 2). General linear regression model established with variables of statistical significance is V = 16.45 + 1.32×D–4.78× (if D* = 1)– 1.55×(if D* = 2) + 0(if D* = 3)– 6.13× (if L = 1) + 0(if L = 2) (Table 3).

Table 2

One-way analysis of variance lesion average diameter (D), lesion distribution (D*) and localization accuracy (L) with resected specimen volume (V)

	df γ	SS	Mean-square deviation	F value	P value
D	1	537.73	537.58	112.78	<0.001
D*	2	161.94	72.83	13.21	<0.001
L	1	329.22	329.22	67.57	<0.001

df: degree of freedom.

Table 3

GLM coefficient test of lesion average diameter (D), lesion distribution (D*) and localization accuracy (L) with resected specimen volume (V)

	df γ	estimated value	b	SE(b)	F value	P value
Constant	1	16.45	0	0.67	19.21	<0.001
D	1	1.32	0.71	0.09	11.36	<0.001
D*(single clustered)	1	– 4.78	– 0.30	0.74	– 4.82	<0.001
D*(multiple clustered)	1	– 1.55	– 0.09	1.53	– 1.13	0.072
D*(regional)	0	0	0	–	–	–
L (≤±1.5 cm)	1	– 6.13	– 0.54	0.62	– 8.01	<0.001
L (> ±1.5 cm)	0	0	0	–	–	–

df: degree of freedom.

The localization accuracy rate among lesion of different size are 16.5%, 83.5%, respectively (Table 4). Breast defect as V/V0 after SNLB for 125patients with benign and atypical hyperplasia lesions was 27.5% (10.1%, 42.3%). Theoretically, 25% breast volume could be defined as a quarter quadrant. That is to say, above 25% breast defect, meaning that the related breast defeat was above a quarter quadrant and the shape of the breast was extremely destroyed. And the correlation analysis showed that, for the D < 1.5 cm group (51/224), the correlation coefficient R of D and ³√V was 0.526. And for the D≥1.5 cm group (173/224), the correlation coefficient R was 0.793.

Table 4

Frequency among localization accuracy (L) and lesion average diameter (D)

	Groups of lesion average diameter (D)
Localization accuracy (L)	D≤1.5 cm	D > 1.5 cm	In total
L (≤ ±1.5 cm)	22 (9.8%)	165 (73.7%)	187 (83.5%)
L (> ±1.5 cm)	29 (12.9%)	8 (3.6%)	37 (16.5%)
In total	51 (22.8%)	173 (77.2%)	224 (100%)

4. Discussion

Mammography was of high sensitivity and specificity for detecting non-palpable breast lesions with microcalcifications and could evaluate the benign and malignant degree of microcalcifications by BI-RADS. SNLB supplied possibility for the localization biopsy and resection of microcalcifications, which were defined as BI-RADS category 4 or 5, even some category 3 with severe anxiety. Researches [13, 14] in the past about localization biopsy of microcalcification were restricted to comparison of calcification imaging manifestation and pathological results to elaborate the application value of SNLB, of which 55–60% of the patients were diagnosed as benign according to localization biopsy pathological results. The resected specimen volume during SNLB directly decided the breast defects post-surgery. As an important organ of female secondary sex characteristic, breast defect could lead to psychological burden to some extents and affect the love, marriage, family life of patients and caused fertility and lactation anxiety. The volume of resected specimen was depended on the objective factors of lesion sizes, distribution characteristic and localization accuracy and patient cooperation degree, which were extrinsic and can be controlled. Therefore, the improvement of localization accuracy during SNLB and patient cooperation degree might be effectively reduce the resected specimen volume and then decrease the breast defect degree to some extent.

The one-way analysis of variance of lesion sizes, distribution characteristic and localization accuracy with resected specimen volume turned out that their effects on the resected specimen volume are statistically significant difference (P < 0.05), which meant that all of them were independent variables affecting resected specimen volume. Generalized linear model (GLM) which had more extensive application range was chosen for fitting since the dependent variable of this research was continuous variables, while the independent variables were mixed variables. GLM is simple least squares regression, which can be used to analyze classified variable or discontinuous variable, instead of only continuous variables complying with normal distribution [18, 19]. This study analyzed the significance of each independent variable on dependent variable with GLM, to clear the magnitude of the influence on the resected specimen volume of objective variables and controllable variables, and then did likelihood-ratio test to the estimation coefficient of the significant variables of the equation. The estimation coefficient of lesion size (D) was 1.32 (P < 0.05), which means lesion size was linearly correlated with the specimen size as a continuous variable. That was to say the resected specimen volume would increase 1.32 cm³ when the lesion size increased 1 cm. Lesion distribution (D*) could be divided into 3 sublayers as categorical data. The likelihood-ratio test of the estimation coefficient was of statistical difference (R = –4.78, P < 0.05) only when the lesion was distributed as single clustered (D* = 1).

The decrease of the resected specimen volume is about 3.23 times of the lesion of “single clustered” distribution comparing with the lesion of “multiple clustered” or “regional” distribution. Moreover, the lesion of “multiple clustered” distribution is 1.55 times smaller than the lesion of “regional” distribution, but the volume of the two sublayers is of no statistical difference. Location accuracy (L) is two-category data, and the coefficient R of “moderate localization” is – 6.13 (P < 0.05), which means the coefficient was statistically significant. In other words, the size of the resected specimen of “moderate localization” was 6.13 times smaller than that of the “incorrect localization”. To analyze the impact significance of the independent variable to dependent variable, three partial regression coefficients of statistical significance were standardized, which were lesion average diameter of (D), “simple clustered” of lesion distribution (D*) and “moderate localization” of location accuracy (L). The absolute values were respectively 0.71, 0.30, and 0.54, which declares that lesion average diameter (D) has the biggest effect on volume of resected specimen (V), localization accuracy (L) was next, and lesion distribution (D*) has the smallest effect on V. Therefore, lesion average diameter directly decided the resected specimen volume.

The analysis of localization accuracy among lesion of different size groups show statistical difference, which meant localization accuracy among lesion of different size was of different efficacy. The ratio was 16.5%, 83.5%, respectively. The localization accuracy of stereotactic wire localization biopsy for microcalcifications D≥1.5 cm group was higher, which might be relevant with the lower deviation rate of localization for lesion of bigger size or diffusely distributed calcification. For lesion size of D < 1.5 cm group, the localization accuracy decreased to 43.1%. For the 51 lesions of which D was <1.5 cm in this study, 29 lesions turned out to be inaccurate localization (19 too deep, 10 too superficial). Nine of them went through two more excision for complete resection, which led to much bigger resected specimen volume than lesion actual volume. Localization accuracy directly influences resected specimen volume as a controllable factor, and was especially important for small lesion with microcalcifications.

The correlation analysis of lesion average diameter (D) and resected specimen volume () among 224 lesions turned out that the correlation between small calcification lesion and resected specimen volume was poor and the obedience is small. The average resected specimen volume of D < 1.5 cm (51/224) group was 7.97±4.21 cm³, and the correlation coefficient was 0.526. But the average resected specimen volume of D≥1.5 cm (173/224) group was 20.97±8.13 cm³(R = 0.793). And for the 9 lesions underwent two more excisions, the average lesion diameter was 1.41±0.58 cm and the resected specimen volume completely excised was 12.39±4.53 cm³, which might be connected with the decrease of lesion localization accuracy for lesion of smaller size and oversize range resection of specimen after two more excisions.

In addition, the breast defect (V/V0) of 125 benign diseases and atypical hyperplasia was 27.5% (10.1%, 42.3%). For more than half of them, the breast defect degree was bigger than 25% (about a quadrant). Breast was not only an important organ of female secondary sex characteristic, but also of important significance for female morphological beauty [20 –22]. Breast defect could lead to negative psychology like self-abasement, anxiety and self-denial to some extent, and affected patients psychological health status, life and sexual quality. Asian female of our country had relatively small breasts. Wide range resection of glandular tissue was bound to cause mammary morphology damage and serious defect.

Therefore, we should pay more attentions to the localization accuracy of stereotactic wire localization biopsy. We think that we should improve our skills according to the following five aspects: (1) Localization environmental requirement. Localization accuracy in terms of equipment depends on the accuracy condition of high precision electronic components, which may be affected by the environment temperature and humidity [23]. The standard conditions are room temperature 18°C∼26°C, humidity 20% ∼90%, and atmospheric pressure 860∼1060 hpa. (2) Adjustment of breast stereotactic instruments. Before localization, horizontal and vertical adjustment for equipment should be done (valid for 24 hours), make sure that every link of the localization system operates normally. The allowed error after adjustment should be less than 0.2 mm. (3) Patients position design [24]. Preview conventional radiography to know the lesion size, distribution and estimate the length of needle to be inserted. Design the shortest inserting path, inserting direction and the patient tolerable body position. (4) Choose the characteristic calcification as target. The target should be as close to the lesion center as possible [25]. (5) Psychological intervention to patients. Any movement of the patients during every step may lead to inaccurate localization. Good communication pre-operation to establish good trust, clear the importance of positive cooperation, dispersion of patients attention during operation to reduce the uncomfortable reaction are effective methods to ensure patients good cooperation [26].

5. Conclusion

SNLB is the most widely used and effective method for NLPBs with microcalcifications qualitative diagnosis and surgical resection. Meanwhile, more than half of the patients who accepted SNLB surgery are benign disease, it is of significant clinical value to retain breast integrity and improve the patient psychological health status after SLNB by improve the localization accuracy during SLNB to reduce breast defect to normal breast glandular tissue and breast resected extent, especially Asian women with small volume breast.

Disclosure

The authors report no conflicts of interest in this work.

Footnotes

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China under Grant No. 81671757 and the CAMS Innovation Fund for Medical Sciences under No.2016-I2M-1-001 and Beijing Hope Run Special Fund of Cancer Foundation of China No. LC2016B07.

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