Introduction

Breast cancer, which is a significant public health concern globally, is one of the deadliest cancers in women.^[1] Especially in such cancer diseases, early diagnosis is very important and may affect the course of the disease. There are many traditional methods for early detection of breast cancer. First, a physical examination is performed after listening to the patient's medical history. Afterward, ductoscopy (examination of milk ducts by entering very thin fiber-optic systems from the mouth of the canal at the nipple) with imaging methods such as mammography or breast ultrasound may be requested. Additional examinations such as ductography (or galactography, imaging with contrast material from the nipple) and magnetic resonance imaging (MR) may also be requested.^[2]

Data mining methods, which are also defined as the process of knowledge discovery from large amounts of data, enable one to make predictions and interpretations about the future by revealing hidden relationship structures.^[3] While machine-learning methods that can work based on association rules, classification, and regression perform data-based learning in the training phase, they aim to make predictions about new data in the testing and validation phase.^[4]

This study aims to classify patients with and without breast cancer using the Stochastic Gradient Boosting (SGB) method. In addition, it is to determine the risk factors related to breast cancer and to find the variable importance of the cancer-related factor.

Materials and Methods

Dataset

The public dataset "UCI (Machine Learning Repository) Data Set" was obtained from https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29  to classify the presence or absence of breast cancer via the SGB method in the study.^[5] Features are computed from a digitized image of a fine needle aspirate (FNA) of a breast mass. They describe the characteristics of the cell nuclei present in the image.  Attribute information is id number, diagnosis (M = malignant, B =

benign), and ten real-valued features are computed for each cell nucleus (radius (mean of distances from center to points on the perimeter), texture (standard deviation of gray-scale values), perimeter, area, smoothness (local variation in radius lengths), compactness (perimeter^2 / area - 1.0), concavity (severity of concave portions of the contour), concave points (number of concave portions of the contour), symmetry, fractal dimension ("coastline approximation" - 1)). The mean, standard error, and "worst" or maximum (mean of the three largest values) of these traits were calculated for each image resulting in 30 features. For example, field 3 is Medium Radius, field 13 is SE Radius, and field 23 is Worst Radius. All feature values are recorded in four substantial digits. There are no missing observations in the data set. 63 % of the data set is benign (357) while 37 % is malignant (212).

Stochastic gradient boosting

The boosting algorithm, designed as a meta classifier, is an ensemble learning method that can also make predictions.^[6] Stochastic gradient boosting (SGB) is a data processing approach introduced by ^[7]. SGB is a crucial technique accustomed to creating forecasts and classification tasks and adjusting forecast performance through the appliance of preprocessing procedures. XGB, SGB, and Lasso methods are both widely and successfully used techniques in breast cancer/mammography research. They are also widely used approaches to select critical predictive variables in health and medical informatics applications. XGB or SGB can effectively identify important variables when the variables have nonlinear and/or high dimensional interactions.^[8] SGB was implemented in R by the Generalized Boosted Regression Models (GMB) Package.^[9] The hyperparameters of the SGB classifier are n.trees, shrinkage, and n.minobsinnode.

Data analysis

Henze zirkler test was used for the assumption of multivariate normality. The median (minimum-maximum) was used to summarize quantitative data, and the numbers were used to summarize qualitative variables (percentages). The Mann-Whitney U test was utilized to see if significant difference in the target exits. The relationship between the variables was evaluated with the spearman correlation coefficient. The model's fit was checked with the Likelihood Ratio Test. P-value <0.05 was regarded as significant. IBM SPSS Statistics 26.0 program was employed in the analysis.

Modeling

SGB, one of the machine learning methods, was used in the modeling. Analyzes were carried out using the 100 repeated bootstrap method. Balanced accuracy, accuracy, sensitivity, specificity, positive/negative predictive values, and F1-score were used as performance evaluation criteria. In parameter optimization, while the surface selection was made as the optimization depth, grid search was used as the scanning method. 5-fold cross-validation was used as a resampling method.

Results and Discussion

In the data set used in the study, there are 357 (63 %) benign cancer patients and 212 (37 %) malignant cancer patients. Distributions of the variables are given (Figure 1).

Descriptive statistics for the variable examined in this study are presented in (Table 1). There is a significant difference between the diagnosis groups regarding other variables (P<0.001) except the radius_mean, fractal_dimension_mean, and smoothness_se variables.

The correlation matrix is indicated (Figure 2) in this study. the matrix that includes a lot of numbers. These numbers range from -1 to 1. A value of 1 mean that the two variables, mean radius and area, are positively interrelated with each other. The zero mean does not correlate with variables such as radial mean and fractal dimension SE. The mean -1 that has two variables, radius and fractal dimension mean are negatively correlated with each other. The correlation between them is not -1, it is -0.3 but the idea is that if the sign of the correlation is negative that means that there is a negative correlation. According to the table, there is no correlation between radius_mean and concavity_mean or there is a very weak negative correlation. However, the relationship is statistically significant. This may be due to the high sample size. Although the result is statistically significant, it may not be clinically significant (r=-0.0917, p=0.029). Similarly, there was no statistically significant correlation between radius_mean and texture_mean variables (r=-0.0113, p=0.789). However, there is a positive, weak and statistically significant correlation between texture_mean and texture_worst variables (r=0.2318, p<0.001). Other variables can be interpreted similarly among themselves.