Vitamin D Deficiency in Women with Breast Cancer: A Correlation with Osteoporosis? A Machine Learning Approach with Multiple Factor Analysis

Abstract

Breast cancer (BC) is the most frequent malignant tumor in women in Europe and North America, and the use of aromatase inhibitors (AIs) is recommended in women affected by estrogen receptor-positive BCs. AIs, by inhibiting the enzyme that converts androgens into estrogen, cause a decrement in bone mineral density (BMD), with a consequent increased risk of fragility fractures. This study aimed to evaluate the role of vitamin D3 deficiency in women with breast cancer and its correlation with osteoporosis and BMD modifications. This observational cross-sectional study collected the following data regarding bone health: osteoporosis and osteopenia diagnosis, lumbar spine (LS) and femoral neck bone mineral density (BMD), serum levels of 25-hydroxyvitamin D3 (25(OH)D3), calcium and parathyroid hormone. The study included 54 women with BC, mean age 67.3 ± 8.16 years. Given a significantly low correlation with the LS BMD value (r² = 0.30, p = 0.025), we assessed the role of vitamin D3 via multiple factor analysis and found that BMD and vitamin D3 contributed to the arrangement of clusters, reported as vectors, providing similar trajectories of influence to the construction of the machine learning model. Thus, in a cohort of women with BC undergoing Ais, we identified a very low prevalence (5.6%) of patients with adequate bone health and a normal vitamin D3 status. According to our cluster model, we may conclude that the assessment and management of bone health and vitamin D3 status are crucial in BC survivors.

Keywords: bone mineral density; breast cancer; cluster analysis; machine learning; multiple factor analysis; osteoporosis; vitamin D.

Figure 1

Differences in cholecalciferol pathways in breast cancer survivors. Gene abbreviation: BCL-2: B-cell lymphoma 2, CHD: Chromodomain-Helicase DNA-binding, CYP: Cytochrome P, ER: Estrogen receptor, MYC: MYeloCytomatosis, PTGER: Prostaglandin E Receptor.

Figure 2

Correlations between quantitative variables and dimensions. The plot depicts the topographical influence in the arrangement of the variables on the graph along the abscissa (Dim1) and the ordinate (Dim2). Thus, we evaluated the weight of the single variables through crossed linear regressions, representing them two-dimensionally on a Cartesian plane. Therefore, the variables, indicated as vectors, according to the position in the represented circle, influence the spatial position of the individuals and consequently their clustering into groups. Abbreviation: BMD = Bone Mineral Density, FN = Femoral Neck, LS = Lumbar Spine.

Figure 3

Contribution to the dimensions 1 and 2 (Cartesian axes). With the bar graphs, the plot contribution represents the weight of the single variables on the representativeness of the abscissa axis (Dimension 1) and of the ordinates (Dimension 2). As regards the horizontal axis of the previous figure, the greatest influence is attributed to the BMD values, while the vertical axis is related to the age and the BMI values. BMD = Bone Mineral Density, FN = Femoral Neck, LS = Lumbar Spine.

Figure 4

Clustered individual factor map. Each individual is positioned according to the Cartesian axes and thickens in specific clusters that reflect the influence of size along the horizontal axis for dimension 1 and along the ordinal axis for dimension 2. Normal subjects cluster at the bottom and right of the graph for the influence of age, BMI, and BMD, as previously described in Figure 2 and Figure 3.