Multivariate statistical analysis for assessment of the relationships between bone density, biogenic elements content, and the level of oxidative stress in osteoporotic women

The aim of the present study is to reveal hidden relationships between bone density, biogenic elements content, and the level of oxidative stress of female patients with osteoporosis and osteopenia. Additionally, specific links between the patients are sought in order to interpret different similarity patterns of objects (patients) helping to a better understanding of the significance of the clinical variables for each identified similarity pattern. Material and Methods: The input dataset consisting of 59 objects (patients) and 11 experimentally determined variables (clinical parameters) was subject to intelligent data analysis including cluster analysis (hierarchical and non-hierarchical mode) and factor analysis. Results and Discussion: In the hierarchical dendrogram for clustering of 11 variables are formed 3 major clusters. We could assume that three factors (impact) are linked to the structure of the data set: descriptors responsible for osteoporosis diagnosis; descriptors (essential elements) related to osteoporosis status; descriptors related to the "overall health status impact”. The patients are clustered in 3 clusters corresponding to 3 different levels of health status (improving, worsening and intermediate) by K-means clustering. The specific descriptors are defined for each identified cluster. Factor analysis shows that 3 latent factors explain nearly 70 % of the total variance of the system ˗ each of them with respective clinical meaning. A relationship is proven between T-score, diagnosis, and antioxidant activity by a 3D plot of factor loadings. Conclusion: The multivariate statistical data interpretation for patients with osteoporosis problems reveals hidden relationships between specific similarity clusters among all patients or between the clinical parameters experimentally measured. It helps to better distinguish the variations between the specific groups and to determine the indicators for the variability. All this helps for more individual approachesto medical treatment.