Probability density functions are frequently used to characterize the distributional properties\ud of large-scale database systems. As functional compositions, densities primarily carry\ud relative information. As such, standard methods of functional data analysis (FDA) are not\ud appropriate for their statistical processing. The specific features of density functions are\ud accounted for in Bayes spaces, which result from the generalization to the infinite dimensional\ud setting of the Aitchison geometry for compositional data. The aim is to build up a\ud concise methodology for functional principal component analysis of densities. A simplicial\ud functional principal component analysis (SFPCA) is proposed, based on the geometry\ud of the Bayes space B2 of functional compositions. SFPCA is performed by exploiting the\ud centred log-ratio transform, an isometric isomorphism between B2 and L2 which enables\ud one to resort to standard FDA tools. The advantages of the proposed approach with respect\ud to existing techniques are demonstrated using simulated data and a real-world example of\ud population pyramids in Upper Austria

The drainage to IMNs is unlikely to have a detrimental effect on patient outcome.

Abstract:In the present study, we determined complex indices of inflammatory activity and compared the performance of these indices as prognostic biomarkers in a cohort of breast cancer patients. All proposed composite biomarkers could be evaluated in 418 out of 474 patients in the cohort with complete data on peripheral blood cell count, urinary neopterin, albumin and C-reactive protein. Neutrophil-to-lymphocyte ratio, lymphocyteto-monocyte ratio, platelet-to-lymphocyte ratio, systemic inflammatory index, Glasgow prognostic index, modified Glasgow prognostic index, prognostic nutritional index and C-reactive protein/albumin ratio were calculated and further complex indices were proposed. Although a number of the investigated indices were significantly associated with survival in the univariate analysis, only age and stage, but none of the laboratory biomarkers or composite biomarkers, were significant predictors of survival in the whole group in the multivariate analysis. In patients evaluated before the start of the treatment, age, stage and urinary neopterin were significant predictors of survival. These results underscore the importance of neopterin as a prognostic biomarker in breast cancer.

The different parts (variables) of a compositional data set cannot be considered independent from each other, since only the ratios between the parts constitute the relevant information to be analysed. Practically, this information can be included in a system of orthonormal coordinates. For the task of regression of one part on other parts, a specific choice of orthonormal coordinates is proposed which allows for an interpretation of the regression parameters in terms of the original parts. In this context, orthogonal regression is appropriate since all compositional parts -also the explanatory variables -are measured with errors. Besides classical (least-squares based) parameter estimation, also robust estimation based on robust principal component analysis is employed. Statistical inference for the regression parameters is obtained by bootstrap; in the robust version the fast and robust bootstrap procedure is used. The methodology is illustrated with a data set from macroeconomics. ARTICLE HISTORY

AbstractThe immune response crucially determines the survival of patients with malignant tumors including breast carcinoma. The aim of the present study was to evaluate retrospectively an association of peripheral blood cell count (PBC)-derived ratios and urinary neopterin concentration with prognosis in breast cancer patients. Urinary neopterin, neutrophil-to-lymphocyte ratio (NLR), lymphocyte-to-monocyte ratio (LMR) and platelet-to-lymphocyte ratio (PLR) were retrospectively analyzed in a cohort of 474 breast cancer patients. NLR and PLR correlated positively with each other and negatively with LMR, but no correlation between neopterin concentrations and PBC-derived ratios was observed. Increased urinary neopterin concentration was a significant predictor of poor survival in patients with active disease, but PLR, NLR or LMR were not significantly associated with survival in multivariate analysis. In conclusion, increased urinary neopterin was a significant predictor of poor survival in patients with breast cancer and active disease.