Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Methylation alterations are not a major cause of PTTG1 misregulation.

BACKGROUND On its physiological cellular context, PTTG1 controls sister chromatid segregation during mitosis. Within its crosstalk to the cellular arrest machinery, relies a checkpoint of integrity for which gained the over name of securin. PTTG1 was found to promote malignant transformation in 3T3 fibroblasts, and further found to be overexpressed in different tumor types. More recently, PTTG1 has been also related to different processes such as DNA repair and found to trans-activate different cellular pathways involving c-myc, bax or p53, among others. PTTG1 over-expression has been correlated to a worse prognosis in thyroid, lung, colorectal cancer patients, and it can not be excluded that this effect may also occur in other tumor types. Despite the clinical relevance and the increasing molecular characterization of PTTG1, the reason for its up-regulation remains unclear. METHOD We analysed PTTG1 differential expression in PC-3, DU-145 and LNCaP tumor cell lines, cultured in the presence of the methyl-transferase inhibitor 5-Aza-2'-deoxycytidine. We also tested whether the CpG island mapping PTTG1 proximal promoter evidenced a differential methylation pattern in differentiated thyroid cancer biopsies concordant to their PTTG1 immunohistochemistry status. Finally, we performed whole-genome LOH studies using Affymetix 50 K microarray technology and FRET analysis to search for allelic imbalances comprising the PTTG1 locus. CONCLUSION Our data suggest that neither methylation alterations nor LOH are involved in PTTG1 over-expression. These data, together with those previously reported, point towards a post-transcriptional level of misregulation associated to PTTG1 over-expression.

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Explaining Fiscal Balances with a Simultaneous Equation Model of Revenue and Expenditure : A Case Study of Swiss Cantons Using Panel Data

Empirical literature on the analysis of the efficiency of measures for reducing persistent government deficits has mainly focused on the direct explanation of deficit. By contrast, this paper aims at modeling government revenue and expenditure within a simultaneous framework and deriving the fiscal balance (surplus or deficit) equation as the difference between the two variables. This setting enables one to not only judge how relevant the explanatory variables are in explaining the fiscal balance but also understand their impact on revenue and/or expenditure. Our empirical results, obtained by using a panel data set on Swiss Cantons for the period 1980-2002, confirm the relevance of the approach followed here, by providing unambiguous evidence of a simultaneous relationship between revenue and expenditure. They also reveal strong dynamic components in revenue, expenditure, and fiscal balance. Among the significant determinants of public fiscal balance we not only find the usual business cycle elements, but also and more importantly institutional factors such as the number of administrative units, and the ease with which people can resort to political (direct democracy) instruments, such as public initiatives and referendum.