Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

L'intelligenza emotiva in età evolutiva

Emotional Intelligence (EI) has increasingly gained widespread popularity amongst both lay people and scientists in a wide range of contexts and across several research areas. In spite of rigorous inquiry into its applications in educational, social, health and clinical settings, substantial disagreement exists regarding the definition of EI, with respect to both terminology and operationalizations. Actually, there is a consensus about a conceptual distinction between Trait EI, or trait emotional self-efficacy (Petrides & Furnham, 2001), and Ability EI, or cognitive-emotional ability (Mayer & Salovey, 1997). Trait EI is measured via self-report questionnaires, whereas Ability EI is assessed via maximum performance tests. Moreover, EI is the broadest of the emotional constructs, and it subsumes various constructs, as Emotional Awareness (Lane & Schwartz, 1987). To date, EI research has focused primarily on adults, with fewer studies conducted with child samples. The aim of the present study is to investigate the role of different models of EI in childhood and early adolescence (N = 670; 353 females; Mage= 10.25 years ; SD = 1.57). In addition, a further goal is to evaluate the relationship of each construct with personality, non verbal cognitive intelligence, school performance, peer relationships, and affective disorders (anxiety and depression). Results shows significant correlations between Trait EI and Emotional Awareness, whereas Trait and Ability EI appear as independent constructs. We also found significant positive associations between age and Ablity EI and Emotional Awareness (although with add of verbal productivity), while gender differences emerged in favour of females in all EI-related measures. The results provide evidence that Trait EI is partially determined by all of the Big Five personality dimensions, but independent of cognitive ability. Finally, the present study highlights the role of EI on social interactions, school performance and, especially, a negative relationship between Trait EI and psychopathology.

Studio multicentrico sulla prevalenza e sulle principali caratteristiche cliniche e biochimiche nei pazienti in dialisi paratiroidectomizzati in italia

Lo studio CAVE PTX ha lo scopo di valutare la reale prevalenza della paratiroidectomia nei pazienti dializzati in Italia, verificare l’aderenza ai targets ematochimici proposti dalle linee guida internazionali K/DOQI e ricercare la presenza di fratture vertebrali e calcificazioni vascolari. Al momento attuale riportiamo i dati preliminari sulla prevalenza e le caratteristiche cliniche generali dei pazienti finora arruolati. Il nostro studio ha ricevuto contributi da 149 centri dialisi italiani, su un totale di 670, pari al 22%. La popolazione dialitica dalla quale sono stati ottenuti i casi di paratiroidectomia è risultata pari a 12515 pazienti;l’87,7% dei pazienti effettuava l’emodialisi mentre il 12,3% la dialisi peritoneale. Cinquecentoventotto, pari al 4,22%, avevano effettuato un intervento di paratiroidectomia (4,5%emodializzati, 1,9% in dialisi peritoneale;p<0.001). Abbiamo considerato tre gruppi differenti di PTH: basso (<150 pg/ml), ottimale (150 -300 pg/ml) ed elevato (>300 pg/ml). I valori medi di PTH e calcemia sono risultati significativamente diversi (più alti) tra casi e controlli nei due gruppi con PTH basso (PTX = 40±39 vs controllo = 92±42 pg/ml; p<.0001) e PTH alto (PTX= 630 ± 417 vs controllo 577 ±331; p<.05). La percentuale di pazienti con PTH troppo basso è risultata più elevata nei pazienti chirurgici rispetto al resto della popolazione (64vs23%; p<0.0001), mentre la percentuale dei casi con PTH troppo alto è risultata significativamente più alta nel gruppo di controllo (38%vs19%; p<0.003). Il 61% dei casi assumeva vitamina D rispetto al 64 % dei controlli; l’88% vs 75% un chelante del fosforo ed il 13%vs 35% il calciomimentico. In conclusione, la paratiroidectomia ha una bassa prevalenza in Italia, i pazienti sono più spesso di sesso femminile, in emodialisi e con età relativamente giovane ma da più tempo in dialisi.