On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Genetic Manipulation, Gene Silencing and Biomarker Development in Multiple Experimental Models.

The thesis is set in three different parts, according to the relative experimental models. First, the domestic pig (Sus scrofa) is part of the study on reproductive biotechnologies: the transgenesis technique of Sperm Mediated Gene Transfer is widely studied starting from the quality of the semen, through the study of multiple uptakes of exogenous DNA and lastly used in the production of multi-transgenic blastocysts. Finally we managed to couple the transgenesis pipeline with sperm sorting and therefore produced transgenic embryos of predetermined sex. In the second part of the thesis the attention is on the fruit fly (Drosophila melanogaster) and on its derived cell line: the S2 cells. The in vitro and in vivo models are used to develop and validate an efficient way to knock down the myc gene. First an efficient in vitro protocol is described, than we demonstrate how the decrease in myc transcript remarkably affects the ribosome biogenesis through the study of Polysome gradients, rRNA content and qPCR. In vivo we identified two optimal drivers for the conditional silencing of myc, once the flies are fed with RU486: the first one is throughout the whole body (Tubulin), while the second is a head fat body driver (S32). With these results we present a very efficient model to study the role of myc in multiple aspects of translation. In the third and last part, the focus is on human derived lung fibroblasts (hLF-1), mouse tail fibroblasts and mouse tissues. We developed an efficient assay to quantify the total protein content of the nucleus on a single cell level via fluorescence. We coupled the protocol with classical immunofluorescence so to have at the same time general and particular information, demonstrating that during senescence nuclear proteins increase by 1.8 fold either in human cells, mouse cells and mouse tissues.

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

Atmospheric radiative transfer in multiple scattering conditions. Application to NWP models.

High spectral resolution radiative transfer (RT) codes are essential tools in the study of the radiative energy transfer in the Earth atmosphere and a support for the development of parameterizations for fast RT codes used in climate and weather prediction models. Cirrus clouds cover permanently 30% of the Earth's surface, representing an important contribution to the Earth-atmosphere radiation balance. The work has been focussed on the development of the RT model LBLMS. The model, widely tested in the infra-red spectral range, has been extended to the short wave spectrum and it has been used in comparison with airborne and satellite measurements to study the optical properties of cirrus clouds. A new database of single scattering properties has been developed for mid latitude cirrus clouds. Ice clouds are treated as a mixture of ice crystals with various habits. The optical properties of the mixture are tested in comparison to radiometric measurements in selected case studies. Finally, a parameterization of the mixture for application to weather prediction and global circulation models has been developed. The bulk optical properties of ice crystals are parameterized as functions of the effective dimension of measured particle size distributions that are representative of mid latitude cirrus clouds. Tests with the Limited Area Weather Prediction model COSMO have shown the impact of the new parameterization with respect to cirrus cloud optical properties based on ice spheres.

Valutazione della qualità ed autenticità di prodotti oleari e lattiero caseari mediante metodi fisici di analisi accoppiati a tecniche statistiche multivariate

Questa tesi descrive alcuni studi di messa a punto di metodi di analisi fisici accoppiati con tecniche statistiche multivariate per valutare la qualità e l’autenticità di oli vegetali e prodotti caseari. L’applicazione di strumenti fisici permette di abbattere i costi ed i tempi necessari per le analisi classiche ed allo stesso tempo può fornire un insieme diverso di informazioni che possono riguardare tanto la qualità come l’autenticità di prodotti. Per il buon funzionamento di tali metodi è necessaria la costruzione di modelli statistici robusti che utilizzino set di dati correttamente raccolti e rappresentativi del campo di applicazione. In questo lavoro di tesi sono stati analizzati oli vegetali e alcune tipologie di formaggi (in particolare pecorini per due lavori di ricerca e Parmigiano-Reggiano per un altro). Sono stati utilizzati diversi strumenti di analisi (metodi fisici), in particolare la spettroscopia, l’analisi termica differenziale, il naso elettronico, oltre a metodiche separative tradizionali. I dati ottenuti dalle analisi sono stati trattati mediante diverse tecniche statistiche, soprattutto: minimi quadrati parziali; regressione lineare multipla ed analisi discriminante lineare.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

A New Prediction Model for Slope Stability Analysis

The instability of river bank can result in considerable human and land losses. The Po river is the most important in Italy, characterized by main banks of significant and constantly increasing height. This study presents multilayer perceptron of artificial neural network (ANN) to construct prediction models for the stability analysis of river banks along the Po River, under various river and groundwater boundary conditions. For this aim, a number of networks of threshold logic unit are tested using different combinations of the input parameters. Factor of safety (FS), as an index of slope stability, is formulated in terms of several influencing geometrical and geotechnical parameters. In order to obtain a comprehensive geotechnical database, several cone penetration tests from the study site have been interpreted. The proposed models are developed upon stability analyses using finite element code over different representative sections of river embankments. For the validity verification, the ANN models are employed to predict the FS values of a part of the database beyond the calibration data domain. The results indicate that the proposed ANN models are effective tools for evaluating the slope stability. The ANN models notably outperform the derived multiple linear regression models.

Sleep disorders in Multiple System Atrophy: a longitudinal study

Introduction: A higher frequency of sleep and breathing disorders in Multiple System Atrophy (MSA) populations is documented in literature. The analysis of disease progression and prognosis in patients with sleep and breathing disorders could shed light on specific neuropathology and pathophysiology of MSA. Objective: To characterize sleep disorders and their longitudinal modifications during disease course in MSA patients, and to determine their prognostic value. Methods: This is a retrospective and prospective cohort study including 182 MSA patients (58.8% males). Type of onset was defined by the first reported motor or autonomic symptom/sign related to MSA. The occurrence of symptoms/signs and milestones of disease progression and their latency were collected. REM sleep behaviour disorder (RBD) and stridor were video-polysomnography (VPSG)-confirmed. VPSG recordings were analysed in a standardized fashion during the disease course. Survival data were based on time to death from the first symptom of disease. Results: Isolated RBD represented the first MSA symptom in 30% of patients, preceding disease onset according to international criteria with a median of 3(1–5) years. Patients developing early stridor or presenting with RBD at disease onset showed a more rapid and severe disease progression. These features had independent negative prognostic value for survival. Sleep architecture was characterized by peculiar features which could represent negative markers in MSA prognosis. Patients with stridor treated with tracheostomy showed a reduced risk of death. Conclusions: This is one of the first studies focusing on longitudinal progression of sleep in MSA. Sleep disorders are key features of disease, playing a role in presentation, prognosis and progression. In our MSA cohort, RBD represented the most frequent mode of disease presentation. Moreover, some specific clinical and instrumental sleep features could represent a hallmark of MSA and could be involved in prognosis and, in particular, in sudden death and death during sleep.

Molecular changes induced by a centrally-induced state of synthetic torpor in multiple organs:a new strategy for radioprotection.

Torpor is a successful survival strategy displayed by several mammalian species to cope with harsh environmental conditions. A complex interplay of ambient, genetic and circadian stimuli acts centrally to induce a severe suppression of metabolic rate, usually followed by an apparently undefended reduction of body temperature. Some animals, such as marmots, are able to maintain this physiological state for months (hibernation), during which torpor bouts are periodically interrupted by short interbouts of normothermia (arousals). Interestingly, torpor adaptations have been shown to be associated with a large resistance towards stressors, such as radiation: indeed, if irradiated during torpor, hibernators can tolerate higher doses of radiation, showing an increased survival rate. New insights for radiotherapy and long-term space exploration could arise from the induction of torpor in non-hibernators, like humans. The present research project is centered on synthetic torpor (ST), a hypometabolic/hypothermic condition induced in a non-hibernator, the rat, through the pharmacological inhibition of the Raphe Pallidus, a key brainstem area controlling thermogenic effectors. By exploiting this procedure, this thesis aimed at: i) providing a multiorgan description of the functional cellular adaptations to ST; ii) exploring the possibility, and the underpinning molecular mechanisms, of enhanced radioresistance induced by ST. To achieve these aims, transcriptional and histological analysis have been performed in multiple organs of synthetic torpid rats and normothermic rats, either exposed or not exposed to 3 Gy total body of X-rays. The results showed that: i) similarly to natural torpor, ST induction leads to the activation of survival and stress resistance responses, which allow the organs to successfully adapt to the new homeostasis; ii) ST provides tissue protection against radiation damage, probably mainly through the cellular adaptations constitutively induced by ST, even though the triggering of specific responses when the animal is irradiated during hypothermia might play a role.

Identification of outcome-oriented cut-offs for copy number alterations in multiple myeloma: predictive biomarkers with improved prognostic accuracy

Aim of the present study was to develop a statistical approach to define the best cut-off Copy number alterations (CNAs) calling from genomic data provided by high throughput experiments, able to predict a specific clinical end-point (early relapse, 18 months) in the context of Multiple Myeloma (MM). 743 newly diagnosed MM patients with SNPs array-derived genomic and clinical data were included in the study. CNAs were called both by a conventional (classic, CL) and an outcome-oriented (OO) method, and Progression Free Survival (PFS) hazard ratios of CNAs called by the two approaches were compared. The OO approach successfully identified patients at higher risk of relapse and the univariate survival analysis showed stronger prognostic effects for OO-defined high-risk alterations, as compared to that defined by CL approach, statistically significant for 12 CNAs. Overall, 155/743 patients relapsed within 18 months from the therapy start. A small number of OO-defined CNAs were significantly recurrent in early-relapsed patients (ER-CNAs) - amp1q, amp2p, del2p, del12p, del17p, del19p -. Two groups of patients were identified either carrying or not ≥1 ER-CNAs (249 vs. 494, respectively), the first one with significantly shorter PFS and overall survivals (OS) (PFS HR 2.15, p<0001; OS HR 2.37, p<0.0001). The risk of relapse defined by the presence of ≥1 ER-CNAs was independent from those conferred both by R-IIS 3 (HR=1.51; p=0.01) and by low quality (< stable disease) clinical response (HR=2.59 p=0.004). Notably, the type of induction therapy was not descriptive, suggesting that ER is strongly related to patients’ baseline genomic architecture. In conclusion, the OO- approach employed allowed to define CNAs-specific dynamic clonality cut-offs, improving the CNAs calls’ accuracy to identify MM patients with the highest probability to ER. As being outcome-dependent, the OO-approach is dynamic and might be adjusted according to the selected outcome variable of interest.