Multiple testing in spatial epidemiology: a Bayesian approach

In this work we aim to propose a new approach for preliminary epidemiological studies on Standardized Mortality Ratios (SMR) collected in many spatial regions. A preliminary study on SMRs aims to formulate hypotheses to be investigated via individual epidemiological studies that avoid bias carried on by aggregated analyses. Starting from collecting disease counts and calculating expected disease counts by means of reference population disease rates, in each area an SMR is derived as the MLE under the Poisson assumption on each observation. Such estimators have high standard errors in small areas, i.e. where the expected count is low either because of the low population underlying the area or the rarity of the disease under study. Disease mapping models and other techniques for screening disease rates among the map aiming to detect anomalies and possible high-risk areas have been proposed in literature according to the classic and the Bayesian paradigm. Our proposal is approaching this issue by a decision-oriented method, which focus on multiple testing control, without however leaving the preliminary study perspective that an analysis on SMR indicators is asked to. We implement the control of the FDR, a quantity largely used to address multiple comparisons problems in the eld of microarray data analysis but which is not usually employed in disease mapping. Controlling the FDR means providing an estimate of the FDR for a set of rejected null hypotheses. The small areas issue arises diculties in applying traditional methods for FDR estimation, that are usually based only on the p-values knowledge (Benjamini and Hochberg, 1995; Storey, 2003). Tests evaluated by a traditional p-value provide weak power in small areas, where the expected number of disease cases is small. Moreover tests cannot be assumed as independent when spatial correlation between SMRs is expected, neither they are identical distributed when population underlying the map is heterogeneous. The Bayesian paradigm oers a way to overcome the inappropriateness of p-values based methods. Another peculiarity of the present work is to propose a hierarchical full Bayesian model for FDR estimation in testing many null hypothesis of absence of risk.We will use concepts of Bayesian models for disease mapping, referring in particular to the Besag York and Mollié model (1991) often used in practice for its exible prior assumption on the risks distribution across regions. The borrowing of strength between prior and likelihood typical of a hierarchical Bayesian model takes the advantage of evaluating a singular test (i.e. a test in a singular area) by means of all observations in the map under study, rather than just by means of the singular observation. This allows to improve the power test in small areas and addressing more appropriately the spatial correlation issue that suggests that relative risks are closer in spatially contiguous regions. The proposed model aims to estimate the FDR by means of the MCMC estimated posterior probabilities b i's of the null hypothesis (absence of risk) for each area. An estimate of the expected FDR conditional on data (\FDR) can be calculated in any set of b i's relative to areas declared at high-risk (where thenull hypothesis is rejected) by averaging the b i's themselves. The\FDR can be used to provide an easy decision rule for selecting high-risk areas, i.e. selecting as many as possible areas such that the\FDR is non-lower than a prexed value; we call them\FDR based decision (or selection) rules. The sensitivity and specicity of such rule depend on the accuracy of the FDR estimate, the over-estimation of FDR causing a loss of power and the under-estimation of FDR producing a loss of specicity. Moreover, our model has the interesting feature of still being able to provide an estimate of relative risk values as in the Besag York and Mollié model (1991). A simulation study to evaluate the model performance in FDR estimation accuracy, sensitivity and specificity of the decision rule, and goodness of estimation of relative risks, was set up. We chose a real map from which we generated several spatial scenarios whose counts of disease vary according to the spatial correlation degree, the size areas, the number of areas where the null hypothesis is true and the risk level in the latter areas. In summarizing simulation results we will always consider the FDR estimation in sets constituted by all b i's selected lower than a threshold t. We will show graphs of the\FDR and the true FDR (known by simulation) plotted against a threshold t to assess the FDR estimation. Varying the threshold we can learn which FDR values can be accurately estimated by the practitioner willing to apply the model (by the closeness between\FDR and true FDR). By plotting the calculated sensitivity and specicity (both known by simulation) vs the\FDR we can check the sensitivity and specicity of the corresponding\FDR based decision rules. For investigating the over-smoothing level of relative risk estimates we will compare box-plots of such estimates in high-risk areas (known by simulation), obtained by both our model and the classic Besag York Mollié model. All the summary tools are worked out for all simulated scenarios (in total 54 scenarios). Results show that FDR is well estimated (in the worst case we get an overestimation, hence a conservative FDR control) in small areas, low risk levels and spatially correlated risks scenarios, that are our primary aims. In such scenarios we have good estimates of the FDR for all values less or equal than 0.10. The sensitivity of\FDR based decision rules is generally low but specicity is high. In such scenario the use of\FDR = 0:05 or\FDR = 0:10 based selection rule can be suggested. In cases where the number of true alternative hypotheses (number of true high-risk areas) is small, also FDR = 0:15 values are well estimated, and \FDR = 0:15 based decision rules gains power maintaining an high specicity. On the other hand, in non-small areas and non-small risk level scenarios the FDR is under-estimated unless for very small values of it (much lower than 0.05); this resulting in a loss of specicity of a\FDR = 0:05 based decision rule. In such scenario\FDR = 0:05 or, even worse,\FDR = 0:1 based decision rules cannot be suggested because the true FDR is actually much higher. As regards the relative risk estimation, our model achieves almost the same results of the classic Besag York Molliè model. For this reason, our model is interesting for its ability to perform both the estimation of relative risk values and the FDR control, except for non-small areas and large risk level scenarios. A case of study is nally presented to show how the method can be used in epidemiology.

L'infiammazione intestinale nell'animale sperimentale come modello per lo sviluppo di nuovi farmaci: ruolo della via tachichininergica nelle malattie infiammatorie intestinali

Background: Several lines of evidence showed that inflammation is associated with changes in the expression of tachykinins both in human and animal models. Tachykinins, including substance P (SP), are small peptides expressed in the extrinsic primary afferent nerve fibres and enteric neurons of the gut: they exert their action through three distinct receptors, termed NK1, NK2 and NK3. SP modulates intestinal motility and enteric secretion, acting preferentially through the NK1 receptor. SP neural network and NK1 receptor expression are increased in patients with inflammatory bowel disease, and similar changes were observed in experimental models of inflammation. The 2,4 Dinitrobenzene Sulphonic Acid (DNBS) model of colitis is useful to study innate immunity, non-specific inflammation and wound healing; it has been suggested that the transmural inflammation seen in this model resembles that found in Crohn’s disease and can therefore be used to study what cells and mediators are involved in this type of inflammation. Aim: To test the possible protective effect of the NK1 receptor antagonist SSR140333 on: 1) acute model of intestinal inflammation; 2) reactivation of DNBS-induced colitis in rats. Methods: Acute colitis was induced in male SD rats by intrarectal administration of DNBS (15 mg/rat in 50% ethanol). Reactivation of colitis was induced by intrarectal injections of DNBS on day 28 (7.5 mg/rat in 35% ethanol). Animals were sacrificed on day 6 (acute colitis) and 29 (reactivation of colitis). SSR140333 (10 mg/kg) was administered orally starting from the day before the induction of colitis for 7 days (acute colitis) or seven days before the reactivation of colitis. Colonic damage was assessed by means of macroscopic and microscopic scores, myeloperoxidase activity (MPO) and TNF-α tissue levels. Enzyme immunoassay was used to measure colonic substance P levels. Statistical analysis was performed using analysis of variance (one-way or two-way, as appropriate) with the Bonferroni’s correction for multiple comparisons. Results: DNBS administration impaired body weight gain and markedly increased all inflammatory parameters (p<0.01). Treatment with SSR140333 10 mg/kg significantly counteracted the impairment in body weight gain, decreased macroscopic and histological scores and reduced colonic myeloperoxidase activity (p<0.01). Drug treatment counteracted TNF-α tissue levels and colonic SP concentrations (acute model). Similar results were obtained administering the NK1 receptor antagonist SSR140333 (3 and 10 mg/kg) for 5 days, starting the day after the induction of colitis. Intrarectal administration of DNBS four weeks after the first DNBS administration resulted in reactivation of colitis, with increases in macroscopic and histological damage scores and increase in MPO activity. Preventive treatment with SSR140333 10 mg/kg decreased macroscopic damage score, significantly reduced microscopic damage score but did not affect MPO activity. Conclusions: Treatment with SSR140333 significantly reduced intestinal damage in acute model of intestinal inflammation in rats. The NK1 receptor antagonist SSR140333 was also able to prevent relapse in experimental colitis. These results support the hypothesis of SP involvement in intestinal inflammation and indicate that NK receptor antagonists may have a therapeutic potential in inflammatory bowel disease.

Valutazione dei disturbi cognitivi nei pazienti sottoposti a Rivascolarizzazione Carotidea (Endoarterectomia vs Stenting) mediante dosaggio di marker di danno neuronale, Mini Mental State Examination e Risonanza Magnetica

Scopo del nostro studio è quello di valutare i disturbi cognitivi in relazione al tasso di microembolia cerebrale in due gruppi di pazienti trattati per lesione carotidea asintomatica con endoarterectomia (CEA) o stenting (CAS). Comparando le due metodiche mediante l’utilizzo di risonanza magnetica in diffusione (DW-MRI), neuromarkers (NSE e S100β) e test neuropsicometrici. MATERIALE E METODI: 60 pazienti sono stati sottoposti a rivascolarizzazione carotidea (CEA n=32 e CAS n=28). Sono stati tutti valutati con DW-MRI e Mini-Mental State Examination (MMSE) test nel preoperatorio, a 24 ore, a 6 ed a 12 mesi dall’intervento. In tutti sono stati dosati i livelli sierici di NSE e S100β mediante 5 prelievi seriati nel tempo, quello basale nel preoperatorio, l’ultimo a 24 ore. L’ananlisi statistica è stata effettuata con test t di Student per confronti multipli per valori continui e con test χ2 quadro e Fisher per le variabili categoriche. Significatività P <0,05. RISULTATI: Non vi è stato alcun decesso. Un paziente del gruppo CAS ha presentato un ictus ischemico. In 6 pazienti CAS ed in 1 paziente CEA si sono osservate nuove lesioni subcliniche alla RMN-DWI post-operatoria (21,4% vs 3% p=0,03). Nel gruppo CAS le nuove lesioni presenti alla RMN sono risultate significativamente associate ad un declino del punteggio del MMSE (p=0,001). L’analisi dei livelli di NSE e S100β ha mostrato un significativo aumento a 24 ore nei pazienti CAS (P = .02). A 12 mesi i pazienti che avevano presentato nuove lesioni ischemiche nel post-operatorio hanno mostrato minor punteggio al MMSE, non statisticamente significativo. CONCLUSIONI: I neuromarkers in combinazione con MMSE e RMN-DWI possono essere utilizzati nella valutazione del declino cognitivo correlato a lesioni silenti nell’immediato postoperatorio di rivascolarizzazione carotidea. Quest’ultime dovrebbero essere valutate quindi non solo rispetto al tasso di mortalità e ictus, ma anche rispetto al tasso di microembolia.

Towards a full cosmological exploitation of cosmic voids

A stately fraction of the Universe volume is dominated by almost empty space. Alongside the luminous filamentary structures that make it up, there are vast and smooth regions that have remained outside the Cosmology spotlight during the past decades: cosmic voids. Although essentially devoid of matter, voids enclose fundamental information about the cosmological framework and have gradually become an effective and competitive cosmological probe. In this Thesis work we present fundamental results about the cosmological exploitation of voids. We focused on the number density of voids as a function of their radius, known as void size function, developing an effective pipeline for its cosmological usage. We proposed a new parametrisation of the most used theoretical void size function to model voids identified in the distribution of biased tracers (i.e. dark matter haloes, galaxies and galaxy clusters), a step of fundamental importance to extend the analysis to real data surveys. We then applied our built methodology to study voids in alternative cosmological scenarios. Firstly we exploited voids with the aim of breaking the degeneracies between cosmological scenarios characterised by modified gravity and the inclusion of massive neutrinos. Secondly we analysed voids in the perspective of the Euclid survey, focusing on the void abundance constraining power on dynamical dark energy models with massive neutrinos. Moreover we explored other void statistics like void profiles and clustering (i.e. the void-galaxy and the void-void correlation), providing cosmological forecasts for the Euclid mission. We finally focused on the probe combination, highlighting the incredible potential of the joint analysis of multiple void statistics and of the combination of the void size function with different cosmological probes. Our results show the fundamental role of the void analysis in constraining the fundamental parameters of the cosmological model and pave the way for future studies on this topic.

Longitudinal evolution of cognitive functions in patients with multiple system atrophy: a prospective study

Introduction and Background: Multiple system atrophy (MSA) is a sporadic, adult-onset, progressive neurodegenerative disease characterized clinically by parkinsonism, cerebellar ataxia, and autonomic failure. We investigated cognitive functions longitudinally in a group of probable MSA patients, matching data with sleep parameters. Patients and Methods: 10 patients (7m/3f) underwent a detailed interview, a general and neurological examination, laboratory exams, MRI scans, a cardiovascular reflexes study, a battery of neuropsychological tests, and video-polysomnographic recording (VPSG). Patients were revaluated (T1) a mean of 16±5 (range: 12-28) months after the initial evaluation (T0). At T1, the neuropsychological assessment and VPSG were repeated. Results: The mean patient age was 57.8±6.4 years (range: 47-64) with a mean age at disease onset of 53.2±7.1 years (range: 43-61) and symptoms duration at T0 of 60±48 months (range: 12-144). At T0, 7 patients showed no cognitive deficits while 3 patients showed isolated cognitive deficits. At T1, 1 patient worsened developing multiple cognitive deficits from a normal condition. At T0 and T1, sleep efficiency was reduced, REM latency increased, NREM sleep stages 1-2 slightly increased. Comparisons between T1 and T0 showed a significant worsening in two tests of attention and no significant differences of VPSG parameters. No correlation was found between neuropsychological results and VPSG findings or RBD duration. Discussion and Conclusions: The majority of our patients do not show any cognitive deficits at T0 and T1, while isolated cognitive deficits are present in the remaining patients. Attention is the cognitive function which significantly worsened. Our data confirm the previous findings concerning the prevalence, type and the evolution of cognitive deficits in MSA. Regarding the developing of a condition of dementia, our data did not show a clear-cut diagnosis of dementia. We confirm a mild alteration of sleep structure. RBD duration does not correlate with neuropsychological findings.

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Permutation-based stochastic ordering using pairwise comparisons

The topic of this work concerns nonparametric permutation-based methods aiming to find a ranking (stochastic ordering) of a given set of groups (populations), gathering together information from multiple variables under more than one experimental designs. The problem of ranking populations arises in several fields of science from the need of comparing G>2 given groups or treatments when the main goal is to find an order while taking into account several aspects. As it can be imagined, this problem is not only of theoretical interest but it also has a recognised relevance in several fields, such as industrial experiments or behavioural sciences, and this is reflected by the vast literature on the topic, although sometimes the problem is associated with different keywords such as: "stochastic ordering", "ranking", "construction of composite indices" etc., or even "ranking probabilities" outside of the strictly-speaking statistical literature. The properties of the proposed method are empirically evaluated by means of an extensive simulation study, where several aspects of interest are let to vary within a reasonable practical range. These aspects comprise: sample size, number of variables, number of groups, and distribution of noise/error. The flexibility of the approach lies mainly in the several available choices for the test-statistic and in the different types of experimental design that can be analysed. This render the method able to be tailored to the specific problem and the to nature of the data at hand. To perform the analyses an R package called SOUP (Stochastic Ordering Using Permutations) has been written and it is available on CRAN.