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.

Spatial mechanisms for modelling the human ankle passive motion

Knowledge on how ligaments and articular surfaces guide passive motion at the human ankle joint complex is fundamental for the design of relevant surgical treatments. The dissertation presents a possible improvement of this knowledge by a new kinematic model of the tibiotalar articulation. In this dissertation two one-DOF spatial equivalent mechanisms are presented for the simulation of the passive motion of the human ankle joint: the 5-5 fully parallel mechanism and the fully parallel spherical wrist mechanism. These mechanisms are based on the main anatomical structures of the ankle joint, namely the talus/calcaneus and the tibio/fibula bones at their interface, and the TiCaL and CaFiL ligaments. In order to show the accuracy of the models and the efficiency of the proposed procedure, these mechanisms are synthesized from experimental data and the results are compared with those obtained both during experimental sessions and with data published in the literature. Experimental results proved the efficiency of the proposed new mechanisms to simulate the ankle passive motion and, at the same time, the potentiality of the mechanism to replicate the ankle’s main anatomical structures quite well. The new mechanisms represent a powerful tool for both pre-operation planning and new prosthesis design.

Spatial and temporal variability and ecological processes in the epibenthic assemblages of the northern Adriatic Sea

Several coralligenous reefs occur in the soft bottoms of the northern Adriatic continental shelf. Mediterranean coralligenous habitats are characterised by high species diversity and are intrinsically valuable for their biological diversity and for the ecological processes they support. The conservation and management of these habitats require quantifying spatial and temporal variability of their benthic assemblages. This PhD thesis aims to give a relevant contribution to the knowledge of the structure and dynamics of the epibenthic assemblages on the coralligenous subtidal reefs occurring in the northern Adriatic Sea. The epibenthic assemblages showed a spatial variation larger compared to temporal changes, with a temporal persistence of reef-forming organisms. Assemblages spatial heterogeneity has been related to morphological features and geographical location of the reefs, together with variation in the hydrological conditions. Manipulative experiments help to understand the ecological processes structuring the benthic assemblages and maintaining their diversity. In this regards a short and long term experiment on colonization patterns of artificial substrata over a 3-year period has been performed in three reefs, corresponding to the three main types of assemblages detected in the previous study. The first colonisers, largely depending by the different larval supply, played a key role in determining the heterogeneity of the assemblages in the early stage of colonisation. Lateral invasion, from the surrounding assemblages, was the driver in structuring the mature assemblages. These complex colonisation dynamics explained the high heterogeneity of the assemblages dwelling on the northern Adriatic biogenic reefs. The buildup of these coralligenous reefs mainly depends by the bioconstruction-erosion processes that has been analysed through a field experiment. Bioconstruction, largely due to serpulid polychaetes, prevailed on erosion processes and occurred at similar rates in all sites. Similarly, the total energy contents in the benthic communities do not differ among sites, despite being provided by different species. Therefore, we can hypothesise that both bioconstruction processes and energetic storage may be limited by the availability of resources. Finally the major contribution of the zoobenthos compared to the phytobenthos to the total energetic content of assemblages suggests that the energy flow in these benthic habitats is primarily supported by planktonic food web trough the filter feeding invertebrates.

Modelling spillover effects in spatial stochastic frontier analysis

In the last two decades, authors have begun to expand classical stochastic frontier (SF) models in order to include also some spatial components. Indeed, firms tend to concentrate in clusters, taking advantage of positive agglomeration externalities due to cooperation, shared ideas and emulation, resulting in increased productivity levels. Until now scholars have introduced spatial dependence into SF models following two different paths: evaluating global and local spatial spillover effects related to the frontier or considering spatial cross-sectional correlation in the inefficiency and/or in the error term. In this thesis, we extend the current literature on spatial SF models introducing two novel specifications for panel data. First, besides considering productivity and input spillovers, we introduce the possibility to evaluate the specific spatial effects arising from each inefficiency determinant through their spatial lags aiming to capture also knowledge spillovers. Second, we develop a very comprehensive spatial SF model that includes both frontier and error-based spillovers in order to consider four different sources of spatial dependence (i.e. productivity and input spillovers related to the frontier function and behavioural and environmental correlation associated with the two error terms). Finally, we test the finite sample properties of the two proposed spatial SF models through simulations, and we provide two empirical applications to the Italian accommodation and agricultural sectors. From a practical perspective, policymakers, based on results from these models, can rely on precise, detailed and distinct insights on the spillover effects affecting the productive performance of neighbouring spatial units obtaining interesting and relevant suggestions for policy decisions.

Moving toward stock units identification based on spatial population structure of marine species in the Mediterranean Sea and adjacent waters through multidisciplinary and holistic approaches for the sustainability of fisheries resources

Investigating stock identity of marine species in a multidisciplinary holistic approach can reveal patterns of complex spatial population structure and signatures of potential local adaptation. The population structure of common sole (Solea solea) in the Mediterranean Sea was delineated using genomic and otolith data, including single nucleotide polymorphisms (SNPs) markers and otolith data. SNPs were correlated with environmental and spatial variables to evaluate the impact of these features on the actual genetic population structure. Integrated holistic approach was applied to combine the tracers with different spatio-temporal scales. SNPs data was also used to illustrate the population structure of European hake (Merluccius merluccius) within the Alboran Sea, extending into the neighboring Mediterranean Sea and Atlantic Ocean. The aim was to identify patterns of neutral and potential adaptive genetic variation by applying seascape genomic framework. Results from both genetic and otolith data suggested significant divergence among putative populations of common sole, confirming a clear separation between Western, Adriatic Sea and Eastern Mediterranean Sea. Evidence of fine-scale population structure in the Western Mediterranean Sea was observed at outlier loci level and in the Adriatic. Our study not only indicates that separation among Mediterranean sole population is led primarily by neutral processes, but it also suggests the presence of local adaptation influenced by environmental and spatial factors. The holistic approach by considering the spatio-temporal scales of variation confirmed that the same pattern of separation between these geographical sites is currently occurring and has occurred for many generations. Results showed the occurrence of population structure in Merluccius merluccius by detecting westward–eastward differentiation among populations and distinct subgroups at a fine geographical scale using outlier SNPs. These results enhance the knowledge of the population structure of commercially relevant species to support the application of spatial stock assessment models, including a redefinition of fishery management units.