Intrinsic dimension as a multi-scale summary statistics in network modeling.

Complex networks are powerful mathematical tools for modelling and understanding the behaviour of highly interconnected systems. However, existing methods for analyzing these networks focus on local properties (e.g. degree distribution, clustering coefficient) or global properties (e.g. diameter, modularity) and fail to characterize the network structure across multiple scales. In this paper, we introduce a rigorous method for calculating the intrinsic dimension of unweighted networks. The intrinsic dimension is a feature that describes the network structure at all scales, from local to global. We propose using this measure as a summary statistic within an Approximate Bayesian Computation framework to infer the parameters of flexible and multi-purpose mechanistic models that generate complex networks. Furthermore, we present a new mechanistic model that can reproduce the intrinsic dimension of networks with large diameters, a task that has been challenging for existing models.

Assessing the heterogeneity of the impact of COVID-19 incidence on all-cause excess mortality among healthcare districts in Lombardy, Italy, to evaluate the local response to the pandemic: an ecological study.

OBJECTIVES: The fragmentation of the response to the COVID-19 pandemic at national, regional and local levels is a possible source of variability in the impact of the pandemic on society. This study aims to assess how much of this variability affected the burden of COVID-19, measured in terms of all-cause 2020 excess mortality. DESIGN: Ecological retrospective study. SETTING: Lombardy region of Italy, 2015-2020. OUTCOME MEASURES: We evaluated the relationship between the intensity of the epidemics and excess mortality, assessing the heterogeneity of this relationship across the 91 districts after adjusting for relevant confounders. RESULTS: The epidemic intensity was quantified as the COVID-19 hospitalisations per 1000 inhabitants. Five confounders were identified through a directed acyclic graph: age distribution, population density, pro-capita gross domestic product, restriction policy and population mobility.Analyses were based on a negative binomial regression model with district-specific random effects. We found a strong, positive association between COVID-19 hospitalisations and 2020 excess mortality (p<0.001), estimating that an increase of one hospitalised COVID-19 patient per 1000 inhabitants resulted in a 15.5% increase in excess mortality. After adjusting for confounders, no district differed in terms of COVID-19-unrelated excess mortality from the average district. Minimal heterogeneity emerged in the district-specific relationships between COVID-19 hospitalisations and excess mortality (6 confidence intervals out of 91 did not cover the null value). CONCLUSIONS: The homogeneous effect of the COVID-19 spread on the excess mortality in the Lombardy districts suggests that, despite the unprecedented conditions, the pandemic reactions did not result in health disparities in the region.

A global perspective on the intrinsic dimensionality of COVID-19 data.

We develop a novel global perspective of the complexity of the relationships between three COVID-19 datasets, the standardised per-capita growth rate of COVID-19 cases and deaths, and the Oxford Coronavirus Government Response Tracker COVID-19 Stringency Index (CSI) which is a measure describing a country's stringency of lockdown policies. We use a state-of-the-art heterogeneous intrinsic dimension estimator implemented as a Bayesian mixture model, called Hidalgo. Our findings suggest that these highly popular COVID-19 statistics may project onto two low-dimensional manifolds without significant information loss, suggesting that COVID-19 data dynamics are generated from a latent mechanism characterised by a few important variables. The low dimensionality imply a strong dependency among the standardised growth rates of cases and deaths per capita and the CSI for countries over 2020-2021. Importantly, we identify spatial autocorrelation in the intrinsic dimension distribution worldwide. The results show how high-income countries are more prone to lie on low-dimensional manifolds, likely arising from aging populations, comorbidities, and increased per capita mortality burden from COVID-19. Finally, the temporal stratification of the dataset allows the examination of the intrinsic dimension at a more granular level throughout the pandemic.

A Common Atoms Model for the Bayesian Nonparametric Analysis of Nested Data.

The use of large datasets for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested common atoms model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units are expected to differ only over a small fraction of the observations sampled from each unit. The proposed CAM allows a two-layered clustering at the distributional and observational level and is amenable to scalable posterior inference through the use of a computationally efficient nested slice sampler algorithm. We further discuss how to extend the proposed modeling framework to handle discrete measurements, and we conduct posterior inference on a real microbiome dataset from a diet swap study to investigate how the alterations in intestinal microbiota composition are associated with different eating habits. We further investigate the performance of our model in capturing true distributional structures in the population by means of a simulation study.

Multiple hypothesis screening using mixtures of non-local distributions with applications to genomic studies.

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian false discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.

Radiomics and machine learning applied to STIR sequence for prediction of quantitative parameters in facioscapulohumeral disease.

Purpose: Quantitative Muscle MRI (qMRI) is a valuable and non-invasive tool to assess disease involvement and progression in neuromuscular disorders being able to detect even subtle changes in muscle pathology. The aim of this study is to evaluate the feasibility of using a conventional short-tau inversion recovery (STIR) sequence to predict fat fraction (FF) and water T2 (wT2) in skeletal muscle introducing a radiomic workflow with standardized feature extraction combined with machine learning algorithms. Methods: Twenty-five patients with facioscapulohumeral muscular dystrophy (FSHD) were scanned at calf level using conventional STIR sequence and qMRI techniques. We applied and compared three different radiomics workflows (WF1, WF2, WF3), combined with seven Machine Learning regression algorithms (linear, ridge and lasso regression, tree, random forest, k-nearest neighbor and support vector machine), on conventional STIR images to predict FF and wT2 for six calf muscles. Results: The combination of WF3 and K-nearest neighbor resulted to be the best predictor model of qMRI parameters with a mean absolute error about ± 5 pp for FF and ± 1.8 ms for wT2. Conclusion: This pilot study demonstrated the possibility to predict qMRI parameters in a cohort of FSHD subjects starting from conventional STIR sequence.

The generalized ratios intrinsic dimension estimator.

Modern datasets are characterized by numerous features related by complex dependency structures. To deal with these data, dimensionality reduction techniques are essential. Many of these techniques rely on the concept of intrinsic dimension (id), a measure of the complexity of the dataset. However, the estimation of this quantity is not trivial: often, the id depends rather dramatically on the scale of the distances among data points. At short distances, the id can be grossly overestimated due to the presence of noise, becoming smaller and approximately scale-independent only at large distances. An immediate approach to examining the scale dependence consists in decimating the dataset, which unavoidably induces non-negligible statistical errors at large scale. This article introduces a novel statistical method, Gride, that allows estimating the id as an explicit function of the scale without performing any decimation. Our approach is based on rigorous distributional results that enable the quantification of uncertainty of the estimates. Moreover, our method is simple and computationally efficient since it relies only on the distances among data points. Through simulation studies, we show that Gride is asymptotically unbiased, provides comparable estimates to other state-of-the-art methods, and is more robust to short-scale noise than other likelihood-based approaches.

Scalable Approximate Bayesian Computation for Growing Network Models via Extrapolated and Sampled Summaries.

Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate model, but because the sizes of the observed and simulated datasets usually need to match, this can be computationally expensive. Additionally, since ABC inference is based on comparisons of summary statistics computed on the observed and simulated data, using computationally expensive summary statistics can lead to further losses in efficiency. ABC has recently been applied to the family of mechanistic network models, an area that has traditionally lacked tools for inference and model choice. Mechanistic models of network growth repeatedly add nodes to a network until it reaches the size of the observed network, which may be of the order of millions of nodes. With ABC, this process can quickly become computationally prohibitive due to the resource intensive nature of network simulations and evaluation of summary statistics. We propose two methodological developments to enable the use of ABC for inference in models for large growing networks. First, to save time needed for forward simulating model realizations, we propose a procedure to extrapolate (via both least squares and Gaussian processes) summary statistics from small to large networks. Second, to reduce computation time for evaluating summary statistics, we use sample-based rather than census-based summary statistics. We show that the ABC posterior obtained through this approach, which adds two additional layers of approximation to the standard ABC, is similar to a classic ABC posterior. Although we deal with growing network models, both extrapolated summaries and sampled summaries are expected to be relevant in other ABC settings where the data are generated incrementally.

Framework for assessing and easing global COVID-19 travel restrictions.

During the COVID-19 pandemic, many countries implemented international travel restrictions that aimed to contain viral spread while still allowing necessary cross-border travel for social and economic reasons. The relative effectiveness of these approaches for controlling the pandemic has gone largely unstudied. Here we developed a flexible network meta-population model to compare the effectiveness of international travel policies, with a focus on evaluating the benefit of policy coordination. Because country-level epidemiological parameters are unknown, they need to be estimated from data; we accomplished this using approximate Bayesian computation, given the nature of our complex stochastic disease transmission model. Based on simulation and theoretical insights we find that, under our proposed policy, international airline travel may resume up to 58% of the pre-pandemic level with pandemic control comparable to that of a complete shutdown of all airline travel. Our results demonstrate that global coordination is necessary to allow for maximum travel with minimum effect on viral spread.

Personalized pathology test for Cardio-vascular disease: Approximate Bayesian computation with discriminative summary statistics learning.

Cardio/cerebrovascular diseases (CVD) have become one of the major health issue in our societies. But recent studies show that the present pathology tests to detect CVD are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions and are incapable to consider inter-individual variability. Here we propose a stochastic platelet deposition model and an inferential scheme to estimate the biologically meaningful model parameters using approximate Bayesian computation with a summary statistic that maximally discriminates between different types of patients. Inferred parameters from data collected on healthy volunteers and different patient types help us to identify specific biological parameters and hence biological reasoning behind the dysfunction for each type of patients. This work opens up an unprecedented opportunity of personalized pathology test for CVD detection and medical treatment.

A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification.

For the analysis of COVID-19 pandemic data, we propose Bayesian multinomial and Dirichlet-multinomial autoregressive models for time-series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number Rt . All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet-multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

Policies for Easing COVID-19 Pandemic Travel Restrictions.

During the COVID-19 pandemic, many countries implemented international travel restrictions that aimed to contain viral spread while still allowing necessary cross-border travel for social and economic reasons. The relative effectiveness of these approaches for controlling the pandemic has gone largely unstudied. Here we developed a flexible network meta-population model to compare the effectiveness of international travel policies, with a focus on evaluating the benefit of policy coordination. Because country-level epidemiological parameters are unknown, they need to be estimated from data; we accomplished this using approximate Bayesian computation, given the nature of our complex stochastic disease transmission model. Based on simulation and theoretical insights we find that, under our proposed policy, international airline travel may resume up to 58% of the pre-pandemic level with pandemic control comparable to that of a complete shutdown of all airline travel. Our results demonstrate that global coordination is necessary to allow for maximum travel with minimum effect on viral spread.

Hindsight is 2020 vision: a characterisation of the global response to the COVID-19 pandemic.

BACKGROUND: The global impact of COVID-19 and the country-specific responses to the pandemic provide an unparalleled opportunity to learn about different patterns of the outbreak and interventions. We model the global pattern of reported COVID-19 cases during the primary response period, with the aim of learning from the past to prepare for the future. METHODS: Using Bayesian methods, we analyse the response to the COVID-19 outbreak for 158 countries for the period 22 January to 9 June 2020. This encompasses the period in which many countries imposed a variety of response measures and initial relaxation strategies. Instead of modelling specific intervention types and timings for each country explicitly, we adopt a stochastic epidemiological model including a feedback mechanism on virus transmission to capture complex nonlinear dynamics arising from continuous changes in community behaviour in response to rising case numbers. We analyse the overall effect of interventions and community responses across diverse regions. This approach mitigates explicit consideration of issues such as period of infectivity and public adherence to government restrictions. RESULTS: Countries with the largest cumulative case tallies are characterised by a delayed response, whereas countries that avoid substantial community transmission during the period of study responded quickly. Countries that recovered rapidly also have a higher case identification rate and small numbers of undocumented community transmission at the early stages of the outbreak. We also demonstrate that uncertainty in numbers of undocumented infections dramatically impacts the risk of multiple waves. Our approach is also effective at pre-empting potential flare-ups. CONCLUSIONS: We demonstrate the utility of modelling to interpret community behaviour in the early epidemic stages. Two lessons learnt that are important for the future are: i) countries that imposed strict containment measures early in the epidemic fared better with respect to numbers of reported cases; and ii) broader testing is required early in the epidemic to understand the magnitude of undocumented infections and recover rapidly. We conclude that clear patterns of containment are essential prior to relaxation of restrictions and show that modelling can provide insights to this end.

Data segmentation based on the local intrinsic dimension.

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded versus unfolded configurations in a protein molecular dynamics trajectory, active versus non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

Spatio-temporal prediction model of out-of-hospital cardiac arrest: Designation of medical priorities and estimation of human resources requirement.

AIMS: To determine the out-of-hospital cardiac arrest (OHCA) rates and occurrences at municipality level through a novel statistical model accounting for temporal and spatial heterogeneity, space-time interactions and demographic features. We also aimed to predict OHCAs rates and number at municipality level for the upcoming years estimating the related resources requirement. METHODS: All the consecutive OHCAs of presumed cardiac origin occurred from 2005 until 2018 in Canton Ticino region were included. We implemented an Integrated Nested Laplace Approximation statistical method for estimation and prediction of municipality OHCA rates, number of events and related uncertainties, using age and sex municipality compositions. Comparisons between predicted and real OHCA maps validated our model, whilst comparisons between estimated OHCA rates in different yeas and municipalities identified significantly different OHCA rates over space and time. Longer-time predicted OHCA maps provided Bayesian predictions of OHCA coverages in varying stressful conditions. RESULTS: 2344 OHCAs were analyzed. OHCA incidence either progressively reduced or continuously increased over time in 6.8% of municipalities despite an overall stable spatio-temporal distribution of OHCAs. The predicted number of OHCAs accounts for 89% (2017) and 90% (2018) of the yearly variability of observed OHCAs with prediction error ≤1OHCA for each year in most municipalities. An increase in OHCAs number with a decline in the Automatic External Defibrillator availability per OHCA at region was estimated. CONCLUSIONS: Our method enables prediction of OHCA risk at municipality level with high accuracy, providing a novel approach to estimate resource allocation and anticipate gaps in demand in upcoming years.

Flexible model selection for mechanistic network models.

Network models are applied across many domains where data can be represented as a network. Two prominent paradigms for modelling networks are statistical models (probabilistic models for the observed network) and mechanistic models (models for network growth and/or evolution). Mechanistic models are better suited for incorporating domain knowledge, to study effects of interventions (such as changes to specific mechanisms) and to forward simulate, but they typically have intractable likelihoods. As such, and in a stark contrast to statistical models, there is a relative dearth of research on model selection for such models despite the otherwise large body of extant work. In this article, we propose a simulator-based procedure for mechanistic network model selection that borrows aspects from Approximate Bayesian Computation along with a means to quantify the uncertainty in the selected model. To select the most suitable network model, we consider and assess the performance of several learning algorithms, most notably the so-called Super Learner, which makes our framework less sensitive to the choice of a particular learning algorithm. Our approach takes advantage of the ease to forward simulate from mechanistic network models to circumvent their intractable likelihoods. The overall process is flexible and widely applicable. Our simulation results demonstrate the approach's ability to accurately discriminate between competing mechanistic models. Finally, we showcase our approach with a protein-protein interaction network model from the literature for yeast (Saccharomyces cerevisiae).

Estimating a novel stochastic model for within-field disease dynamics of banana bunchy top virus via approximate Bayesian computation.

The Banana Bunchy Top Virus (BBTV) is one of the most economically important vector-borne banana diseases throughout the Asia-Pacific Basin and presents a significant challenge to the agricultural sector. Current models of BBTV are largely deterministic, limited by an incomplete understanding of interactions in complex natural systems, and the appropriate identification of parameters. A stochastic network-based Susceptible-Infected-Susceptible model has been created which simulates the spread of BBTV across the subsections of a banana plantation, parameterising nodal recovery, neighbouring and distant infectivity across summer and winter. Findings from posterior results achieved through Markov Chain Monte Carlo approach to approximate Bayesian computation suggest seasonality in all parameters, which are influenced by correlated changes in inspection accuracy, temperatures and aphid activity. This paper demonstrates how the model may be used for monitoring and forecasting of various disease management strategies to support policy-level decision making.

A Bayesian spatiotemporal statistical analysis of out-of-hospital cardiac arrests.

We propose a Bayesian spatiotemporal statistical model for predicting out-of-hospital cardiac arrests (OHCAs). Risk maps for Ticino, adjusted for demographic covariates, are built for explaining and forecasting the spatial distribution of OHCAs and their temporal dynamics. The occurrence intensity of the OHCA event in each area of interest, and the cardiac risk-based clustering of municipalities are efficiently estimated, through a statistical model that decomposes OHCA intensity into overall intensity, demographic fixed effects, spatially structured and unstructured random effects, time polynomial dependence, and spatiotemporal random effect. In the studied geography, time evolution and dependence on demographic features are robust over different categories of OHCAs, but with variability in their spatial and spatiotemporal structure. Two main OHCA incidence-based clusters of municipalities are identified.

Scientific output scales with resources. A comparison of US and European universities.

By using a comprehensive dataset of US and European universities, we demonstrate super-linear scaling between university revenues and their volume of publications and (field-normalized) citations. We show that this relationship holds both in the US and in Europe. In terms of resources, our data show that three characteristics differentiate the US system: (1) a significantly higher level of resources for the entire system, (2) a clearer distinction between education-oriented institutions and doctoral universities and (3) a higher concentration of resources among doctoral universities. Accordingly, a group of US universities receive a much larger amount of resources and have a far higher number of publications and citations when compared to their European counterparts. These results demonstrate empirically that international rankings are by and large richness measures and, therefore, can be interpreted only by introducing a measure of resources. Implications for public policies and institutional evaluation are finally discussed.

Evaluating health facility access using Bayesian spatial models and location analysis methods.

BACKGROUND: Floating catchment methods have recently been applied to identify priority regions for Automated External Defibrillator (AED) deployment, to aid in improving Out of Hospital Cardiac Arrest (OHCA) survival. This approach models access as a supply-to-demand ratio for each area, targeting areas with high demand and low supply for AED placement. These methods incorporate spatial covariates on OHCA occurrence, but do not provide precise AED locations, which are critical to the initial intent of such location analysis research. Exact AED locations can be determined using optimisation methods, but they do not incorporate known spatial risk factors for OHCA, such as income and demographics. Combining these two approaches would evaluate AED placement impact, describe drivers of OHCA occurrence, and identify areas that may not be appropriately covered by AED placement strategies. There are two aims in this paper. First, to develop geospatial models of OHCA that account for and display uncertainty. Second, to evaluate the AED placement methods using geospatial models of accessibility. We first identify communities with the greatest gap between demand and supply for allocating AEDs. We then use this information to evaluate models for precise AED location deployment. METHODS: Case study data set consisted of 2802 OHCA events and 719 AEDs. Spatial OHCA occurrence was described using a geospatial model, with possible spatial correlation accommodated by introducing a conditional autoregressive (CAR) prior on the municipality-level spatial random effect. This model was fit with Integrated Nested Laplacian Approximation (INLA), using covariates for population density, proportion male, proportion over 65 years, financial strength, and the proportion of land used for transport, commercial, buildings, recreation, and urban areas. Optimisation methods for AED locations were applied to find the top 100 AED placement locations. AED access was calculated for current access and 100 AED placements. Priority rankings were then given for each area based on their access score and predicted number of OHCA events. RESULTS: Of the 2802 OHCA events, 64.28% occurred in rural areas, and 35.72% in urban areas. Additionally, over 70% of individuals were aged over 65. Supply of AEDs was less than demand in most areas. Priority regions for AED placement were identified, and access scores were evaluated for AED placement methodology by ranking the access scores and the predicted OHCA count. AED placement methodology placed AEDs in areas with the highest priority, but placed more AEDs in areas with more predicted OHCA events in each grid cell. CONCLUSION: The methods in this paper incorporate OHCA spatial risk factors and OHCA coverage to identify spatial regions most in need of resources. These methods can be used to help understand how AED allocation methods affect OHCA accessibility, which is of significant practical value for communities when deciding AED placements.