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When Covid-19 arrived in Italy in early 2020, a group of statisticians came together to provide tools to make sense of the unfolding epidemic and to counter misleading media narratives. Here, members of StatGroup-19 reflect on their work to date

In mediational settings, the main focus is on the estimation of the indirect effect of an exposure on an outcome through a third variable called mediator. The traditional maximum likelihood estimation method presents several problems in the estimation of the standard error and the confidence interval of the indirect effect. In this paper, we propose a Bayesian approach to obtain the posterior distribution of the indirect effect through MCMC, in the context of mediational mixed models for longitudinal data. A simulation study shows that our method outperforms the traditional maximum likelihood approach in terms of bias and coverage rates.

We introduce an extended generalised logistic growth model for discrete outcomes, in which spatial and temporal dependence are dealt with the specification of a network structure within an Auto-Regressive approach. A major challenge concerns the specification of the network structure, crucial to consistently estimate the canonical parameters of the generalised logistic curve, e.g. peak time and height. We compared a network based on geographic proximity and one built on historical data of transport exchanges between regions. Parameters are estimated under the Bayesian framework, using Stan probabilistic programming language. The proposed approach is motivated by the analysis of both the first and the second wave of COVID-19 in Italy, i.e. from February 2020 to July 2020 and from July 2020 to December 2020, respectively. We analyse data at the regional level and, interestingly enough, prove that substantial spatial and temporal dependence occurred in both waves, although strong restrictive measures were implemented during the first wave. Accurate predictions are obtained, improving those of the model where independence across regions is assumed.

Background Residential greenness has been associated with health benefits, but its biological mechanism is largely unknown. Investigation of greenness-related DNA methylation profiles can contribute to mechanistic understanding of the health benefits of residential greenness. Objective To identify DNA methylation profiles associated with greenness in the immediate surroundings of the residence. Methods We analyzed genome-wide DNA methylation in 1938 blood samples (982 participants) from the Swiss Cohort Study on Air Pollution and Lung and Heart Diseases in Adults (SAPALDIA). We estimated residential greenness based on normalized difference vegetation index at 30 × 30 m cell (green30) and 500 m buffer (green500) around the residential address. We conducted epigenome-wide association study (EWAS) to identify differentially methylated CpGs and regions, and enrichment tests by comparing to the CpGs that previous EWAS identified as associated with allergy, physical activity, and allostatic load-relevant biomarkers. Results We identified no genome-wide significant CpGs, but 163 and 56 differentially methylated regions for green30 and green500, respectively. Green30-related DNA methylation profiles showed enrichments in allergy, physical activity, and allostatic load, while green500-related methylation was enriched in allergy and allostatic load. Conclusions Residential greenness may have health impacts through allergic sensitization, stress coping, or behavioral changes. Exposure to more proximal greenness may be more health-relevant.

The use of network analysis to investigate social structures has recently seen a rise due to the high availability of data and the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different perspective by considering the whole network as a random variable conveying the effect of an exposure on a response. This point of view represents a classical mediation setting, where the interest lies in estimating the indirect effect, that is, the effect propagated through the mediating variable. We introduce a latent space model mapping the network into a space of smaller dimension by considering the hidden positions of the units in the network. The coordinates of each node are used as mediators in the relationship between the exposure and the response. We further extend mediation analysis in the latent space framework by using Generalised Linear Models instead of linear ones, as previously done in the literature, adopting an approach based on derivatives to obtain the effects of interest. A Bayesian approach allows us to get the entire distribution of the indirect effect, generally unknown, and compute the corresponding highest density interval, which gives accurate and interpretable bounds for the mediated effect. Finally, an application to social interactions among a group of adolescents and their attitude toward substance use is presented.

We compare the expected all-cause mortality with the observed one for different age classes during the pandemic in Lombardy, which was the epicenter of the epidemic in Italy and still is the region most affected by the pandemic. A generalized linear mixed model is introduced to model weekly mortality from 2011 to 2019, taking into account seasonal patterns and year-specific trends. Based on the 2019 year-specific conditional best linear unbiased predictions, a significant excess of mortality is estimated in 2020, leading to approximately 35000 more deaths than expected, mainly arising during the first wave. In 2021, instead, the excess mortality is not significantly different from zero, for the 85+ and 15-64 age classes, and significant reductions with respect to the 2020 estimated excess mortality are estimated for other age classes.

A novel parametric regression model is proposed to fit incidence data typically collected during epidemics. The proposal is motivated by real-time monitoring and short-term forecasting of the main epidemiological indicators within the first outbreak of COVID-19 in Italy. Accurate short-term predictions, including the potential effect of exogenous or external variables are provided. This ensures to accurately predict important characteristics of the epidemic (e.g., peak time and height), allowing for a better allocation of health resources over time. Parameter estimation is carried out in a maximum likelihood framework. All computational details required to reproduce the approach and replicate the results are provided. publishedVersion

The availability of intensive care beds during the COVID‐19 epidemic is crucial to guarantee the best possible treatment to severely affected patients. In this work we show a simple strategy for short‐term prediction of COVID‐19 intensive care unit (ICU) beds, that has proved very effective during the Italian outbreak in February to May 2020. Our approach is based on an optimal ensemble of two simple methods: a generalized linear mixed regression model, which pools information over different areas, and an area‐specific nonstationary integer autoregressive methodology. Optimal weights are estimated using a leave‐last‐out rationale. The approach has been set up and validated during the first epidemic wave in Italy. A report of its performance for predicting ICU occupancy at regional level is included.

Although evidence for the heterogeneity of asthma accumulated, consensus for definitions of asthma phenotypes is still lacking. Obesity may have heterogeneous effects on various asthma phenotypes. We aimed to distinguish asthma phenotypes by latent class analysis and to investigate their associations with different obesity parameters in adults using a population-based Swiss cohort (SAPALDIA). We applied latent class analysis to 959 self-reported asthmatics using information on disease activity, atopy, and age of onset. Associations with obesity were examined by multinomial logistic regression, after adjustments for age, sex, smoking status, educational level, and study centre. Body mass index, percent body fat, waist hip ratio, waist height ratio, and waist circumference were used as obesity measure. Four asthma classes were identified, including persistent multiple symptom-presenting asthma (nÂ=Â122), symptom-presenting asthma (nÂ=Â290), symptom-free atopic asthma (nÂ=Â294), and symptom-free non-atopic asthma (nÂ=Â253). Obesity was positively associated with symptom-presenting asthma classes but not with symptom-free ones. Percent body fat showed the strongest association with the persistent multiple symptom-presenting asthma. We observed heterogeneity of associations with obesity across asthma classes, indicating different asthma aetiologies.

A high body mass (BMI) index has repeatedly been associated with non-atopic asthma, but the biological mechanism linking obesity to asthma is still poorly understood. We aimed to test the hypothesis that inflammation and/or innate immunity plays a role in the obesity-asthma link. DNA methylome was measured in blood samples of 61 non-atopic participants with asthma and 146 non-atopic participants without asthma (non-smokers for at least 10 years) taking part in the Swiss Cohort Study on Air Pollution and Lung and Heart Diseases in Adults (SAPALDIA) study. Modification by DNA methylation of the association of BMI or BMI change over 10 years with adult-onset asthma was examined at each CpG site and differentially methylated region. Pathway enrichment tests were conducted for genes in a priori curated inflammatory pathways and the NLRP3-IL1B-IL17 axis. The latter was chosen on the basis of previous work in mice. Inflammatory pathways including glucocorticoid/PPAR signaling (p = 0.0023), MAPK signaling (p = 0.013), NF-&kappa, B signaling (p = 0.031), and PI3K/AKT signaling (p = 0.031) were enriched for the effect modification of BMI, while NLRP3-IL1B-IL17 axis was enriched for the effect modification of BMI change over 10 years (p = 0.046). DNA methylation measured in peripheral blood is consistent with inflammation as a link between BMI and adult-onset asthma and with the NLRP3-IL1B-IL17 axis as a link between BMI change over 10 years and adult-onset asthma in non-atopic participants.

This working paper has a twofold goal. On one hand, it provides a recap of Linear Mixed Models (LMMs): far from trying to be exhaustive, this first part of the working paper focusses on the derivation of theoretical results on estimation of LMMs that are scattered in the literature or whose mathematical derivation is sometimes missing or too quickly sketched. On the other hand, it discusses various definitions that are available in the literature for the hat-matrix of Linear Mixed Models, showing their limitations and proving their equivalence.

Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios to be estimated also increases, and estimation gets problematic. In this work we propose a non-parametric approach for the maximum likelihood (ML) estimation of a BOLM, wherein penalties to the differences between adjacent row and column effects are applied. Our proposal is then compared to the Goodman and Dale models. Some simulation results as well as analyses of two real data sets are presented and discussed.

We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper–Haseman's Correlated-Binomial distribution, we believe its introduction is useful, both in terms of interpretability and mathematical tractability and in terms of generalizability to the Multinomial case.

Adjusted responses, adjusted fitted values and adjusted residuals are known to play in Generalized Linear Models the role played in Linear Models by observations, fitted values and ordinary residuals. We think this parallelism, which was widely recognized and used in the early literature on Generalized Linear Models, has been somewhat overlooked in more recent presentations. We revise this parallelism, systematizing and proving some results that are either scattered or not satisfactorily spelled out in the literature. In particular, we formally derive the asymptotic dispersion matrix of the (scaled) adjusted residuals, by proving that in Generalized Linear Models the fitted values are asymptotically uncorrelated with the raw residuals and hence deriving the asymptotic dispersion matrix of these latter residuals. Also, we show that an orthogonal decomposition of the error vector between adjusted response and true linear predictor, parallel to the familiar decomposition in Linear Models, holds approximately. Finally, we provide some new perspective, both in Linear and Generalized Linear Models, on adjusted residuals for model comparison, and their relationships with test-statistics used to compare the fit of nested models.

The response of orthotropic rhizome elongation and primary production of Posidonia oceanica to anthropogenic perturbations and potential confounding effects of shoot age were assessed using a Linear Multilevel Model (LMM). This model examined the confounding effect of age by comparing the estimates of impact and variance components obtained by excluding and including Age as an explanatory variable. Age had a negative effect on rhizome elongation and primary production with an annual decrease of 0.6 mm y − 1 and 7 mg dw y − 1 respectively. According to the LMM when age effect was omitted, the differences between disturbed and control locations in rhizome elongation and primary production were 2.62 mm y − 1 and 0.044 g dw y − 1 respectively. These effects were statistically not significant. On the contrary, when age effect was included in the statistical model, impacts became evident for both variables, with significant differences between disturbed and control locations of 5.85 mm y − 1 and 0.081 g dw y − 1 for rhizome elongation and primary production, respectively. Thus, particular attention should be paid to the potential confounding effect of shoots age in analyses of impacts on growth performance of P. oceanica .

Matrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.

Cox (1972) introduced a log-linear representation for the joint distribution of n binary-dependent responses. Altham (1978) derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox's representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.

A log-linear modelling approach is proposed for dealing with polytomous, unordered exposure variables in case-control epidemiological studies with matched pairs. Hypotheses concerning epidemiological parameters are shown to be expressable in terms of log-linear models for the expected frequencies of the case-by-control square concordance table representation of the matched data; relevant maximum likelihood estimates and goodness-of-fit statistics are presented. Possible extensions to account for ordered categorical risk factors and multiple controls are illustrated, and comparisons with previous work are discussed. Finally, the possibility of implementing the proposed method with GLIM is illustrated within the context of a data set already analyzed by other authors.

The statistical analysis of annual growth of Posidonia oceanica is traditionally carried out through Gaussian linear models applied to untransformed, or log-transformed, data. In this paper, we claim that there are good reasons for re-considering this established practice, since real data on annual growth often violate the assumptions of Gaussian linear models, and show that the class of Generalized Linear Models (GLMs) represents a useful alternative for handling such violations. By analyzing Sicily PosiData-1, a real dataset on P. oceanica growth data gathered in the period 2000–2002 along the coasts of Sicily, we find that in the majority of cases Normality is rejected and the effect of age on growth is nonlinear. A GLM with Gamma distribution and identity or log link appears to be a satisfactory choice in most cases. Furthermore, when back-dating techniques are employed, each plant provides a longitudinal set of dependent data, and a proper statistical analysis should take such dependence into account. We show that the class of Generalized Linear Mixed Models (GLMM), an extension of GLM's, provides an effective way to analyze longitudinal P. oceanica growth data. Again, by using examples taken from Sicily PosiData-1, we show that misleading results can be obtained if dependence is ignored and that other techniques, like sub-sampling, are not a good option for overcoming the so-called “pseudo-replications” problem. Copyright © 2010 John Wiley & Sons, Ltd.

In a regression context, the dichotomization of a continuous outcome variable is often motivated by the need to express results in terms of the odds ratio, as a measure of association between the response and one or more risk factors. Starting from the recent work of Moser and Coombs (Odds ratios for a continuous outcome variable without dichotomizing, Statistics in Medicine, 2004, 23, 1843-1860), in this article we explore in a mixed model framework the possibility of obtaining odds ratio estimates from a regression linear model without the need of dichotomizing the response variable. It is shown that the odds ratio estimators derived from a linear mixed model outperform those from a binomial generalized linear mixed model, especially when the data exhibit high levels of heterogeneity.

The identity of the Rao score and PearsonX 2 statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results.

The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).

Composite sampling is emerging as a cost efficient sampling method in environmental studies. Treating the process of sample selection (i.e., identification of sampling units to be included in the sample) as distinct from that of sample quantification (i.e., making measurements on the selected sample units), it is possible to achieve two conflicting goals simultaneously. On one hand, one can select a large number of sample units to ensure the desired sample support, so that the results of the analysis will be sufficiently reliable. On the other hand, by compositing several individual samples into fewer composites, one reduces the number of analytical measurements so that a study can be carried out without affecting the available financial resources. In this paper, we review some prominent composite sample techniques to design and analyze composite sample data, with special emphasis on environmental applications.

This paper describes an analysis of the quality of hospital discharge data stored in an Italian regional registry.Although limited in scope, this analysis sheds some light on the level of quality that users can expect in official health data and describes some factors which can influence such quality. Attention focuses on the accuracy with which official administrators code Diseases of Circulatory System (DCS) in a specified health district, using the discharge diagnosis formulated on the case-notes.Investigation of the data, a random sample of 993 medical records, shows a disturbing level of inaccuracy in the assignment of the primary diagnosis to the (DCS) group and sub-groups, especially when compared with other international experiences.Two factors, namely the type of hospital where official administrators routinely collect the data and the age of the in-patients, are found to significantly influence such inaccuracy.Explanations of these findings are suggested and proposals for the improved accuracy of hospital discharge data are presented.

The use of network analysis for the investigation of social structures has recently seen a rise, due both to the high availability of data and to the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different point of view, by considering the whole network as a random variable conveying the effect of an exposure on a response. This point of view represents a classical mediation setting, where the interest lies in the estimation of the indirect effect, that is, the effect propagated through the mediating variable. We introduce a latent space model mapping the network into a space of smaller dimension by considering the hidden positions of the units in the network. Furthermore, the mediation analysis is extended by using generalised linear models. A Bayesian approach allows to obtain the entire distribution of the indirect effect, generally unknown, and to compute highest density intervals, which give accurate and interpretable bounds for the mediated effect. Finally, an application to social interactions among a group of adolescents and their attitude toward smoking is presented.

We compare the expected all-cause mortality with the observed one for different age classes during the pandemic in Lombardy, which was the epicenter of the epidemic in Italy. The first case in Italy was found in Lombardy in early 2020, and the first wave was mainly centered in Lombardy. The other three waves, in Autumn 2020, March 2021 and Summer 2021 are also characterized by a high number of cases in absolute terms. A generalized linear mixed model is introduced to model weekly mortality from 2011 to 2019, taking into account seasonal patterns and year-specific trends. Based on the 2019 year-specific conditional best linear unbiased predictions, a significant excess of mortality is estimated in 2020, leading to approximately 35000 more deaths than expected, mainly arising during the first wave. In 2021, instead, the excess mortality is not significantly different from zero, for the 85+ and 15–64 age classes, and significant reductions with respect to the 2020 estimated excess mortality are estimated for other age classes. Supplementary Information The online version contains supplementary material available at 10.1007/s40520-021-02060-1.

Posidonia oceanica represents the key species of the most important ecosystem in subtidal habitats of the Mediterranean Sea. Being sensitive to changes in the environment, it is considered a crucial indicator of the quality of coastal marine waters. A peculiarity of P. oceanica is the presence of reiterative modules characterizing its growth, which lend themselves to back-dating techniques, allowing for the reconstruction of past history of growth variables (annual rhizome elongation and diameter, primary production, etc.). Such back-dating techniques provide, for each sampled shoot, a longitudinal series of multivariate data; this is an instance of what Hurlbert (1984) in a seminal paper defined as “pseudo-replications”, for which it becomes crucial to take into account the possible dependence of the data. A common solution to the “pseudo-replications” in the ecological literature is represented by “pseudo-replications”: given repeated measurements on the same unit, only a random sub-sample of such measurements is analyzed, in order to attenuate correlation and obtain approximately independently distributed observations, to which standard statistical methods can be applied. In its most extreme version, only one measurement is randomly drawn for each unit, i.e. the sub-sampling size is one. If on one hand sub-sampling attenuates correlation, on the other it implies a loss of information (due to the reduction of the total sample size) and then requires a higher number of sampling units to ensure a specified level of efficiency and power. In the talk, we contrast sub-sampling with the alternative approach of handling dependence directly in the modelling stage, using the class of Generalized Linear Mixed Models. We show that this approach permits remarkable gains of precision in estimation and power in testing, without requiring the increase in sample sizes involved in sub-sampling, and thus avoiding the practice of over-sampling, which has a negative impact on aquatic ecosystems.