Bayes estimators of log-normal means with finite quadratic expected loss

The log-normal distribution is a popular model in biostatistics as in many other fields of statistics. Bayesian inference on the mean and median of the distribution is problematic because, for many popular choices of the prior for variance (on the log-scale) parameter, the posterior distribution has no finite moments, leading to Bayes estimators with infinite expected loss for the most common choices of the loss function. In this paper we propose a generalized inverse Gaussian prior for the variance parameter, that leads to a log-generalized hyperbolic posterior, a distribution for which it is easy to calculate quantiles and moments, provided that they exist. We derive the constraints on the prior parameters that yields finite posterior moments of order r. For the quadratic and relative quadratic loss functions, we investigate the choice of prior parameters leading to Bayes estimators with optimal frequentist mean square error. For the estimation of the lognormal mean we show, using simulation, that the Bayes estimator under quadratic loss compares favorably in terms of frequentist mean square error to known estimators. The theory does not apply only to the mean or median estimation but to all parameters that may be written as the exponential of a linear combination of the distribution's two

Small area estimation of labor productivity for the Italian manufacturing SME cross-classified by region, industry and size

In this paper we propose a new small area estimation methodology aimed at the estimation of Value Added, Labor Cost and related competitiveness indicators for subsets of the population of Italian small and medium sized manufacturing firms classified according to geographical region, industrial sector and firms size. This disaggregation is needed in regional comparisons in order to avoid the confounding effect of sectorial and firm size composition of a region?s manufacturing industry. We use data on the Small and Medium Enterprises sample survey conducted by the Italian National Statistical Institute (year 2009) that provided us this information in the framework of the BLUE-ETS project. The estimates obtained with our method are more reliable than those that would have been obtained using standard survey weighted estimators, and offer therefore the basis for more sound economic analysis. The small area methods that we propose are model based and take into account the peculiarities of business such as the skewness of target variables? distributions. For this reason the model we propose is based on the log-normal distribution. We consider a multivariate model in which two different variables (Value Added and Labor Cost) and jointly modeled in order to exploit their correlation. We adopt a Bayesian approach to inference. The problem of prior specification is considered and two alternative solutions compared. Since we produce estimates for several variables and hundreds of subset of the target population results are difficult to summarize. A general conclusion may be that, for Italy, the North-South divide in productivity levels is more apparent in capital and knowledge intensive sectors, especially when industrial districts are present. The productivity gap tends to grow for larger firms, but there exists several exception to this rule. Many industries traditionally associated to the Italian productive system (furniture, clothing, textile) are characterized by low labor productivity levels: in these cases the productivity gap between Northern and Southern regions is less pronounced or absent. As the paper is mostly about the methodology needed to obtain the estimates, it is relevant not only for those interested in Italian economy. The same ideas may be applied to data from other countries. The relevance of the mentioned indicators is highlighted by the increasing divergences in economic competitiveness among regions within the different EU member states observed in these last years

Type 3 Deiodinase and Consumptive Hypothyroidism: A Common Mechanism for a Rare Disease

The major product secreted by the thyroid is thyroxine (T4), whereas most of the biologically active triiodothyronine (T3) derives from the peripheral conversion of T4 into T3. The deiodinase enzymes are involved in activation and inactivation of thyroid hormones (THs). Type 1 and type 2 deiodinase (D1 and D2) convert T4 into T3 whereas D3 degrades T4 and T3 into inactive metabolites and is thus the major physiological TH inactivator. The hypothalamic-pituitary-thyroid axis maintains circulating TH levels constant, while the deiodinases tissue-specifically regulate intracellular thyroid status by controlling TH action in a precise spatio-temporal fashion. Here we review the data related to the recent identification of a paraneoplastic syndrome called “consumptive hypothyroidism,” which exemplifies how deiodinases alter substantially the concentration of TH in blood. This syndrome results from the aberrant uncontrolled expression of D3 that can induce a severe form of hypothyroidism by inactivating T4 and T3 in defined tumor tissue. This rare TH insufficiency generally affects patients in the first years of life, and has distinct features in terms of diagnosis, treatment, and prognosis with respect to other forms of hypothyroidism

Hierarchical Space-time Modelling of PM10 Pollution in the Emilia-Romagna Region

In questo lavoro si propone un modello gerarchico per lo studio della distribuzione spazio-temporale dell’inquinamento da PM10 in Emilia-Romagna. L’obiettivo è quello di fornire una prima caratterizzazione della variabilità spaziale e temporale delle concentrazioni e di misurarne la dipendenza dalle principali grandezze meteorologiche. I risultati mostrano come la variabilità temporale sia largamente dominante rispetto all’eterogeneità spaziale ed alla variabilità non spiegat

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

In the last two decades, significant research efforts have been dedicated to addressing the issue of spatial confounding in linear regression models. Confounding occurs when the relationship between the covariate and the response variable is influenced by an unmeasured confounder associated with both. This results in biased estimators for the regression coefficients reduced efficiency, and misleading interpretations. This article aims to understand how confounding relates to the parameters of the data generating process. The sampling properties of the regression coefficient estimator are derived as ratios of dependent quadratic forms in Gaussian random variables: this allows us to obtain exact expressions for the marginal bias and variance of the estimator, that were not obtained in previous studies. Moreover, we provide an approximate measure of the marginal bias that gives insights of the main determinants of bias. Applications in the framework of geostatistical and areal data modeling are presented. Particular attention is devoted to the difference between smoothness and variability of random vectors involved in the data generating process. Results indicate that marginal covariance between the covariate and the confounder, along with marginal variability of the covariate, play the most relevant role in determining the magnitude of confounding, as measured by the bias

Poverty and Inequality Mapping Based on a Unit-Level Log-Normal Mixture Model

Estimating poverty and inequality parameters for small sub-populations with adequate precision is often beyond the reach of ordinary survey-weighted methods because of small sample sizes. In small area estimation, survey data and auxiliary information are combined, in most cases using a model. In this paper, motivated by the analysis of EU-SILC data for Italy, we target the estimation of a selection of poverty and inequality indicators, that is mean, headcount ratio and quintile share ratio, adopting a Bayesian approach. We consider unit-level models specified on the log transformation of a skewed variable (equivalized income). We show how a finite mixture of log-normals provides a substantial improvement in the quality of fit with respect to a single log-normal model. Unfortunately, working with these distributions leads, for some estimands, to the non-existence of posterior moments whenever priors for the variance components are not carefully chosen, as our theoretical results show. To allow the use of moments in posterior summaries, we recommend generalized inverse Gaussian distributions as priors for variance components, guiding the choice of hyperparameters

Poverty and inequality mapping based on a unit-level log-normal mixture model

Estimating poverty and inequality parameters for small sub-populations with adequate precision is often beyond the reach of ordinary survey-weighted methods because of small sample sizes. In small area estimation, survey data and auxiliary information are combined, in most cases using a model. In this paper, motivated by the analysis of EU-SILC data for Italy, we target the estimation of a selection of poverty and inequality indicators, that is mean, headcount ratio and quintile share ratio, adopting a Bayesian approach. We consider unit-level models specified on the log transformation of a skewed variable (equivalized income). We show how a finite mixture of log-normals provides a substantial improvement in the quality of fit with respect to a single log-normal model. Unfortunately, working with these distributions leads, for some estimands, to the non-existence of posterior moments whenever priors for the variance components are not carefully chosen, as our theoretical results show. To allow the use of moments in posterior summaries, we recommend generalized inverse Gaussian distributions as priors for variance components, guiding the choice of hyperparameters

Design and Structure Dependent Priors for Scale Parameters in Latent Gaussian Models

Bayesian inference in latent Gaussian models necessitates the specification of prior distributions for scale parameters, which govern the behavior of model components. This task is particularly delicate and many contributions in the literature are devoted to the topic. We show that the scale parameter plays a crucial role in determining the prior variability of the model components, which is influenced by factors such as correlation structure, design matrices, and potential linear constraints. This intricate relationship adds complexity, making it difficult to interpret and compare priors across diverse applications. To tackle this challenge, we propose a novel approach for prior specification based on the theory of distribution of quadratic forms. Our strategy involves the use of design and structure-dependent (DSD) priors, which ensure a consistent interpretation across diverse applications. By introducing a single parameter that governs the prior variability of the linear predictor, we simplify the process of prior specification, making it more manageable and interpretable. We derive analytical expressions for DSD priors on scale parameters and establish conditions that guarantee their existence. To demonstrate the efficacy of our proposed prior elicitation strategy, we conduct a simulation study, examining the sampling properties of the estimators. Additionally, we explore several real data applications to investigate prior sensitivity and the allocation of explained variance among model components

Neurophysiological Findings in Neuronal Ceroid Lipofuscinoses

Neuronal ceroid lipofuscinoses (NCLs) are a heterogeneous group of neurodegenerative diseases, characterized by progressive cerebral atrophy due to lysosomal storage disorder. Common clinical features include epileptic seizures, progressive cognitive and motor decline, and visual failure, which occur over different time courses according to subtypes. During the latest years, many advances have been done in the field of targeted treatments, and in the next future, gene therapies and enzyme replacement treatments may be available for several NCL variants. Considering that there is rapid disease progression in NCLs, an early diagnosis is crucial, and neurophysiological features might have a key role for this purpose. Across the different subtypes of NCLs, electroencephalogram (EEG) is characterized by a progressive deterioration of cerebral activity with slowing of background activity and disappearance of spindles during sleep. Some types of heterogeneous abnormalities, diffuse or focal, prevalent over temporal and occipital regions, are described in many NCL variants. Photoparoxysmal response to low-frequency intermittent photic stimulation (IPS) is a typical EEG finding, mostly described in CLN2, CLN5, and CLN6 diseases. Visual evoked potentials (VEPs) allow to monitor the visual functions, and the lack of response at electroretinogram (ERG) reflects retinal neurodegeneration. Taken together, EEG, VEPs, and ERG may represent essential tools toward an early diagnosis of NCLs

Therapeutic Drug Monitoring of Quinidine in Pediatric Patients with KCNT1 Genetic Variants

Quinidine (QND) is an old antimalarial drug that was used in the early 20th century as an antiarrhythmic agent. Currently, QND is receiving attention for its use in epilepsy of infancy with migrating focal seizures (EIMFS) due to potassium sodium-activated channel subfamily T member 1 (KCNT1) genetic variants. Here, we report the application of Therapeutic Drug Monitoring (TDM) in pediatric patients carrying KCNT1 genetic variants and orally treated with QND for developmental and epileptic encephalopathies (DEE). We measured plasma levels of QND and its metabolite hydroquinidine (H-QND) by using a validated method based on liquid chromatography coupled with mass spectrometry (LC-MS/MS). Three pediatric patients (median age 4.125 years, IQR 2.375-4.125) received increasing doses of QND. Cardiac toxicity was monitored at every dose change. Reduction in seizure frequency ranged from 50 to 90%. Our results show that QND is a promising drug for pediatric patients with DEE due to KCNT1 genetic variants. Although QND blood levels were significantly lower than the therapeutic range as an anti-arrhythmic drug, patients showed a significant improvement in seizure burden. These data underlie the utility of TDM for QND not only to monitor its toxic effects but also to evaluate possible drug-drug interactions