Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures oft $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

Identifying outbreaks in sewer networks: An adaptive sampling scheme under network's uncertainty

Motivated by the implementation of a SARS-Cov-2 sewer surveillance system in Chile during the COVID-19 pandemic, we propose a set of mathematical and algorithmic tools that aim to identify the location of an outbreak under uncertainty in the network structure. Given an upper bound on the number of samples we can take on any given day, our framework allows us to detect an unknown infected node by adaptively sampling different network nodes on different days. Crucially, despite the uncertainty of the network, the method allows univocal detection of the infected node, albeit at an extra cost in time. This framework relies on a specific and well-chosen strategy that defines new nodes to test sequentially, with a heuristic that balances the granularity of the information obtained from the samples. We extensively tested our model in real and synthetic networks, showing that the uncertainty of the underlying graph only incurs a limited increase in the number of iterations, indicating that the methodology is applicable in practice.

A Bayesian approach for mixed effects state-space models under skewness and heavy tails

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.

Electrocoagulation treatment of furniture industry wastewater

Electrocoagulation was investigated as a method for treating wastewater containing polyvinyl acetate (PVAc) from the furniture industry. The study evaluated the evolution of iron concentration and passivation during the treatment process. Laboratory-scale experiments were conducted to evaluate the effects of inter-electrode distance (d), current density, and mode on treatment performance. Three values of d (0.3, 0.6, and 0.9 cm) were studied and found to have no significant effect on performance. However, lower d values resulted in reduced energy consumption due to a decrease in applied voltage. Three values of current density (132, 158, and 197 A m^-2) were studied under two current modes, Direct Current (DC) and Alternating Pulsed Current (APC). The best treatment performance for DC occurred under 158 A m^-2 (the treated wastewater was characterized by pH = 4.59 ± 0.02, conductivity = 996 ± 21 μS cm^-1, COD = 1940 ± 55 mgO₂ L^-1, TSS = 105 ± 14 mg L^-1, and Fe = 50.39 ± 1.87 mgFe L^-1). For APC, the best performance was achieved under 197 A m^-2 (the treated wastewater was characterized by pH = 6.33 ± 0.06, conductivity = 988 ± 17 μS cm^-1, COD = 1942 ± 312 mgO₂ L^-1, TSS = 199 ± 55 mg L^-1, and Fe = 44.68 ± 4.60 mgFe L^-1). Despite the promising results, treatment performance was insufficient to meet the legal requirements for water discharge. APC was found to be a more economically viable approach, as it reduced anode wear, electrode passivation, and energy consumption. The quantity of iron released increased with d, and the effect of current density on iron concentration was found to be non-linear. However, applying APC reduced the iron content for all tested current densities. The tests showed that EC was effective in removing chemical oxygen demand (COD) and total suspended solids (TSS), achieving removal efficiencies above 92% and 99%, respectively. However, the studied treatment procedures were insufficient to meet the EU legal requirements for water discharge. Therefore, the obtained wastewater should undergo a post-treatment process.

Extending multivariate Student's- t $$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's t $$ t $$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Bayesian analysis of survival data with missing censoring indicators

In some large clinical studies, it may be impractical to perform the physical examination to every subject at his/her last monitoring time in order to diagnose the occurrence of the event of interest. This gives rise to survival data with missing censoring indicators where the probability of missing may depend on time of last monitoring and some covariates. We present a fully Bayesian semi-parametric method for such survival data to estimate regression parameters of the proportional hazards model of Cox. Theoretical investigation and simulation studies show that our method performs better than competing methods. We apply the proposed method to analyze the survival data with missing censoring indicators from the Orofacial Pain: Prospective Evaluation and Risk Assessment study.

Antihelminthic action of the Anethum graveolens essential oil on Haemonchus contortus eggs and larvae

Gastrointestinal nematodes are responsible for great economic losses in sheep raising, and their control has long been carried out almost exclusively by the administration of anthelmintics, which have led to serious resistance problems. In the search for alternative control measures, phytotherapic research is highlighted. The aim of this study was to evaluate the action of Anethum graveolens (dill) essential oil on different stages of Haemonchus contortus life cycle, as well its cytotoxicity MDBK (Madin-Darby bovine kidney) cells. H. contortus larvae and eggs were obtained from infected sheep feces, and essential oil extracted from plant seeds through the Clevenger apparatus. 9.4, 4.7, 2.35, 1.17. 0.58 and 0.29 mg/mL concentrations were evaluated. The Egg Hatch Inhibition (HI), Larval Development Inhibition (LDI) and Larval Migration Inhibition (LMI) techniques were used. Thybendazole 0.025 mg/mL in HI and Levamisole 0.02 mg/mL in the LDI and LMI tests were used as positive controls, while distilled water and a Tween 80 solution were used as positive negative controls. The inhibition results obtained for the highest oil concentration were: HI 100%, LDI 98.58% and LMI 63.7%, differing (𝑝 <0.05) from negative controls. Main A. graveolens oil components present in 95.93% of the total oil were Dihydrocarvone (39.1%), Carvone (22.24%), D-Limonene (16.84%), Apiol (10.49%) and Trans-dihydrocarvone (7.26%). Minimum A. graveolens essential oil concentrations required to inhibit 50% (IC50) of egg hatching, larval development and larval migration were 0.006 mg/mL, 2.536 mg/mL and 3.963 mg/mL, respectively. Cell viability in MDBK (Madin-Darby bovine kidney) cells, when incubated with A. graveolens essential oil, was 86% for the highest (9.4 mg/mL) and 99% for the lowest concentration (0.29 mg/mL). A. graveolens essential oil, according to the results obtained in this study, is a promising alternative in sheep gastrointestinal nematode control.

Flexible longitudinal linear mixed models for multiple censored responses data

In biomedical studies and clinical trials, repeated measures are often subject to some upper and/or lower limits of detection. Hence, the responses are either left or right censored. A complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution. The multivariate censored linear mixed effect (MLMEC) model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this context, we develop a robust generalization of the MLMEC based on the scale mixtures of normal distributions. To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. For this complex longitudinal structure, we propose an exact estimation procedure to obtain the maximum-likelihood estimates of the fixed effects and variance components using a stochastic approximation of the EM algorithm. This approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects, the predictions of unobservable values of the responses, and the log-likelihood function as a byproduct. The proposed method is applied to analyze a set of AIDS data and is examined via a simulation study.

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

Genomewide association mapping and pathway analysis of meat tenderness in Polled Nellore cattle

Brazil is one of the world's largest beef exporters, although the product has a low price due to quality issues. The meat exported by Brazil is considered medium and low quality by international buyers, mainly due to lack of tenderness. The predominant Zebu breeds (80% Nellore) are known for producing tougher beef than taurine breeds. Nonetheless, some studies have shown that there is substantial genetic variability for tenderness within the Nellore breed, although it is a difficult trait to improve by conventional selection methods. Therefore, the aim of this study was to perform a genomewide association study (GWAS) and a gene set enrichment analysis to identify genomic regions and biologically relevant pathways associated with meat tenderness in Polled Nellore cattle. Data consisted of Warner-Bratzler shear force values of LM from 427 Polled Nellore animals divided into 3 experimental slaughters (years 2005, 2008, and 2010). The animals were genotyped with either the Illumina BovineHD BeadChip (777k, on 61 samples) or the GGP Indicus HD chip (77k, on 366 samples). Single nucleotide polymorphisms were excluded when the call rate was <90%, the Hardy-Weinberg proportions -value was <1% (Fisher exact test, Bonferroni adjusted), and the minor allele frequency was <1%. Imputation from the GGP Indicus HD chip to the Illumina BovineHD BeadChip was performed using the FImput program. Genomewide association analysis was performed using the Efficient Mixed Model Association eXpedited (EMMAx) and the population parameters previously determined (P3D) methods. The GWAS was complemented with a gene set enrichment analysis performed using the FatiGO procedure. Significant markers ( < 0.0001) explaining a larger proportion of variation than other significant SNPs were located on chromosomes 3, 13, 17, 20, 21, and 25, indicating QTL associated with meat tenderness throughout the genome. Additionally, gene set analysis identified 22 Gene Ontology functional terms and 2 InterPro entries that showed significant enrichment of genes associated with tenderness. The functional categories included protein tyrosine and serine/threonine kinase activity, calcium ion binding, lipid metabolic process, and growth factors, among others. These results help to elucidate the genetic architecture and metabolic pathways underlying this trait, which is of extreme economic and social importance to Brazil, because Nellore is the dominant beef cattle breed in the country.

Quality of the Solimões River water for domestic use by the riverine community situated in Manacapuru-Amazonas-Brazil

The Amazon has the largest watershed in the world, with abundant fresh water reserves. Such abundance contrasts with the quality of the water consumed in the riverine communities. This work highlights the importance of assessing the quality of water of the Solimões River in the stretch situated opposite the Community Nossa Senhora das Graças-Costa do Pesqueiro, in front of the town of Manacapuru-Amazonas-Brazil. The research aimed to evaluate environmental indicators for the quality of the river water as well as in households in this community, according to the regional seasonality. The monitored parameters such as conductivity, dissolved oxygen, turbidity, color, pH, nitrate, nitrite, and sulfate were compared with the water quality standards in force in Brazil. Values well above the maximum level allowed (MLA) for color and turbidity parameters were found in some households, indicating that the water collected from the river is not getting appropriate treatment. The analysis of the correlation matrix of the parameters in the flood period of the river evidenced high correlation among dissolved oxygen (D.O), NO3 (-), Cl(-), SO4 (2-), and color. In this study, by principal component analysis (PCA), it was observed that the characteristics of the water, obtained from the river to be consumed in the households, in the flood period showed similarities with the river water samples, indicating absence of efficient treatment for human consumption.

Censored linear regression models for irregularly observed longitudinal data using the multivariate- t distribution

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Quantum spin-1 anisotropic ferromagnetic Heisenberg model in a crystal field: a variational approach

A variational approach based on Bogoliubov inequality for the free energy is employed in order to treat the quantum spin-1 anisotropic ferromagnetic Heisenberg model in the presence of a crystal field. Within the Bogoliubov scheme an improved pair approximation has been used. The temperature-dependent thermodynamic functions have been obtained and provide much better results than the previous simple mean-field scheme. In one dimension, which is still nonintegrable for quantum spin-1, we get the exact results in the classical limit, or near-exact results in the quantum case, for the free energy, magnetization, and quadrupole moment, as well for the transition temperature. In two and three dimensions the corresponding global phase diagrams have been obtained as a function of the parameters of the Hamiltonian. First-order transition lines, second-order transition lines, tricritical and tetracritical points, and critical endpoints have been located through the analysis of the minimum of the Helmholtz free energy and a Landau-like expansion in the approximated free energy. Only first-order quantum transitions have been found at zero temperature. Limiting cases, such as isotropic Heisenberg, Blume-Capel, and Ising models, have been analyzed and compared to previous results obtained from other analytical approaches as well as from Monte Carlo simulations.

Identification of the 1PL model with guessing parameter: parametric and semi-parametric results

In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution G generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution G is not identified. It is finally shown that, after introducing two identification restrictions, either on the distribution G or on the item parameters, the distribution G and the item parameters are identified provided an infinite quantity of items is available.

Skew-normal/independent linear mixed models for censored responses with applications to HIV viral loads

Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew-normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.

Connexin36, an essential element in the rod pathway, is highly expressed in the essentially rodless retina of Gallus gallus

Electrical coupling provided by connexins (Cx) in gap junctions (GJ) plays important roles in both the developing and the mature retina. In mammalian nocturnal species, Cx36 is an essential component in the rod pathway, the retinal circuit specialized for night, scotopic vision. Here, we report the expression of Cx36 in a species (Gallus gallus) that phylogenetic development endows with an essentially rodless retina. Cx36 gene is very highly expressed in comparison with other Cxs previously described in the adult retina, such as Cx43, Cx45, and Cx50. Moreover, real-time PCR, Western blot, and immunofluorescence all revealed that Cx36 expression massively increased over time during development. We thoroughly examined Cx36 in the inner and outer plexiform layers, where this protein was particularly abundant. Cx36 was observed mainly in the off sublamina of the inner plexiform layer rather than in the on sublamina previously described in the mammalian retina. In addition, Cx36 colocalized with specific cell markers, revealing the expression of this protein in distinct amacrine cells. To investigate further the involvement of Cx36 in visual processing, we examined its functional regulation in retinas from dark-adapted animals. Light deprivation markedly up-regulates Cx36 gene expression in the retina, resulting in an increased accumulation of the protein within and between cone synaptic terminals. In summary, the developmental regulation of Cx36 expression results in particular circuitry-related roles in the chick retina. Moreover, this study demonstrated that Cx36 onto- and phylogenesis in the vertebrate retina simultaneously exhibit similarities and particularities.

[Preparation and analysis of dehydrated mixtures of vegetables and underutilized fish species flours: I. Dehydrated mixtures of cereal-fish]

For the purpose of providing possible solutions to the malnutrition problems affecting those populations where cereals and tubers form an important portion of their daily intake, products were prepared from dehydrated mixtures of cereals and under-utilized fish, but which contain high-quality protein. Two cereals were selected for our experiments: rice and corn, and a marine under-utilized fish species (Macrodon ancyclodon). The minced fish muscle recovered by mechanical deboning was mixed with the cereal, obtaining mixtures with 5%, 10% and 15% fish on a dry basis. Feeding experiments using Wistar weaning rats were then carried out to evaluate the most important characteristics. An amino acid profile which reflected high-quality protein was obtained, as evidenced by the excellent PER, NPU, NPR and digestibility values determined. The dehydrated mixtures of fish/cereal flour prepared with 5% and up to 10% fish (dry basis), did not present any odour, but as of the 15% level, fish odour was perceived. Therefore, the use of dehydrated mixtures of fish/cereal flours with up to 10% fish in preparing food products, is recommended, since these would be of great help in solving the scarcity of good-quality protein, particularly in the developing countries.