Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Biological response of pulps submitted to different capping materials

Pulp capping is a procedure that comprises adequate protection of the pulp tissue exposed to the oral environment, aiming at the preservation of its vitality and functions. This study evaluated the response of the dental pulps of dog teeth to capping with mineral trioxide aggregate (MTA) or calcium hydroxide P.A. For that purpose, 37 teeth were divided into two groups, according to the capping material employed. Two dogs were anesthetized and, after placement of a rubber dam, their pulps were exposed in a standardized manner and protected with the experimental capping materials. The cavities were then sealed with resin-modified glass ionomer cement and restored with composite resin. After sixty days, the animals were killed and the specimens were processed in order to be analyzed with optic microscopy. It was observed that MTA presented a higher success rate compared to calcium hydroxide, presenting a lower occurrence of infection and pulp necrosis.

Genetic effects on preweaning weight gain of Nelore-Hereford calves according to different models and estimation methods

Additive and nonadditive genetic effects on preweaning weight gain (PWG) of a commercial crossbred population were estimated using different genetic models and estimation methods. The data set consisted of 103,445 records on purebred and crossbred Nelore-Hereford calves raised under pasture conditions on farms located in south, southeast, and middle west Brazilian regions. In addition to breed additive and dominance effects, the models including different epistasis covariables were tested. Models considering joint additive and environment (latitude) by genetic effects interactions were also applied. In a first step, analyses were carried out under animal models. In a second step, preadjusted records were analyzed using ordinary least squares (OLS) and ridge regression (RR). The results reinforced evidence that breed additive and dominance effects are not sufficient to explain the observed variability in preweaning traits of Bos taurus x Bos indicus calves, and that genotype x environment interaction plays an important role in the evaluation of crossbred calves. Data were ill-conditioned to estimate the effects of genotype x environment interactions. Models including these effects presented multicolinearity problems. In this case, RR seemed to be a powerful tool for obtaining more plausible and stable estimates. Estimated prediction error variances and variance inflation factors were drastically reduced, and many effects that were not significant under ordinary least squares became significant under RR. Predictions of PWG based on RR estimates were more acceptable from a biological perspective. In temperate and subtropical regions, calves with intermediate genetic compositions (close to 1/2 Nelore) exhibited greater predicted PWG. In the tropics, predicted PWG increased linearly as genotype got closer to Nelore. ©2006 American Society of Animal Science. All rights reserved.

The structural origin and biological function of pH-sensitivity in firefly luciferases

Firefly luciferases are called pH-sensitive because their bioluminescence spectra display a typical red-shift at acidic pH, higher temperatures, and in the presence of heavy metal cations, whereas other beetle luciferases (click beetles and railroadworms) do not, and for this reason they are called pH-insensitive. Despite many studies on firefly luciferases, the origin of pH-sensitivity is far from being understood. This subject is revised in view of recent results. Some substitutions of amino-acid residues influencing pH-sensitivity in firefly luciferases have been identified. Sequence comparison, site-directed mutagenesis and modeling studies have shown a set of residues differing between pH-sensitive and pH-insensitive luciferases which affect bioluminescence colors. Some substitutions dramatically affecting bioluminescence colors in both groups of luciferases are clustered in the loop between residues 223-235 (Photinus pyralis sequence). A network of hydrogen bonds and salt bridges involving the residues N229-S284-E311-R337 was found to be important for affecting bioluminescence colors. It is suggested that these structural elements may affect the benzothiazolyl side of the luciferin-binding site affecting bioluminescence colors. Experimental evidence suggest that the residual red light emission in pH-sensitive luciferases could be a vestige that may have biological importance in some firefly species. Furthermore, the potential utility of pH-sensitivity for intracellular biosensing applications is considered. © The Royal Society of Chemistry and Owner Societies.

Management of vomplex systems: Modeling the biological pest control

The aim of this paper is to study the cropping system as complex one, applying methods from theory of dynamic systems and from the control theory to the mathematical modeling of the biological pest control. The complex system can be described by different mathematical models. Based on three models of the pest control, the various scenarios have been simulated in order to obtain the pest control strategy only through natural enemies' introduction. © 2008 World Scientific Publishing Company.

Chemometric analysis of Hymenoptera toxins and defensins: A model for predicting the biological activity of novel peptides from venoms and hemolymph

When searching for prospective novel peptides, it is difficult to determine the biological activity of a peptide based only on its sequence. The trial and error approach is generally laborious, expensive and time consuming due to the large number of different experimental setups required to cover a reasonable number of biological assays. To simulate a virtual model for Hymenoptera insects, 166 peptides were selected from the venoms and hemolymphs of wasps, bees and ants and applied to a mathematical model of multivariate analysis, with nine different chemometric components: GRAVY, aliphaticity index, number of disulfide bonds, total residues, net charge, pI value, Boman index, percentage of alpha helix, and flexibility prediction. Principal component analysis (PCA) with non-linear iterative projections by alternating least-squares (NIPALS) algorithm was performed, without including any information about the biological activity of the peptides. This analysis permitted the grouping of peptides in a way that strongly correlated to the biological function of the peptides. Six different groupings were observed, which seemed to correspond to the following groups: chemotactic peptides, mastoparans, tachykinins, kinins, antibiotic peptides, and a group of long peptides with one or two disulfide bonds and with biological activities that are not yet clearly defined. The partial overlap between the mastoparans group and the chemotactic peptides, tachykinins, kinins and antibiotic peptides in the PCA score plot may be used to explain the frequent reports in the literature about the multifunctionality of some of these peptides. The mathematical model used in the present investigation can be used to predict the biological activities of novel peptides in this system, and it may also be easily applied to other biological systems. © 2011 Elsevier Inc.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Anti-inflammatory mechanisms of the annexin A1 protein and its mimetic peptide Ac2-26 in models of ocular inflammation in vivo and in vitro

Annexin A1 (AnxA1) is a protein that displays potent anti-inflammatory properties, but its expression in eye tissue and its role in ocular inflammatory diseases have not been well studied. We investigated the mechanism of action and potential uses of AnxA1 and its mimetic peptide (Ac2-26) in the endotoxin-induced uveitis (EIU) rodent model and in human ARPE-19 cells activated by LPS. In rats, analysis of untreated EIU after 24 and 48 h or EIU treated with topical applications or with a single s.c. injection of Ac2-26 revealed the anti-inflammatory actions of Ac2-26 on leukocyte infiltration and on the release of inflammatory mediators; the systemic administration of Boc2, a formylated peptide receptor (fpr) antagonist, abrogated the peptide's protective effects. Moreover, AnxA1-/- mice exhibited exacerbated EIU compared with wild-type animals. Immunohistochemical studies of ocular tissue showed a specific AnxA1 posttranslational modification in EIU and indicated that the fpr2 receptor mediated the anti-inflammatory actions of AnxA1. In vitro studies confirmed the roles of AnxA1 and fpr2 and the protective effects of Ac2-26 on the release of chemical mediators in ARPE-19 cells. Molecular analysis of NF-κB translocation and IL-6, IL-8, and cyclooxygenase-2 gene expression indicated that the protective effects of AnxA1 occur independently of the NF-κB signaling pathway and possibly in a posttranscriptional manner. Together, our data highlight the role of AnxA1 in ocular inflammation, especially uveitis, and suggest the use of AnxA1 or its mimetic peptide Ac2-26 as a therapeutic approach. Copyright © 2013 by The American Association of Immunologists, Inc.

Evidence for biological inheritance of the eosinophil response to internal parasites in southeastern Brazil

Uma amostra de 177 indivíduos pertencentes a 120 famílias nucleares, completas ou incompletas, de Bambui, Estado de Minas Gerais, sudeste do Brasil, foi estudada com o objetivo de apurar algumas das causas da variabilidade da taxa de eosinófilos em pessoas parasitadas por vermes intestinais com ciclo de vida extra-digestivo. A análise de segregação, aplicada aos dados sem correção para a assimetria, mostrou que a hipótese de um gene principal aditivo é consistente com os dados, enquanto que as hipóteses que supõem a ação de um gene dominante, de um gene recessivo ou ainda herança multifatorial não explicam, adequadamente, a significante agregação familial observada. A correção mais parcimoniosa para assimetria mostrou resultados semelhantes, mas não permitiu a distinção entre os modelos dominante e recessivo, embora permitisse a rejeição do modelo codominante. Considerando que esse modelo supõe ser a assimetria devida ao entrelaçamento de duas distribuições, esses resultados parecem concordar com aqueles obtidos quando os dados não foram corrigidos. Pode-se sugerir que o papel desempenhado por vários fatores genéticos independentes na resistência/suscetibilidade à infestação por helmintos seja determinado, principalmente, por suas capacidades de agir no estabelecimento de uma resposta eosinofílica.

Protective effects of the galectin-1 protein on in vivo and in vitro models of ocular inflammation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Does the gastroprotective action of a medicinal plant ensure healing effects? An integrative study of the biological effects of Serjania marginata Casar. (Sapindaceae) in rats

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.

Comparative analysis of the pathological events involved in immune and non-immune TRALI models

Background and Objectives Transfusion-related acute lung injury (TRALI) is characterized by leukocyte transmigration and alveolar capillary leakage shortly after transfusion. TRALI pathogenesis has not been fully elucidated. In some cases, the infusion of alloantibodies (immune model), whereas in others the combination of neutrophil priming by proinflammatory molecules with the subsequent infusion of biological response modifiers (BRMs) in the hemocomponent (non-immune model) have been implicated. Our aim was to compare the pathological events involved in TRALI induced by antibodies or BRMs using murine models. Materials and Methods In the immune model, human HNA-2+ neutrophils were incubated in vitro with a monoclonal antibody (anti-CD177, clone 7D8) directed against the HNA-2 antigen and injected i.v. in NOD/SCID mice. In the non-immune model, BALB/c mice were treated with low doses of lipopolysaccharide (LPS) followed by platelet-activating factor (PAF) infusion 2 h later. Forty minutes after PAF administration, or 6 h after neutrophil injection, lungs were isolated and histological analysis, determination of a variety of cytokines and chemokines including keratinocyte-derived chemokine (KC), MIP-2, the interleukins IL-1 beta, IL-6, IL-8 as well as TNFa, cell influx and alveolar capillary leakage were performed. Results In both models, characteristic histological findings of TRALI and an increase in KC and MIP-2 levels were detected. In contrast to the immune model, in the non-immune model, there was a dramatic increase in IL-1 beta and TNFa. However, capillary leakage was only detected if PAF was administrated. Conclusions Regardless of the triggering event(s), KC, MIP-2 and integrins participate in TRALI pathogenesis, whereas PAF is essential for capillary leakage when two events are involved.