Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Pre-processing for noise detection in gene expression classification data

Due to the imprecise nature of biological experiments, biological data is often characterized by the presence of redundant and noisy data. This may be due to errors that occurred during data collection, such as contaminations in laboratorial samples. It is the case of gene expression data, where the equipments and tools currently used frequently produce noisy biological data. Machine Learning algorithms have been successfully used in gene expression data analysis. Although many Machine Learning algorithms can deal with noise, detecting and removing noisy instances from the training data set can help the induction of the target hypothesis. This paper evaluates the use of distance-based pre-processing techniques for noise detection in gene expression data classification problems. This evaluation analyzes the effectiveness of the techniques investigated in removing noisy data, measured by the accuracy obtained by different Machine Learning classifiers over the pre-processed data.

Searching for molecular markers in head and neck squamous cell carcinomas (HNSCC) by statistical and bioinformatic analysis of larynx-derived SAGE libraries

Background: Head and neck squamous cell carcinoma (HNSCC) is one of the most common malignancies in humans. The average 5-year survival rate is one of the lowest among aggressive cancers, showing no significant improvement in recent years. When detected early, HNSCC has a good prognosis, but most patients present metastatic disease at the time of diagnosis, which significantly reduces survival rate. Despite extensive research, no molecular markers are currently available for diagnostic or prognostic purposes. Methods: Aiming to identify differentially-expressed genes involved in laryngeal squamous cell carcinoma (LSCC) development and progression, we generated individual Serial Analysis of Gene Expression (SAGE) libraries from a metastatic and non-metastatic larynx carcinoma, as well as from a normal larynx mucosa sample. Approximately 54,000 unique tags were sequenced in three libraries. Results: Statistical data analysis identified a subset of 1,216 differentially expressed tags between tumor and normal libraries, and 894 differentially expressed tags between metastatic and non-metastatic carcinomas. Three genes displaying differential regulation, one down-regulated (KRT31) and two up-regulated (BST2, MFAP2), as well as one with a non-significant differential expression pattern (GNA15) in our SAGE data were selected for real-time polymerase chain reaction (PCR) in a set of HNSCC samples. Consistent with our statistical analysis, quantitative PCR confirmed the upregulation of BST2 and MFAP2 and the downregulation of KRT31 when samples of HNSCC were compared to tumor-free surgical margins. As expected, GNA15 presented a non-significant differential expression pattern when tumor samples were compared to normal tissues. Conclusion: To the best of our knowledge, this is the first study reporting SAGE data in head and neck squamous cell tumors. Statistical analysis was effective in identifying differentially expressed genes reportedly involved in cancer development. The differential expression of a subset of genes was confirmed in additional larynx carcinoma samples and in carcinomas from a distinct head and neck subsite. This result suggests the existence of potential common biomarkers for prognosis and targeted-therapy development in this heterogeneous type of tumor.

Trends in dermatomyositis- and polymyositis-related mortality in the state of Sao Paulo, Brazil, 1985-2007: multiple cause-of-death analysis

Background: Dermatomyositis (DM) and polymyositis (PM) are rare systemic autoimmune rheumatic diseases with high fatality rates. There have been few population-based mortality studies of dermatomyositis and polymyositis in the world, and none have been conducted in Brazil. The objective of the present study was to employ multiple-cause of-death methodology in the analysis of trends in mortality related to dermatomyositis and polymyositis in the state of Sao Paulo, Brazil, between 1985 and 2007. Methods: We analyzed mortality data from the Sao Paulo State Data Analysis System, selecting all death certificates on which DM or PM was listed as a cause of death. The variables sex, age and underlying, associated or total mentions of causes of death were studied using mortality rates, proportions and historical trends. Statistical analysis were performed by chi-square and H Kruskal-Wallis tests, variance analysis and linear regression. A p value less than 0.05 was regarded as significant. Results: Over a 23-year period, there were 318 DM-related deaths and 316 PM-related deaths. Overall, DM/PM was designated as an underlying cause in 55.2% and as an associated cause in 44.8%; among 634 total deaths females accounted for 71.5%. During the study period, age-and gender-adjusted DM mortality rates did not change significantly, although PM as an underlying cause and total mentions of PM trended lower (p < 0.05). The mean ages at death were 47.76 +/- 20.81 years for DM and 54.24 +/- 17.94 years for PM (p = 0.0003). For DM/PM, respectively, as underlying causes, the principal associated causes of death were as follows: pneumonia (in 43.8%/33.5%); respiratory failure (in 34.4%/32.3%); interstitial pulmonary diseases and other pulmonary conditions (in 28.9%/17.6%); and septicemia (in 22.8%/15.9%). For DM/PM, respectively, as associated causes, the following were the principal underlying causes of death: respiratory disorders (in 28.3%/26.0%); circulatory disorders (in 17.4%/20.5%); neoplasms (in 16.7%/13.7%); infectious and parasitic diseases (in 11.6%/9.6%); and gastrointestinal disorders (in 8.0%/4.8%). Of the 318 DM-related deaths, 36 involved neoplasms, compared with 20 of the 316 PM-related deaths (p = 0.03). Conclusions: Our study using multiple cause of deaths found that DM/PM were identified as the underlying cause of death in only 55.2% of the deaths, indicating that both diseases were underestimated in the primary mortality statistics. We observed a predominance of deaths in women and in older individuals, as well as a trend toward stability in the mortality rates. We have confirmed that the risk of death is greater when either disease is accompanied by neoplasm, albeit to lesser degree in individuals with PM. The investigation of the underlying and associated causes of death related to DM/PM broaden the knowledge of the natural history of both diseases and could help integrate mortality data for use in the evaluation of control measures for DM/PM.

Recurrence quantification analysis of turbulent fluctuations in the plasma edge of Tokamak Chauffage Alfveacuten Breacutesilien tokamak

Recurrences are close returns of a given state in a time series, and can be used to identify different dynamical regimes and other related phenomena, being particularly suited for analyzing experimental data. In this work, we use recurrence quantification analysis to investigate dynamical patterns in scalar data series obtained from measurements of floating potential and ion saturation current at the plasma edge of the Tokamak Chauffage Alfveacuten Breacutesilien [R. M. O. Galva approximate to o , Plasma Phys. Controlled Fusion 43, 1181 (2001)]. We consider plasma discharges with and without the application of radial electric bias, and also with two different regimes of current ramp. Our results indicate that biasing improves confinement through destroying highly recurrent regions within the plasma column that enhance particle and heat transport.

LATENT RANK CHANGE DETECTION FOR ANALYSIS OF SPLICE-JUNCTION MICROARRAYS WITH NONLINEAR EFFECTS

Alternative splicing of gene transcripts greatly expands the functional capacity of the genome, and certain splice isoforms may indicate specific disease states such as cancer. Splice junction microarrays interrogate thousands of splice junctions, but data analysis is difficult and error prone because of the increased complexity compared to differential gene expression analysis. We present Rank Change Detection (RCD) as a method to identify differential splicing events based upon a straightforward probabilistic model comparing the over-or underrepresentation of two or more competing isoforms. RCD has advantages over commonly used methods because it is robust to false positive errors due to nonlinear trends in microarray measurements. Further, RCD does not depend on prior knowledge of splice isoforms, yet it takes advantage of the inherent structure of mutually exclusive junctions, and it is conceptually generalizable to other types of splicing arrays or RNA-Seq. RCD specifically identifies the biologically important cases when a splice junction becomes more or less prevalent compared to other mutually exclusive junctions. The example data is from different cell lines of glioblastoma tumors assayed with Agilent microarrays.

An exploratory analysis of relationships between socioeconomic, land use, activity participation variables and travel patterns

This paper aims to find relations between the socioeconomic characteristics, activity participation, land use patterns and travel behavior of the residents in the Sao Paulo Metropolitan Area (SPMA) by using Exploratory Multivariate Data Analysis (EMDA) techniques. The variables influencing travel pattern choices are investigated using: (a) Cluster Analysis (CA), grouping and characterizing the Traffic Zones (17), proposing the independent variable called Origin Cluster and, (b) Decision Tree (DT) to find a priori unknown relations among socioeconomic characteristics, land use attributes of the origin TZ and destination choices. The analysis was based on the origin-destination home-interview survey carried out in SPMA in 1997. The DT application revealed the variables of greatest influence on the travel pattern choice. The most important independent variable considered by DT is car ownership, followed by the Use of Transportation ""credits"" for Transit tariff, and, finally, activity participation variables and Origin Cluster. With these results, it was possible to analyze the influence of a family income, car ownership, position of the individual in the family, use of transportation ""credits"" for transit tariff (mainly for travel mode sequence choice), activities participation (activity sequence choice) and Origin Cluster (destination/travel distance choice). (c) 2010 Elsevier Ltd. All rights reserved.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Qualitative assessment of stock prices listed on the Sao Paulo stock exchange: An approach from the perspective of homogeneity analysis

The stock market suffers uncertain relations throughout the entire negotiation process, with different variables exerting direct and indirect influence on stock prices. This study focuses on the analysis of certain aspects that may influence these values offered by the capital market, based on the Brazil Index of the Sao Paulo Stock Exchange (Bovespa), which selects 100 stocks among the most traded on Bovespa in terms of number of trades and financial volume. The selected variables are characterized by the companies` activity area and the business volume in the month of data collection, i.e. April/2007. This article proposes an analysis that joins the accounting view of the stock price variables that can be influenced with the use of multivariate qualitative data analysis. Data were explored through Correspondence Analysis (Anacor) and Homogeneity Analysis (Homals). According to the research, the selected variables are associated with the values presented by the stocks, which become an internal control instrument and a decision-making tool when it comes to choosing investments.

Covariance functions for body weight from birth to maturity in Nellore cows

The objective of this study was to estimate (co)variance functions using random regression models on Legendre polynomials for the analysis of repeated measures of BW from birth to adult age. A total of 82,064 records from 8,145 females were analyzed. Different models were compared. The models included additive direct and maternal effects, and animal and maternal permanent environmental effects as random terms. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of animal age (cubic regression) were considered as random co-variables. Eight models with polynomials of third to sixth order were used to describe additive direct and maternal effects, and animal and maternal permanent environmental effects. Residual effects were modeled using 1 (i.e., assuming homogeneity of variances across all ages) or 5 age classes. The model with 5 classes was the best to describe the trajectory of residuals along the growth curve. The model including fourth- and sixth-order polynomials for additive direct and animal permanent environmental effects, respectively, and third-order polynomials for maternal genetic and maternal permanent environmental effects were the best. Estimates of (co) variance obtained with the multi-trait and random regression models were similar. Direct heritability estimates obtained with the random regression models followed a trend similar to that obtained with the multi-trait model. The largest estimates of maternal heritability were those of BW taken close to 240 d of age. In general, estimates of correlation between BW from birth to 8 yr of age decreased with increasing distance between ages.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

Short-term in situ/ex vivo study of the anticariogenic potential of a resin-modified glass-ionomer cement associated with adhesive systems

Objective: As resin-modified glass-ionomer cement (RMGIC) is an adhesive material, its association to dentin bonding agents (DBAs) was previously proposed. This study investigated the adjunctive behavior of an RMGIC with etch-and-rinse bonding systems under in situ/ex vivo cariogenic challenge. Method and Materials: Bovine enamel blocks (3 3 2 mm) were randomly assigned to group VP, Vitremer + its own primer (3M ESPE); group VSB, Vitremer + Single Bond (3M ESPE); and group VPB, Vitremer + Prime & Bond 2.1 (Dentsply). Two blocks of each group were randomly placed in an acrylic palatal appliance, so each appliance included six blocks. Volunteers (n = 10) wore these appliances according to given instructions to promote a sucrose challenge eight times/day for 15 days. After this period, the blocks were removed from the devices and cleaned, and demineralization was assessed through longitudinal microhardness analysis (Knoop indenter, 25 g/5 s). Data were submitted to three-way ANOVA and Tukey test (P < .05). Results: No treatment was able to completely avoid demineralization. All materials showed a statistically significant difference in mineral loss when the microhardness on the outer enamel was compared with deeper regions (P < .05). Conclusion: Association of the tested RMGICs with etch-and-rinse DBAs did not seem to be more beneficial against caries than the conventional treatment with RMGIC. (Quintessence Int 2010; 41: e192-e199)

PCA Tomography: how to extract information from data cubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies, it is possible to obtain data cubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of data cube (data from single field observations, containing two spatial and one spectral dimension) that uses Principal Component Analysis (PCA) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data on to these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal, and this information is fundamental for their handling and interpretation. When the data cube shows objects that present uncorrelated physical phenomena, the eigenvector`s orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms, one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the low ionization nuclear emission region (LINER) galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore, we show that it is displaced from the centre of its stellar bulge.