Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model I assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2. (C) 2007 Elsevier B.V. All rights reserved.

Estimation of Maximal Work Rate Based on the 6-Minute Walk Test and Fat-Free Mass in Chronic Obstructive Pulmonary Disease

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

The six-minute walk test and body weight-walk distance product in healthy Brazilian subjects

We assessed the 6-min walk distance (6MWD) and body weight x distance product (6MWw) in healthy Brazilian subjects and compared measured 6MWD with values predicted in five reference equations developed for other populations. Anthropometry, spirometry, reported physical activity, and two walk tests in a 30-m corridor were evaluated in 134 subjects (73 females, 13-84 years). Mean 6MWD and 6MWw were significantly greater in males than in females (622 ± 80 m, 46,322 ± 10,539 kg.m vs 551 ± 71 m, 36,356 ± 8,289 kg.m, P < 0.05). Four equations significantly overestimated measured 6MWD (range, 32 ± 71 to 137 ± 74 m; P < 0.001), and one significantly underestimated it (-36 ± 86 m; P < 0.001). 6MWD significantly correlated with age (r = -0.39), height (r = 0.44), body mass index (r = -0.24), and reported physical activity (r = 0.25). 6MWw significantly correlated with age (r = -0.21), height (r = 0.66) and reported physical activity (r = 0.25). The reference equation devised for walk distance was 6MWDm = 622.461 - (1.846 x Ageyears) + (61.503 x Gendermales = 1; females = 0); r2 = 0.300. In an additional group of 85 subjects prospectively studied, the difference between measured and the 6MWD predicted with the equation proposed here was not significant (-3 ± 68 m; P = 0.938). The measured 6MWD represented 99.6 ± 11.9% of the predicted value. We conclude that 6MWD and 6MWw variances were adequately explained by demographic and anthropometric attributes. This reference equation is probably most appropriate for evaluating the exercise capacity of Brazilian patients with chronic diseases.

The Incremental Shuttle Walk Test in Older Brazilian Adults

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

Correlated matings in dioecious tropical tree, Myracrodruon urundeuva fr. all.

The correlated matings in two populations (Selvíria - SEL and Paulo de Faria - PFA) of dioecious Myracrodruon urundeuva were studied in the Southwest of Brazil, by allozyme analysis of progeny arrays using the sibling-pair model. Open-pollinated seeds were collected from 25 to 30 trees within populations. Departure from random matings were evident from the differences in pollen and ovule allele frequencies. The high and significant correlation of paternity (SEL r̂p = 0.671 ± 0.074; PFA r̂p = 0.371 ± 0.062) and a low number of effective pollinating trees (ranging from 2 to 3) were detected in the populations, suggesting high proportion of full-sibs progenies. According to these results, the estimate of coancestry within families (θ = 0.209 - SEL; θ = 0.171 - PFA.) exceeded the expectation of the half-sib progenies (θ = 0.125). Result outcomes are discussed from a conservation and breeding point of view.

Decreasing pH of mammary gland secretions is associated with parturition and is correlated with electrolyte concentrations in prefoaling mares

The objectives of this study were to determine pH of the mammary gland secretions and the corresponding electrolyte concentrations in prefoaling mares. Pregnant mares (seven primiparous and seven multiparous) were monitored daily from 310.320 days of gestation until parturition. Prefoaling mammary gland secretions were collected, and pH was immediately determined with a pH meter and pH strip test. An aliquot of prefoaling mammary secretions was frozen and stored until further analyses. After parturition, samples from day .4 to 0 (day of foaling) were thawed and electrolyte concentrations (ie, Ca2+, Mg2+, Na+, K+ and Cl-) were determined with an automated analyser. Data were analysed via a mixed model with the mare as a random effect. Correlations were determined between pH and electrolyte concentrations by the Pearson product-moment for each pair. There was significant reduction in pH of mammary secretions on the day of foaling (P<0.0001), and most mares (11/14) with a pH .7 foaled within 24 hours. There was high correlation between the two pH methods (r=0.93). Additionally, there were significant (P<0.05) increases in Ca2+ and K+ concentrations, and significant decreases in Na+ and Cl- concentrations from one day before to the day of foaling. The pH of mammary secretions was highly and significantly (P<0.001) correlated with Na + (r=0.87), Cl- (r=0.85), Ca2+ (r=-0.88); and K+(r=.0.80) concentrations, and moderately correlated with Mg 2+ (r=-0.58). Daily evening pH measure of the mammary gland secretions can predict foaling in most mares.

Imperceptible electrical noise attenuates isometric plantar flexion force fluctuations with correlated reductions in postural sway

Optimal levels of noise stimulation have been shown to enhance the detection and transmission of neural signals thereby improving the performance of sensory and motor systems. The first series of experiments in the present study aimed to investigate whether subsensory electrical noise stimulation applied over the triceps surae (TS) in seated subjects decreases torque variability during a force-matching task of isometric plantar flexion and whether the same electrical noise stimulation decreases postural sway during quiet stance. Correlation tests were applied to investigate whether the noise-induced postural sway decrease is linearly predicted by the noise-induced torque variability decrease. A second series of experiments was conducted to investigate whether there are differences in torque variability between conditions in which the subsensory electrical noise is applied only to the TS, only to the tibialis anterior (TA) and to both TS and TA, during the force-matching task with seated subjects. Noise stimulation applied over the TS muscles caused a significant reduction in force variability during the maintained isometric force paradigm and also decreased postural oscillations during quiet stance. Moreover, there was a significant correlation between the reduction in force fluctuation and the decrease in postural sway with the electrical noise stimulation. This last result indicates that changes in plantar flexion force variability in response to a given subsensory random stimulation of the TS may provide an estimate of the variations in postural sway caused by the same subsensory stimulation of the TS. We suggest that the decreases in force variability and postural sway found here are due to stochastic resonance that causes an improved transmission of proprioceptive information. In the second series of experiments, the reduction in force variability found when noise was applied to the TA muscle alone did not reach statistical significance, suggesting that TS proprioception gives a better feedback to reduce force fluctuation in isometric plantar flexion conditions.

Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data

In this paper, we propose nonlinear elliptical models for correlated data with heteroscedastic and/or autoregressive structures. Our aim is to extend the models proposed by Russo et al. [22] by considering a more sophisticated scale structure to deal with variations in data dispersion and/or a possible autocorrelation among measurements taken throughout the same experimental unit. Moreover, to avoid the possible influence of outlying observations or to take into account the non-normal symmetric tails of the data, we assume elliptical contours for the joint distribution of random effects and errors, which allows us to attribute different weights to the observations. We propose an iterative algorithm to obtain the maximum-likelihood estimates for the parameters and derive the local influence curvatures for some specific perturbation schemes. The motivation for this work comes from a pharmacokinetic indomethacin data set, which was analysed previously by Bocheng and Xuping [1] under normality.

Six minute walk test Z score: Correlations with cystic fibrosis severity markers

Background: The six-minute-walk-test (6MWT) has been increasingly used in cystic fibrosis (CF) patients. However, few studies in children have correlated 6MWT with current parameters used to evaluate CF severity. Moreover, no study transformed the values of distance walked from meters into Z scores to avoid bias like age and gender, which are sources of 6MWT variability. Methods: A cross-sectional descriptive study was performed to analyze the correlations (Spearman) among forced expiratory volume in one second (FEV1), body mass index (BMI), chest radiography (CXR), chest tomography (CT), and 6MWT Z score (Z-6MWT). Clinically stable CF patients, aged 6-21 years, were included. Results: 34 patients, 14F/20M, mean age 12.1 +/- 4.0 years were studied. The mean Z-6MWT was -1.1 +/- 1.106. The following correlations versus Z-6MWT were found: FEV1 (r=0.59, r(2)=0.32, p=0.0002), BMI Z score (r=0.42, r(2)=0.17, p=0.013), CXR (r=0.34, r(2)=0.15, p=0.0472) and CT (r=-0.45, r(2)=0.23, p=0.0073). Conclusions: In conclusion there was a significant, but poor, correlation between the six minute walk test Z score and the cystic fibrosis severity markers currently in use. (C) 2011 European Cystic Fibrosis Society. Published by Elsevier B.V. All rights reserved.

Segmental dataset and whole body expression data do not support the hypothesis that non-random movement is an intrinsic property of Drosophila retrogenes

Background: Several studies in Drosophila have shown excessive movement of retrogenes from the X chromosome to autosomes, and that these genes are frequently expressed in the testis. This phenomenon has led to several hypotheses invoking natural selection as the process driving male-biased genes to the autosomes. Metta and Schlotterer (BMC Evol Biol 2010, 10:114) analyzed a set of retrogenes where the parental gene has been subsequently lost. They assumed that this class of retrogenes replaced the ancestral functions of the parental gene, and reported that these retrogenes, although mostly originating from movement out of the X chromosome, showed female-biased or unbiased expression. These observations led the authors to suggest that selective forces (such as meiotic sex chromosome inactivation and sexual antagonism) were not responsible for the observed pattern of retrogene movement out of the X chromosome. Results: We reanalyzed the dataset published by Metta and Schlotterer and found several issues that led us to a different conclusion. In particular, Metta and Schlotterer used a dataset combined with expression data in which significant sex-biased expression is not detectable. First, the authors used a segmental dataset where the genes selected for analysis were less testis-biased in expression than those that were excluded from the study. Second, sex-biased expression was defined by comparing male and female whole-body data and not the expression of these genes in gonadal tissues. This approach significantly reduces the probability of detecting sex-biased expressed genes, which explains why the vast majority of the genes analyzed (parental and retrogenes) were equally expressed in both males and females. Third, the female-biased expression observed by Metta and Schltterer is mostly found for parental genes located on the X chromosome, which is known to be enriched with genes with female-biased expression. Fourth, using additional gonad expression data, we found that autosomal genes analyzed by Metta and Schlotterer are less up regulated in ovaries and have higher chance to be expressed in meiotic cells of spermatogenesis when compared to X-linked genes. Conclusions: The criteria used to select retrogenes and the sex-biased expression data based on whole adult flies generated a segmental dataset of female-biased and unbiased expressed genes that was unable to detect the higher propensity of autosomal retrogenes to be expressed in males. Thus, there is no support for the authors' view that the movement of new retrogenes, which originated from X-linked parental genes, was not driven by selection. Therefore, selection-based genetic models remain the most parsimonious explanations for the observed chromosomal distribution of retrogenes.

Steroid hormone related male biased parasitism in chamois, Rupicapra rupicapra rupicapra

Parasites are linked with their host in a trophic interaction with implications for both hosts and parasites. Interaction stretches from the host's immune response to the structuring of communities and the evolution of biodiversity. As in many species sex determines life history strategy, response to parasites may be sex-specific. Males of vertebrate species tend to exhibit higher rates of parasites than females. Sex-associated hormones may influence immunocompetence and are hypothesised to lead to this bias. In a field study, we tested the prediction of male biased parasitism (MBP) in free ranging chamois (Rupicapra rupicapra rupicapra), which are infested intensely by gastrointestinal and lung helminths. We further investigated sex differences in faecal androgen (testosterone and epiandrosterone), cortisol and oestrogen metabolites using enzyme immunoassays (EIA) to evaluate the impact of these hormones on sex dependent parasite susceptibility. Non-invasive methods were used and the study was conducted throughout a year to detect seasonal patterns. Hormone levels and parasite counts varied significantly throughout the year. Male chamois had a higher output of gastrointestinal eggs and lungworm larvae when compared to females. The hypothesis of MBP originating in sex related hormone levels was confirmed for the elevated output of lungworm larvae, but not for the gastrointestinal nematodes. The faecal output of lungworm larvae was significantly correlated with androgen and cortisol metabolite levels. Our study shows that sex differences in steroid levels play an important role to explain MBP, although they alone cannot fully explain the phenomenon.

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual; bias is reduced only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals can be considered independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.