Copulas in QTL mapping

The standard variance components method for mapping quantitative trait loci is derived on the assumption of normality. Unsurprisingly, statistical tests based on this method do not perform so well if this assumption is not satisfied. We use the statistical concept of copulas to relax the assumption of normality and derive a test that can perform well under any distribution of the continuous trait. In particular, we discuss bivariate normal copulas in the context of sib-pair studies. Our approach is illustrated by a linkage analysis of lipoprotein(a) levels, whose distribution is highly skewed. We demonstrate that the asymptotic critical levels of the test can still be calculated using the interval mapping approach. The new method can be extended to more general pedigrees and multivariate phenotypes in a similar way as the original variance components method.

Nutrient partitioning during treatment of tuberculosis: gain in body fat mass but not in protein mass

Background: Tuberculosis is an important cause of wasting. The functional consequences of wasting and recovery may depend on the distribution of lost and gained nutrient stores between protein and fat masses. Objective: The goal was to study nutrient partitioning, ie, the proportion of weight change attributable to changes in fat mass (FM) versus protein mass (PM), during anti mycobacterial treatment. Design: Body-composition measures were made of 21 men and 9 women with pulmonary tuberculosis at baseline and after 1 and 6 mo of treatment. All subjects underwent dual-energy X-ray absorptiometry and deuterium bromide dilution tests, and a four-compartment model of FM, total body water (TBW), bone minerals (BM), and PM was derived. The ratio of PM to FM at any time was expressed as the energy content (p-ratio). Changes in the p-ratio were related to disease severity as measured by radiologic criteria. Results: Patients gained 10% in body weight (P < 0.001) from baseline to month 6. This was mainly due to a 44% gain in FM (P < 0.001); PM, BM, and TBW did not change significantly. Results were similar in men and women. The p-ratio decreased from baseline to month 1 and then fell further by month 6. Radiologic disease severity was not correlated with changes in the p-ratio. Conclusions: Microbiological cure of tuberculosis does not restore PM within 6 mo, despite a strong anabolic response. Change in the p-ratio is a suitable parameter for use in studying the effect of disease on body composition because it allows transformation of such effects into a normal distribution across a wide range of baseline proportion between fat and protein mass.

Energy and calcium stores are preserved in girls and young women with CF, independent of disease severity: An explanation for the 'gender gap'?

Bioenergetics differ between males and females of many species. Human females apportion a substantial proportion of energy resources towards gynoid fat storage, to support the energetic burden of reproduction. Similarly, axial calcium accrual is favoured in females compared with males. Nutritional status is a prognostic indicator in cystic fibrosis (CF), but girls and young women are at greater risk of death despite equivalent nutritional status to males. The aim of this study was to compare fat (energy) and calcium stores (bone density) in males and females with CF over a spectrum of disease severity. Methods: Fat as % body weight (fat%) and lumbar spine (LS) and total body (TB) bone mineral density (BMD) were measured using dual absorption X-ray photometry in 127(59M) control and 101(54M) CF subjects, aged 9–25 years. An equation for predicted age at death had been determined using survival data and history of pulmonary function for the whole clinic, based on a trivariate normal model using maximum likelihood methods (1). For the CF group, a disease severity index (predicted age at death) was calculated from the derived equations according to each subjects history of pulmonary function, current age, and gender. Disease severity was classified according to percentile of predicted age at death (‘mild’ ≥75th, ‘moderate’ 25th–75th, ‘severe’ ≤25th percentile). Wt for age z-score was calculated. Serum testosterone and oestrogen were measured in males and females respectively. Fat% and LSBMD were compared between the groups using ANOVA. Results: There was an interaction between disease severity and gender: increasing disease severity was associated with greater deficits in TB (p=0.01), LSBMD (p

Modelling the distribution of stamp paper thickness via finite normal mixtures: The 1872 Hidalgo stamp issue of Mexico revisited

Izenman and Sommer (1988) used a non-parametric Kernel density estimation technique to fit a seven-component model to the paper thickness of the 1872 Hidalgo stamp issue of Mexico. They observed an apparent conflict when fitting a normal mixture model with three components with unequal variances. This conflict is examined further by investigating the most appropriate number of components when fitting a normal mixture of components with equal variances.

Distribution of transferrin saturation in an Australian population: Relevance to the early diagnosis of hemochromatosis

Background & Aims: An elevated transferrin saturation is the earliest phenotypic abnormality in hereditary hemochromatosis. Determination of transferrin saturation remains the most useful noninvasive screening test for affected individuals, but there is debate as to the appropriate screening level. The aims of this study were to estimate the mean transferrin saturation in hemochromatosis heterozygotes and normal individuals and to evaluate potential transferrin saturation screening levels. Methods: Statistical mixture modeling was applied to data from a survey of asymptomatic Australians to estimate the mean transferrin saturation in hemochromatosis heterozygotes and normal individuals. To evaluate potential transferrin saturation screening levels, modeling results were compared with data from identified hemochromatosis heterozygotes and homozygotes. Results: After removal of hemochromatosis homozygotes, two populations of transferrin saturation were identified in asymptomatic Australians (P < 0.01). In men, 88.2% of the truncated sample had a lower mean transferrin saturation of 24.1%, whereas 11.8% had an increased mean transferrin saturation of 37.3%. Similar results were found in women, A transferrin saturation threshold of 45% identified 98% of homozygotes without misidentifying any normal individuals. Conclusions: The results confirm that hemochromatosis heterozygotes form a distinct transferrin saturation subpopulation and support the use of transferrin saturation as an inexpensive screening test for hemochromatosis. In practice, a fasting transferrin saturation of greater than or equal to 45% identifies virtually all affected homozygous subjects without necessitating further investigation of unaffected normal individuals.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

The Fornax spectroscopic survey I. Survey strategy and preliminary results on the redshift distribution of a complete sample of stars and galaxies

The Fornax Spectroscopic Survey will use the Two degree Field spectrograph (2dF) of the Angle-Australian Telescope to obtain spectra for a complete sample of all 14000 objects with 16.5 less than or equal to b(j) less than or equal to 19.7 in a 12 square degree area centred on the Fornax Cluster. The aims of this project include the study of dwarf galaxies in the cluster (both known low surface brightness objects and putative normal surface brightness dwarfs) and a comparison sample of background field galaxies. We will also measure quasars and other active galaxies, any previously unrecognised compact galaxies and a large sample of Galactic stars. By selecting all objects-both stars and galaxies-independent of morphology, we cover a much larger range of surface brightness and scale size than previous surveys. In this paper we first describe the design of the survey. Our targets are selected from UK Schmidt Telescope sky survey plates digitised by the Automated Plate Measuring (APM) facility. We then describe the photometric and astrometric calibration of these data and show that the APM astrometry is accurate enough for use with the 2dF. We also describe a general approach to object identification using cross-correlations which allows us to identify and classify both stellar and galaxy spectra. We present results from the first 2dF field. Redshift distributions and velocity structures are shown for all observed objects in the direction of Fornax, including Galactic stars? galaxies in and around the Fornax Cluster, and for the background galaxy population. The velocity data for the stars show the contributions from the different Galactic components, plus a small tail to high velocities. We find no galaxies in the foreground to the cluster in our 2dF field. The Fornax Cluster is clearly defined kinematically. The mean velocity from the 26 cluster members having reliable redshifts is 1560 +/- 80 km s(-1). They show a velocity dispersion of 380 +/- 50 km s(-1). Large-scale structure can be traced behind the cluster to a redshift beyond z = 0.3. Background compact galaxies and low surface brightness galaxies are found to follow the general galaxy distribution.

Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

The effects of perfusion conditions on melphalan distribution in the isolated perfused rat hindlimb bearing a human melanoma xenograft

An isolated rat hindlimb perfusion model carrying xenografts of the human melanoma cell line MM96 was used to study the effects of perfusion conditions on melphalan distribution. Krebs-Henseleit buffer and Hartmann's solution containing 4.7% bovine serum albumin (BSA) or 2.8% dextran 40 were used as perfusates. Melphalan concentrations in perfusate, tumour nodules and normal tissues were measured using high-performance liquid chromatography (HPLC). Increasing the perfusion flow rates (from 4 to 8 mi min(-1)) resulted in higher tissue blood flow (determined with Cr-51-labelled microspheres) and melphalan uptake by tumour and normal tissues. me distribution of melphalan within tumour nodules and normal tissues was similar for both Krebs-Henseleit buffer and Hartmann's solution; however, tissue concentrations of melphalan were significantly higher for a perfusate containing 2.8% dextran 40 than for one containing 4.7% BSA. The melphalan concentration in the tumour was one-third of that found in the skin if the perfusate contained 4.7% BSA. In conclusion, this study has shown that a high perfusion flow enhances the delivery of melphalan into implanted tumour nodules and normal tissues, and a perfusate with low melphalan binding (no albumin) is preferred for maximum uptake of drug by the tumour.

Virus-specific CD8+ T lymphocytes within the normal human liver

The frequency and phenotype of human antiviral memory CD8(+) T cells in blood are well studied, yet little is known about their distribution within tissues. Analysis of antiviral CD8(+) T cell populations derived from a unique set of normal liver and blood samples identified a consistent population of virus-specific cells within the liver. In comparison to the circulating T cells, the liver-derived T cells were present at frequencies which were variably enriched compared to that in the blood, and showed significant differences with regard to the expression of CD45RA, CD45RO, CD95, CCR7, CD27 and CD28. The differences in these cell surface markers are consistent with a mature 'effector memory' phenotype of antigen-specific CD8(+) T cells within the liver. An enrichment of an activated subset of NKT cells (Valpha24/Vbeta11) was also observed, a finding which may be relevant to the regulation of the antiviral population:.

Hepatic pharmacokinetics of taurocholate in the normal and cholestatic rat liver

1 The disposition kinetics of [H-3] taurocholate ([H-3]TC) in perfused normal and cholestatic rat livers were studied using the multiple indicator dilution technique and several physiologically based pharmacokinetic models. 2 The serum biochemistry levels, the outflow profiles and biliary recovery of [H-3] TC were measured in three experimental groups: (i) control; (ii) 17α-ethynylestradiol (EE)-treated (low dose); and (iii) EE-treated (high dose) rats. EE treatment caused cholestasis in a dose-dependent manner. 3 A hepatobiliary TC transport model, which recognizes capillary mixing, active cellular uptake, and active efflux into bile and plasma described the disposition of [H-3]TC in the normal and cholestatic livers better than the other pharmacokinetic models. 4 An estimated five- and 18-fold decrease in biliary elimination rate constant, 1.7- and 2.7-fold increase in hepatocyte to plasma efflux rate constant, and 1.8- and 2.8-fold decrease in [H-3]TC biliary recovery ratio was found in moderate and severe cholestasis, respectively, relative to normal. 5 There were good correlations between the predicted and observed pharmacokinetic parameters of [H-3]TC based on liver pathophysiology (e.g. serum bilirubin level and biliary excretion of [H-3]TC). In conclusion, these results show that altered hepatic TC pharmacokinetics in cholestatic rat livers can be correlated with the relevant changes in liver pathophysiology in cholestasis.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.