Mixture modelling for cluster analysis

Cluster analysis via a finite mixture model approach is considered. With this approach to clustering, the data can be partitioned into a specified number of clusters g by first fitting a mixture model with g components. An outright clustering of the data is then obtained by assigning an observation to the component to which it has the highest estimated posterior probability of belonging; that is, the ith cluster consists of those observations assigned to the ith component (i = 1,..., g). The focus is on the use of mixtures of normal components for the cluster analysis of data that can be regarded as being continuous. But attention is also given to the case of mixed data, where the observations consist of both continuous and discrete variables.

Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm. to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker. demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.

Magnetic resonance imaging analysis of the upper cervical spine extensor musculature in an asymptomatic cohort: an index of fat within muscle

AIM: To establish a simple method to quantify muscle/fat constituents in cervical muscles of asymptomatic women using magnetic resonance imaging (MRI), and to determine whether there is an age effect within a defined age range. MATERIALS AND METHODS: MRI of the upper cervical spine was performed for 42 asymptomatic women aged 18-45 years. The muscle and fat signal intensities on axial spin echo T1-weighted images were quantitatively classified by taking a ratio of the pixel intensity profiles of muscle against those of intermuscular fat for the rectus capitis posterior major and minor and inferior obliquus capitis muscles bilaterally. Inter- and intra-examiner agreement was scrutinized. RESULTS: The average relative values of fat within the upper cervical musculature compared with intermuscular fat indicated that there were only slight variations in indices between the three sets of muscles. There was no significant correlation between age and fat indices. There were significant differences for the relative fat within the muscle compared with intermuscular fat and body mass index for the right rectus capitis posterior major and right and left inferior obliquus capitis muscles (p = 0.032). Intraclass correlation coefficients for intraobserver agreement ranged from 0.94 to 0.98. Inter-rater agreement of the measurements ranged from 0.75 to 0.97. CONCLUSION: A quantitative measure of muscle/fat constituents has been developed, and results of this study indicate that relative fatty infiltration is not a feature of age in the upper cervical extensor muscles of women aged 18-45 years. (C) 2005 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.

Cold periods and coronary events: an analysis of populations worldwide

Study objective: To investigate the association between cold periods and coronary events, and the extent to which climate, sex, age, and previous cardiac history increase risk during cold weather. Design: A hierarchical analyses of populations from the World Health Organisation's MONICA project. Setting: Twenty four populations from the WHO's MONICA project, a 21 country register made between 1980 and 1995. Patients: People aged 35 - 64 years who had a coronary event. Main results: Daily rates of coronary events were correlated with the average temperature over the current and previous three days. In cold periods, coronary event rates increased more in populations living in warm climates than in populations living in cold climates, where the increases were slight. The increase was greater in women than in men, especially in warm climates. On average, the odds for women having an event in the cold periods were 1.07 higher than the odds for men (95% posterior interval: 1.03 to 1.11). The effects of cold periods were similar in those with and without a history of a previous myocardial infarction. Conclusions: Rates of coronary events increased during comparatively cold periods, especially in warm climates. The smaller increases in colder climates suggest that some events in warmer climates are preventable. It is suggested that people living in warm climates, particularly women, should keep warm on cold days.

Analysis of population pharmacokinetic data using NONMEM and WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.

Expression analysis of the Epha1 receptor tyrosine kinase and its high-affinity ligands Efna1 and Efna3 during early mouse development

Interaction of Eph receptor tyrosine kinases with their membrane bound ephrin ligands initiates bidirectional signaling events that regulate cell migratory and adhesive behavior. Whole-mount in situ hybridization revealed overlapping expression of the Epha1 receptor and its high-affinity ligands ephrin A1 (Efna1) and ephrin A3 (Efna3) in the primitive streak and the posterior paraxial mesoderm during early mouse development. These results show complex and dynamic expression for all three genes with expression domains that are successively complementary, overlapping, and divergent. (c) 2006 Elsevier B.V. All rights reserved.

Bayesian population pharmacokinetic analysis of sirolimus

Objective: It is usual that data collected from routine clinical care is sparse and unable to support the more complex pharmacokinetic (PK) models that may have been reported in previous rich data studies. Informative priors may be a pre-requisite for model development. The aim of this study was to estimate the population PK parameters of sirolimus using a fully Bayesian approach with informative priors. Methods: Informative priors including prior mean and precision of the prior mean were elicited from previous published studies using a meta-analytic technique. Precision of between-subject variability was determined by simulations from a Wishart distribution using MATLAB (version 6.5). Concentration-time data of sirolimus retrospectively collected from kidney transplant patients were analysed using WinBUGS (version 1.3). The candidate models were either one- or two-compartment with first order absorption and first order elimination. Model discrimination was based on computation of the posterior odds supporting the model. Results: A total of 315 concentration-time points were obtained from 25 patients. Most data were clustered at trough concentrations with range of 1.6 to 77 hours post-dose. Using informative priors, either a one- or two-compartment model could be used to describe the data. When a one-compartment model was applied, information was gained from the data for the value of apparent clearance (CL/F = 18.5 L/h), and apparent volume of distribution (V/F = 1406 L) but no information was gained about the absorption rate constant (ka). When a two-compartment model was fitted to the data, the data were informative about CL/F, apparent inter-compartmental clearance, and apparent volume of distribution of the peripheral compartment (13.2 L/h, 20.8 L/h, and 579 L, respectively). The posterior distribution of the volume distribution of central compartment and ka were the same as priors. The posterior odds for the two-compartment model was 8.1, indicating the data supported the two-compartment model. Conclusion: The use of informative priors supported the choice of a more complex and informative model that would otherwise have not been supported by the sparse data.

ESTUDO COMPARATIVO DA POSIÇÃO ÂNTERO POSTERIOR DOS PRIMEIROS MOLARES INFERIORES NO TRATAMENTO ORTODÔNTICO, UTILIZANDO AS TÉCNICAS STRAIGHT-WIRE E EDGEWISE, EM CASOS DE MÁ OCLUSÃO DE CLASSE I DE ANGLE, COM EXTRAÇÃO DE PRIMEIROS PRÉ-MOLARES

Este estudo avaliou o posicionamento ântero posterior dos primeiros molares inferiores, durante o tratamento ortodôntico, utilizando o arco lingual inferior como acessório de ancoragem na técnica Straight-Wire, em comparação aos casos tratados pela técnica Edgewise, sem a utilização do arco lingual. Dois grupos foram selecionados, ambos apresentando má oclusão de Classe I de Angle7, tratados com extração dos primeiros pré-molares superiores e inferiores. Foi utilizada uma amostra de 255 telerradiografias em norma lateral, obtidas de pacientes brasileiros, de ambos os sexos, com média de idade de 13 anos e 6 meses e com diferentes padrões de crescimento facial. Embasado na análise e discussão dos resultados, concluiu-se que: 1) do início do tratamento ao fim da fase de nivelamento, a perda de ancoragem coronária do primeiro molar inferior foi maior nos casos tratados com a técnica Straight-Wire; 2) do fim da fase de nivelamento ao fim do tratamento, a perda de ancoragem coronária e radicular do primeiro molar inferior foi maior na técnica Edgewise; 3) do início ao fim tratamento a perda de ancoragem radicular foi maior nos pacientes tratados com a técnica Edgewise; e 4) o deslocamento ântero-posterior dos incisivos inferiores não apresentou diferença estatisticamente significante para ambas as técnicas, em todas as etapas observadas.(AU)

AVALIAÇÃO DAS ALTERAÇÕES NA SOBREMORDIDA E NAS ALTURAS FACIAIS ANTERIOR E POSTERIOR, DECORRENTES DO TRATAMENTO ORTODÔNTICO COM EXTRAÇÃO DE PRÉ-MOLARES, EM PACIENTES COM DIFERENTES TIPOS FACIAIS.

O presente estudo investigou as alterações no trespasse vertical e na altura facial ântero-inferior em pacientes com má-oclusão de Classe I e diferentes tipos faciais com apinhamento submetidos a extração de quatro pré-molares, no pré e pós-tratamento ortodôntico. Foram selecionadas telerradiografias em norma lateral de 36 indivíduos na faixa etária de 12 anos e 2 meses a 16 anos e 5 meses, que realizaram o tratamento ortodôntico com o emprego de aparelho pré-ajustado Straight Wire..Para a análise as medidas utilizadas foram AFA, AFAI, AFP, FMA, SN.GoGn, além de medidas lineares descritas por Hans et al. As alterações nas alturas faciais anterior, antero-inferior e posterior foram similares nos três grupos estudados, apresentando aumento ao final do tratamento ortodôntico, porém sem significância estatística nas alturas faciais anteriores no grupo dos braquifaciais. Em FMA, foram estatisticamente significantes apenas para os braquifaciais e de SN.GoGn para braqui e dolicofaciais. Quanto às medidas lineares de Hans verificou-se que o grupo dos braquifaciais apresentou aumento estatisticamente significante em TLI e MNSK, no grupo dos mesofaciais, o mesmo ocorreu em BUI e MNSK e nos dolicofaciais todas as medidas exceto TUI apresentaram aumento significativo. Em todos os grupos foi observada uma diminuição da sobremordida.(AU)

Neuropathological heterogeneity in Alzheimer's disease:A study of 80 cases using principal components analysis

Three hypotheses have been proposed to explain neuropathological heterogeneity in Alzheimer's disease (AD): the presence of distinct subtypes ('subtype hypothesis'), variation in the stage of the disease ('phase hypothesis') and variation in the origin and progression of the disease ('compensation hypothesis'). To test these hypotheses, variation in the distribution and severity of senile plaques (SP) and neurofibrillary tangles (NFT) was studied in 80 cases of AD using principal components analysis (PCA). Principal components analysis using the cases as variables (Q-type analysis) suggested that individual differences between patients were continuously distributed rather than the cases being clustered into distinct subtypes. In addition, PCA using the abundances of SP and NFT as variables (R-type analysis) suggested that variations in the presence and abundance of lesions in the frontal and occipital lobes, the cingulate gyrus and the posterior parahippocampal gyrus were the most important sources of heterogeneity consistent with the presence of different stages of the disease. In addition, in a subgroup of patients, individual differences were related to apolipoprotein E (ApoE) genotype, the presence and severity of SP in the frontal and occipital cortex being significantly increased in patients expressing apolipoprotein (Apo)E allele ε4. It was concluded that some of the neuropathological heterogeneity in our AD cases may be consistent with the 'phase hypothesis'. A major factor determining this variation in late-onset cases was ApoE genotype with accelerated rates of spread of the pathology in patients expressing allele ε4.

Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

The influence of posterior corneal surface astigmatism on residual astigmatism

It has often been found that corneal astigmatism exceeds the amount exhibited by the eye as a whole. This difference is usually referred to as residual astigmatism. Scrutiny of the studies of corneal astigmatismreveal that what has actually been measured is the astigmatic contributionof the anterior corneal surface alone. This anterior surface is easily measured whereas measurement of the posterior corneal surface is much more difficult. A method was therefore developed to measure the radius and toricity of the posterior corneal surface. The method relies upon photography of the first and second Purkinje images in three fixed meridians. Keratometry, comparison of anterior and posterior corneal Purkinje images and pachometricdata were applied to three meridional analysis equations, allowing the posterior corneal surface to be described in sphero-cylindrical form. Measurements were taken from 80 healthy subjects from two distinct age groups. The first consisted of 60 young subjects, mean age 22.04 years and the second consisted of 20 old subjects, mean age 74.64 years. The young group consisted of 28 myopes, 24 emmetropes and 8 hyperopes. The old group consisted of 6 myopes and 14 hyperopes. There was an equal number of males and females in each group. These groupings allowed the study of the effects of age, ametropia and gender on the posterior corneal toricity. The effect of the posterior corneal surface on residual astigmatism was assessed and was found to cause an overall reduction. This reduction was due primarily to the posterior corneal surface being consistently steeper relative to the anterior surface in the vertical meridian compared to the horizontal meridian.

Multispectral retinal image analysis:a novel non-invasive tool for retinal imaging

Purpose-To develop a non-invasive method for quantification of blood and pigment distributions across the posterior pole of the fundus from multispectral images using a computer-generated reflectance model of the fundus. Methods - A computer model was developed to simulate light interaction with the fundus at different wavelengths. The distribution of macular pigment (MP) and retinal haemoglobins in the fundus was obtained by comparing the model predictions with multispectral image data at each pixel. Fundus images were acquired from 16 healthy subjects from various ethnic backgrounds and parametric maps showing the distribution of MP and of retinal haemoglobins throughout the posterior pole were computed. Results - The relative distributions of MP and retinal haemoglobins in the subjects were successfully derived from multispectral images acquired at wavelengths 507, 525, 552, 585, 596, and 611?nm, providing certain conditions were met and eye movement between exposures was minimal. Recovery of other fundus pigments was not feasible and further development of the imaging technique and refinement of the software are necessary to understand the full potential of multispectral retinal image analysis. Conclusion - The distributions of MP and retinal haemoglobins obtained in this preliminary investigation are in good agreement with published data on normal subjects. The ongoing development of the imaging system should allow for absolute parameter values to be computed. A further study will investigate subjects with known pathologies to determine the effectiveness of the method as a screening and diagnostic tool.

Quantitative analysis of multi-spectral fundus images

We have developed a new technique for extracting histological parameters from multi-spectral images of the ocular fundus. The new method uses a Monte Carlo simulation of the reflectance of the fundus to model how the spectral reflectance of the tissue varies with differing tissue histology. The model is parameterised by the concentrations of the five main absorbers found in the fundus: retinal haemoglobins, choroidal haemoglobins, choroidal melanin, RPE melanin and macular pigment. These parameters are shown to give rise to distinct variations in the tissue colouration. We use the results of the Monte Carlo simulations to construct an inverse model which maps tissue colouration onto the model parameters. This allows the concentration and distribution of the five main absorbers to be determined from suitable multi-spectral images. We propose the use of "image quotients" to allow this information to be extracted from uncalibrated image data. The filters used to acquire the images are selected to ensure a one-to-one mapping between model parameters and image quotients. To recover five model parameters uniquely, images must be acquired in six distinct spectral bands. Theoretical investigations suggest that retinal haemoglobins and macular pigment can be recovered with RMS errors of less than 10%. We present parametric maps showing the variation of these parameters across the posterior pole of the fundus. The results are in agreement with known tissue histology for normal healthy subjects. We also present an early result which suggests that, with further development, the technique could be used to successfully detect retinal haemorrhages.

A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.