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.

Numerical modelling of single-layer folding: clarification of an issue regarding the possible effect of computer codes and the influence of initial irregularities

The influence of initial perturbation geometry and material propel-ties on final fold geometry has been investigated using finite-difference (FLAC) and finite-element (MARC) numerical models. Previous studies using these two different codes reported very different folding behaviour although the material properties, boundary conditions and initial perturbation geometries were similar. The current results establish that the discrepancy was not due to the different computer codes but due to the different strain rates employed in the two previous studies (i.e. 10(-6) s(-1) in the FLAC models and 10(-14) s(-1) in the MARC models). As a result, different parts of the elasto-viscous rheological field were bring investigated. For the same material properties, strain rate and boundary conditions, the present results using the two different codes are consistent. A transition in Folding behaviour, from a situation where the geometry of initial perturbation determines final fold shape to a situation where material properties control the final geometry, is produced using both models. This transition takes place with increasing strain rate, decreasing elastic moduli or increasing viscosity (reflecting in each case the increasing influence of the elastic component in the Maxwell elastoviscous rheology). The transition described here is mechanically feasible but is associated with very high stresses in the competent layer (on the order of GPa), which is improbable under natural conditions. (C) 2000 Elsevier Science Ltd. All rights reserved.

Screening for abdominal aortic aneurysm: lessons from a population-based study

Objectives: To test the acceptability of screening and to identify modifiable risk factors for abdominal aortic aneurysm (AAA) in men. Design: A trial of ultrasound screening for AAA in a population-based random sample of men aged 65-83 years, and a cross-sectional case-control comparison of men in the same sample. Participants: 12203 men who had an ultrasound examination of their abdominal aorta, and completed a questionnaire covering demographic, behavioural and medical factors. Main outcome measures: Prevalence of AAA, and independent associations of AAA with demographic, medical and lifestyle factors. Results: Invitations to screening produced a corrected response of 70.5%. The prevalence of AAAs (> 30 mm) rose from 4.8% in men aged 65-69 years to 10.8% in those aged 80-83 years. The overall prevalence of large (> 50 mm) aneurysms was 0.69%. In a multivariate logistic model Mediterranean-born men had a 40% lower risk of AAA (> 30 mm) compared with men born in Australia (odds ratio [OR], 0.6; 95% CI, 0.4-0.8), while ex-smokers had a significantly increased risk of AAA (OR, 2.3; 95% CI, 1.9-2.8), and current smokers had even higher risks. AAA was significantly associated with established coronary and peripheral arterial disease and a waist:hip ratio greater than 0.9; men who regularly undertook vigorous exercise had a lower risk (OR, 0.8; 95% CI, 0.7-1.0). Conclusion: Ultrasound screening for AAA is acceptable to men in the likely target population. AAA shares some but not all of the risk factors for occlusive vascular disease, but the scope for primary prevention of AAA in later life is limited.

Dental set-vice provision in private general practice for an insured population in New South Wales, Australia

Objective To determine patterns of dental set-vices provided to a cohort of the insured population 18 years and over, in private general practice in New South Wales, Australia. Basic research design A cohort study using the person-years method and Poisson regression for analysis. Setting Data were derived from claims records submitted by members of a health insurance fund (Government Employees Health Fund-GEHF) for rebates during the study period 1 January 1992-31 December 1995. Participants There were 133,467 members aged 18 years and over from New South Wales. Main outcome measures To determine, by age group, for those members who used private general practice and made a claim (referred to as 'patients') the annual number of visits, total number of services received per year and number of services received at a visit, Results The mean number of visits per patient was 2.4 per year with patients under 45 years making fewer visits than the 45-54 age group reference category. Mean number of services utilised per patient-year was 5.9, with services provided increasing from 3.5 for the 18-24-year-old group, reaching a plateau of approximately 6.2 for those aged 45 years or more. The number of services received per visit was 2.4 and there were no differences by age. Service mix was dominated by restorative (35%), diagnostic (27%), and preventive services (18%); with age specific variations observed. Conclusions Age was found to be an important determinant in the use of dental services, independent of membership duration and gender.

Review of "Comorbidity, disability and the need for treatment for DSM-IV psychiatric disorders in an insured population"

Background: This study presents estimates of 12 month and current prevalences of DSM-IV disorders, and the related comor-bidity, disability and service utilization, derived from a national probability sample in Australia. Methods: The DSM-IV psychiatric disorders among persons aged 18 and over in the Australian population were assessed with data collected by lay interviewers using the Composite International Diagnostic Interview, other screening interviews and measures of disability and service utilization. The response rate was 78.1% and the final sample size was 10,641 adults. Results: Close to 20% reported at least one twelve month disorder and 13% a disorder current within the past 30 days. ICD-10 diagnoses were also derived, DSM-IV was the more conservative classification whether or not the new clinical significance criteria was applied. Major depression, any personality disorder, and alcohol dependence were the three most common twelve month disorders, generalized anxiety disorder replaced alcohol dependence as the third most common current disorder. The sexes has similar rates of any disorder, but women had higher rates of affective and anxiety disorders, men higher rates of substance use disorders. Prevalence of most disorders declined with age and education, and were lower among those employed or married. Respondents whose symptoms met criteria for three or more disorders in the past year had greatly increased rates of disability and of mental health consultations. The affective and somatoform disorders were associated with the highest rates of disability. Only 36% of people with a mental disorder this year had consulted for a mental problem, and most had seen a general practitioner. We identified those with a current disorder who were disabled or multiply comorbid - only half had consulted and of those who had not, more than half said they did not need treatment. Conclusions: The 12 month prevalence was lower than reported in the US National Comorbidity Survey but method factors might account for this. The relationships between prevalence and demographic variables, and between comorbidity, disability and service utilization were similar to those found in the US survey. Australia has a national health insurance scheme with total coverage and access to medical help is available to all, commonly at little or no cost. We identify the high rate of not consulting among those with a current disorder, and additional disability or multiple comorbidity, as an important public health problem. Kessler argued for more research on barriers to professional help seeking. This report reinforces his conclusion and shows that economic barriers are not the dominant issue.

Hybrid modelling of coupled pore fluid-solid deformation problems

A hybrid formulation for coupled pore fluid-solid deformation problems is proposed. The scheme is a hybrid in the sense that we use a vertex centered finite volume formulation for the analysis of the pore fluid and a particle method for the solid in our model. The pore fluid formally occupies the same space as the solid particles. The size of the particles is not necessarily equal to the physical size of materials. A finite volume mesh for the pore fluid flow is generated by Delaunay triangulation. Each triangle possesses an initial porosity. Changes of the porosity are specified by the translations of the mass centers of particles. Net pore pressure gradients are applied to the particle centers and are considered in the particle momentum balance. The potential of our model is illustrated by means of a simulation of coupled fracture and fluid flow developed in porous rock under biaxial compression condition.

A model for predicting the future incidence of coronary heart disease within percentiles of coronary heart disease risk

Background We present a method (The CHD Prevention Model) for modelling the incidence of fatal and nonfatal coronary heart disease (CHD) within various CHD risk percentiles of an adult population. The model provides a relatively simple tool for lifetime risk prediction for subgroups within a population. It allows an estimation of the absolute primary CHD risk in different populations and will help identify subgroups of the adult population where primary CHD prevention is most appropriate and cost-effective. Methods The CHD risk distribution within the Australian population was modelled, based on the prevalence of CHD risk, individual estimates of integrated CHD risk, and current CHD mortality rates. Predicted incidence of first fatal and nonfatal myocardial infarction within CHD risk strata of the Australian population was determined. Results Approximately 25% of CHD deaths were predicted to occur amongst those in the top 10 percentiles of integrated CHD risk, regardless of age group or gender. It was found that while all causes survival did not differ markedly between percentiles of CHD risk before the ages of around 50-60, event-free survival began visibly to differ about 5 years earlier. Conclusions The CHD Prevention Model provides a means of predicting future CHD incidence amongst various strata of integrated CHD risk within an adult population. It has significant application both in individual risk counselling and in the identification of subgroups of the population where drug therapy to reduce CHD risk is most cost-effective. J Cardiovasc Risk 8:31-37 (C) 2001 Lippincott Williams & Wilkins.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Hormonal factors and risk of aneurysmal subarachnoid hemorrhage - An international population-based, case-control study

Background and Purpose-Subarachnoid hemorrhage (SAH) is more common in women than in men, but the role of hormonal factors in its etiology remains uncertain. The aim of this study was to examine the relationship between hormonal factors and risk of SAH in women. Methods-This was a prospective, multicenter, population-based, case-control study performed in 4 major urban centers in Australia and New Zealand. Two hundred sixty-eight female cases of first-ever aneurysmal SAH occurred during 1995-1998. Controls were 286 frequency-matched women from the general population of each center. Outcome measures included risk of SAH associated with use of oral contraceptive pills (OCPs), hormone replacement therapy (HRT), and various endogenous hormonal factors including menstrual patterns, parity, age at birth of first child, and breast-feeding practices. Results-Cases and controls did not differ with regard to menstrual and reproductive history except in age at bir th of first child, where older age was associated with reduced risk of SAH (odds ratio [OR], 0.63; 95% CI, 0.43, 0.91). Relative to never use of HRT, the adjusted OR for over use of HRT was 0.64 (95% CI, 0.41, 0.98), which did not alter significantly after further adjustment for possible confounding factors. Borderline evidence of an inverse association was detected for past use of HRT (adjusted OR, 0.59; 95% CI, 0.30, 1.13) and current use of HRT (adjusted OR, 0.67; 95% CI, 0.40, 1.13), but there was no evidence of an association for use of OCPs (adjusted OR, 0.97; 95% CI, 0.58, 1.60). Conclusions-The risks of SAH are lower in women whose first pregnancy is at an older age and women who have ever used HRT but not OCPs. The findings suggest an independent etiologic role for hormonal factors in the pathogenesis of aneurysmal SAH and provide support for a protective role fur HRT on risk of SAH in postmenopausal women.

Initial results of ultrasound screening for aneurysm of the abdominal aorta in Western Australia: relevance for endoluminal treatment of aneurysm disease

Background. Increased life expectancy in men during the last thirty years is largely due to the decrease in mortality from cardiovascular disease in the age group 29-69 yr. This change has resulted in a change in the disease profile of the population with conditions such as aneurysm of the abdominal aorta (AAA) becoming more prevalent. The advent of endoluminal treatment for AAA has encouraged prophylactic intervention and fuelled the argument to screen for the disease. The feasibility of inserting an endoluminal graft is dependent on the morphology and growth characteristics of the aneurysm. This study used data from a randomized controlled trial of ultrasound screening for AAA in men aged 65-83 yr in Western Australia for the purpose of determining the norms of the living anatomy in the pressurized infrarenal aorta. Aims. To examine (1) the diameters of the infra-renal aorta in aneurysmal and non-aneurysmal cases, (2) the implications for treatment modalities, with particular reference to endoluminal grafting, which is most dependent on normal and aneurysmal morphology, and (3) any evidence to support the notion that northern Europeans are predisposed to aneurysmal disease. Methods. Using ultrasound, a randomized control trial was established in Western Australia to assess the value of a screening program in males aged 65-83 yr, The infra-renal aorta was defined as aneurysmal if the maximum diameter was 30 mm or more. Aortic diameter was modelled both as a continuous tin mm) and as a binary outcome variable, for those men who had an infra-renal diameter of 30 mm or more. ANOVA and linear regression were used for modelling aortic diameter as a continuum, while chi-square analysis and logistic regression were used in comparing men with and without the diagnosis of AAA. Findings. By December 1998, of 19.583 men had been invited to undergo ultrasound screening for AAA, 12.203 accepted the invitation (corrected response fraction 70.8%). The prevalence of AAA increased with age from 4.8% at 65 yr to 10.8% at 80 yr (chi (2) = 77.9, df = 3, P<0.001). The median (IQR) diameter for the non-aneurysmal group was 21.4 mm (3.3 mm) and there was an increase (<chi>(2) = 76.0, df = 1, P<0.001) in the diameter of the infra-renal aorta with age. Since 27 mm is the 95th centile for the non-aneurysmal infra-renal aorta, a diameter of 30 mm or more is justified as defining an aneurysm. The risk of AAA was higher in men of Australian (OR = 1.0) and northern European origin (OR = 1.0, 95%CL: 0.9. 1.2) compared with those of Mediterranean origin (OR = 0.5, 99%CL: 0.4, 0.7). Conclusion. Although screening has not yet been shown to reduce mortality from AAA. these population-based data assist the understanding of aneurysmal disease and the further development and use of endoluminal grafts for this condition. (C) 2001 Published by Elsevier Science Ltd on behalf of The International Society for Cardiovascular Surgery.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.