A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

A mixture model-based approach to the clustering of microarray expression data

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

Estimating Two-Stage Models for Genetic Influences on Alcohol, Tobacco or Drug Use Initiation and Dependence Vulnerability in Twin and Family Data

Genetic research on risk of alcohol, tobacco or drug dependence must make allowance for the partial overlap of risk-factors for initiation of use, and risk-factors for dependence or other outcomes in users. Except in the extreme cases where genetic and environmental risk-factors for initiation and dependence overlap completely or are uncorrelated, there is no consensus about how best to estimate the magnitude of genetic or environmental correlations between Initiation and Dependence in twin and family data. We explore by computer simulation the biases to estimates of genetic and environmental parameters caused by model misspecification when Initiation can only be defined as a binary variable. For plausible simulated parameter values, the two-stage genetic models that we consider yield estimates of genetic and environmental variances for Dependence that, although biased, are not very discrepant from the true values. However, estimates of genetic (or environmental) correlations between Initiation and Dependence may be seriously biased, and may differ markedly under different two-stage models. Such estimates may have little credibility unless external data favor selection of one particular model. These problems can be avoided if Initiation can be assessed as a multiple-category variable (e.g. never versus early-onset versus later onset user), with at least two categories measurable in users at risk for dependence. Under these conditions, under certain distributional assumptions., recovery of simulated genetic and environmental correlations becomes possible, Illustrative application of the model to Australian twin data on smoking confirmed substantial heritability of smoking persistence (42%) with minimal overlap with genetic influences on initiation.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Testing insect movement theory: empirical analysis of pest data routinely collected from agricultural crops

Observations of an insect's movement lead to theory on the insect's flight behaviour and the role of movement in the species' population dynamics. This theory leads to predictions of the way the population changes in time under different conditions. If a hypothesis on movement predicts a specific change in the population, then the hypothesis can be tested against observations of population change. Routine pest monitoring of agricultural crops provides a convenient source of data for studying movement into a region and among fields within a region. Examples of the use of statistical and computational methods for testing hypotheses with such data are presented. The types of questions that can be addressed with these methods and the limitations of pest monitoring data when used for this purpose are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Petrology and geochemistry of the Bandas del Sur Formation, Las Canadas Edifice, Tenerife (Canary Islands)

The Bandas del Sur Formation preserves a Quaternary extra-caldera record of central phonolitic explosive volcanism of the Las Canadas volcano at Tenerife. Volcanic rocks are bimodal in composition, being predominantly phonolitic pyroclastic deposits, several eruptions of which resulted in summit caldera collapse, alkali basaltic lavas erupted from many fissures around the flanks. For the pyroclastic deposits, there is a broad range of pumice glass compositions from phonotephrite to phonolite. The phonolite pyroclastic deposits are also characterized by a diverse, 7-8-phase phenocryst assemblage (alkali feldspar + biotite + sodian diopside + titanomagnetite + ilmenite + nosean-hauyne + titanite + apatite) with alkali feldspar dominant, in contrast to interbedded phonolite lavas that typically have lower phenocryst contents and lack hydrous phases. Petrological and geochemical data are consistent with fractional crystallization (involving the observed phenocryst assemblages) as the dominant process in the development of phonolite magmas. New stratigraphically constrained data indicate that petrological and geochemical differences exist between pyroclastic deposits of the last two explosive cycles of phonolitic volcanism. Cycle 2 (0.85-0.57 Ma) pyroclastic fall deposits commonly show a cryptic compositional zonation indicating that several eruptions tapped chemically, and probably thermally stratified magma systems. Evidence for magma mixing is most widespread in the pyroclastic deposits of Cycle 3 (0.37-0.17 Ma), which includes the presence of reversely and normally zoned phenocrysts, quenched mafic glass blebs in pumice, banded pumice, and bimodal to polymodal phenocryst compositional populations. Syn-eruptive mixing events involved mostly phonolite and tephriphonolite magmas, whereas a pre-eruptive mixing event involving basaltic magma is recorded in several banded pumice-bearing ignimbrites of Cycle 3. The periodic addition and mixing of basaltic magma ultimately may have triggered several eruptions. Recharge and underplating by basaltic magma is interpreted to have elevated sulphur contents (occurring as an exsolved gas phase) in the capping phonolitic magma reservoir. This promoted nosean-hauyne crystallization over nepheline, elevated SO3 contents in apatite, and possibly resulted in large, climatologically important SO2 emissions.

Phase equilibrium data and liquidus for the system "MnO"-CaO-(Al2O3+SiO2) at Al2O3/SiO2 of 0.41

Phase-equilibrium data and the liquidus for the system. "MnO"-CaO-(Al2O3-SiO2) at a manganese-rich alloy saturation have been determined in the temperature range from 1423 to 1723 K. The results are presented in the form of a pseudoternary section "MnO"-CaO-(Al2O3 + SiO2) with an Al2O3/SiO2 weight ratio of 0.41. The following primary phases are present in the range of conditions investigated:, 3Al(2)O(3).2SiO(2); SiO2; MnO.Al2O3-2SiO(2); (Mn,Ca)O.SiO2; 2(Mn,Ca)O.SiO2; MnO.Al2O3; (Mn,Ca)O; alpha-2CaO.SiO2; alpha'-2CaO.SiO2; 2CaO.Al2O3.SiO2; CaO.SiO2, and CaO.Al2O3.2SiO(2). The presence of alumina in this system is shown to have a significant effect on the liquidus compared to the system "MnO"-CaO-SiO2, leading to, the stabilization of the anorthite and gehlenite phases.

Alcohol, tobacco and breast cancer - collaborative reanalysis of individual data from 53 epidemiological studies, including 58 515 women with breast cancer and 95 067 women without the disease

Alcohol and tobacco consumption are closely correlated and published results on their association with breast cancer have not always allowed adequately for confounding between these exposures. Over 80% of the relevant information worldwide on alcohol and tobacco consumption and breast cancer were collated, checked and analysed centrally. Analyses included 58515 women with invasive breast cancer and 95067 controls from 53 studies. Relative risks of breast cancer were estimated, after stratifying by study, age, parity and, where appropriate, women's age when their first child was born and consumption of alcohol and tobacco. The average consumption of alcohol reported by controls from developed countries was 6.0 g per day, i.e. about half a unit/drink of alcohol per day, and was greater in ever-smokers than never-smokers, (8.4 g per day and 5.0 g per day, respectively). Compared with women who reported drinking no alcohol, the relative risk of breast cancer was 1.32 (1.19 - 1.45, P < 0.00001) for an intake of 35 - 44 g per day alcohol, and 1.46 (1.33 - 1.61, P < 0.00001) for greater than or equal to 45 g per day alcohol. The relative risk of breast cancer increased by 7.1% (95% CI 5.5-8.7%; P