Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

Model-based clustering in gene expression microarrays: An application to breast cancer data

In microarray studies, the application of clustering techniques is often used to derive meaningful insights into the data. In the past, hierarchical methods have been the primary clustering tool employed to perform this task. The hierarchical algorithms have been mainly applied heuristically to these cluster analysis problems. Further, a major limitation of these methods is their inability to determine the number of clusters. Thus there is a need for a model-based approach to these. clustering problems. To this end, McLachlan et al. [7] developed a mixture model-based algorithm (EMMIX-GENE) for the clustering of tissue samples. To further investigate the EMMIX-GENE procedure as a model-based -approach, we present a case study involving the application of EMMIX-GENE to the breast cancer data as studied recently in van 't Veer et al. [10]. Our analysis considers the problem of clustering the tissue samples on the basis of the genes which is a non-standard problem because the number of genes greatly exceed the number of tissue samples. We demonstrate how EMMIX-GENE can be useful in reducing the initial set of genes down to a more computationally manageable size. The results from this analysis also emphasise the difficulty associated with the task of separating two tissue groups on the basis of a particular subset of genes. These results also shed light on why supervised methods have such a high misallocation error rate for the breast cancer data.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Adsorption in mesopores: A molecular-continuum model with application to MCM-41

The classical model of surface layering followed by capillary condensation during adsorption in mesopores, is modified here by consideration of the adsorbate solid interaction potential. The new theory accurately predicts the capillary coexistence curve as well as pore criticality, matching that predicted by density functional theory. The model also satisfactorily predicts the isotherm for nitrogen adsorption at 77.4 K on MCM-41 material of various pore sizes, synthesized and characterized in our laboratory, including the multilayer region, using only data on the variation of condensation pressures with pore diameter. The results indicate a minimum mesopore diameter for the surface layering model to hold as 14.1 Å, below which size micropore filling must occur, and a minimum pore diameter for mechanical stability of the hemispherical meniscus during desorption as 34.2 Å. For pores in-between these two sizes reversible condensation is predicted to occur, in accord with the experimental data for nitrogen adsorption on MCM-41 at 77.4 K.

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the 'state-space' and 'parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-dispersion model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

The Three-dimensional Solution Structure of NaD1, a New Floral Defensin from Nicotiana alata and its Application to a Homology Model of the Crop Defense Protein alfAFP

NMR spectroscopy and simulated annealing calculations have been used to determine the three-dimensional structure of NaD1, a novel antifungal and insecticidal protein isolated from the flowers of Nicotiana alata. NaD1 is a basic, cysteine-rich protein of 47 residues and is the first example of a plant defensin from flowers to be characterized structurally. Its three-dimensional structure consists of an a-helix and a triple-stranded anti-parallel beta-sheet that are stabilized by four intramolecular disulfide bonds. NaD1 features all the characteristics of the cysteine-stabilized up motif that has been described for a variety of proteins of differing functions ranging from antibacterial insect defensins and ion channel-perturbing scorpion toxins to an elicitor of the sweet taste response. The protein is biologically active against insect pests, which makes it a potential candidate for use in crop protection. NaD1 shares 31% sequence identity with alfAFP, an antifungal protein from alfalfa that confers resistance to a fungal pathogen in transgenic potatoes. The structure of NaD1 was used to obtain a homology model of alfAFP, since NaD1 has the highest level of sequence identity with alfAFP of any structurally characterized antifungal defensin. The structures of NaD1 and alfAFP were used in conjunction with structure - activity data for the radish defensin Rs-AFP2 to provide an insight into structure-function relationships. In particular, a putative effector site was identified in the structure of NaD1 and in the corresponding homology model of alfAFP. (C) 2002 Elsevier Science Ltd. All rights reserved.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Finite mixture regression model with random effects: application to neonatal hospital length of stay

A two-component mixture regression model that allows simultaneously for heterogeneity and dependency among observations is proposed. By specifying random effects explicitly in the linear predictor of the mixture probability and the mixture components, parameter estimation is achieved by maximising the corresponding best linear unbiased prediction type log-likelihood. Approximate residual maximum likelihood estimates are obtained via an EM algorithm in the manner of generalised linear mixed model (GLMM). The method can be extended to a g-component mixture regression model with the component density from the exponential family, leading to the development of the class of finite mixture GLMM. For illustration, the method is applied to analyse neonatal length of stay (LOS). It is shown that identification of pertinent factors that influence hospital LOS can provide important information for health care planning and resource allocation. (C) 2002 Elsevier Science B.V. All rights reserved.

A carbon activation model with application to longan seed char gasification

In this paper a new structural model is presented to describe the evolution of porosity of char during the gasification process. The model assumes the char structure to be composed of bundles of parallel graphite layers, and the reactivities of each layer with the gasification agent are assumed to be different to represent the different degree of heterogeneity of each layer (i.e. each layer will react with the gasification agent at a different rate). It is this difference in the reactivity that allows micropores to be created during the course of gasification. This simple structural model enables the evolution of pore volume, pore geometrical surface area and the pore size distribution to be described with respect to the extent of char burn-off. The model is tested against the experimental data of gasification of longan seed-derived char with carbon dioxide and it is found that the agreement between the model and the data is reasonably satisfactory, especially the evolution of surface area and pore volume with burn-off.

Edge-to-edge matching and its applications - Part II. Application to Mg-Al, Mg-Y and Mg-Mn alloys

A model for the crystallography and morphology of diffusion-controlled phase transformations - edge-to-edge matching - has been used to predict the orientation relationships (OR) and habit planes of precipitates Mg17Al12 in Mg-Al alloy, Mg24Y5 in Mg-Y alloy and alpha-Mn in Mg-Mn alloy. Based on the crystal structures and lattice parameters only, the model predicts that the possible ORs between Mg17Al12 and Mg matrix are the near Burgers OR, the Potter OR, the Gjonnes-Ostmoe OR and the Crawley OR. In the Mg-Y alloy, the OR between Mg24Y5 precipitates and the Mg matrix is predicted to be the Burgers OR only. The model also predicts that there are no reproducible ORs between alpha-Mn and Mg in the Mg-Mn alloy. Combining the edge-to-edge matching model and W. Zhang's Deltag approach, the habit plane and side facets of the precipitate for each OR can be determined. All the predicted ORs and the corresponding habit planes in Mg-Al and Mg-Y alloys agree very well with the experimental results. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 1. Description of the model and its application to the MgO, MgO-SiO2, Al2O3-MgO and CaO-MgO sub-systems

A structurally-based quasi-chemical viscosity model for fully liquid slags in the Al2O3 CaO-'FeO'-MgO-SiO2 system has been developed. The model links the slag viscosities to the internal structures of the melts through the concentrations of various Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of these structural units are derived from a quasi-chemical thermodynamic model of the system. The model described in this series of papers enables the viscosities of liquid slags to be predicted within experimental uncertainties over the whole range of temperatures and compositions in the Al2O3 CaOMgO-SiO2 system.