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.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

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.

C-reactive protein levels and the expansion of screen-detected abdominal aortic aneurysms in men

Background-C- reactive protein (CRP) levels have been shown to predict a number of cardiovascular outcomes. CRP levels have also been found to be elevated in patients with abdominal aortic aneurysms (AAAs). The aim of this study was to assess the relation between CRP levels and rates of expansion of small AAAs. Methods and Results-A cohort of men with small aneurysms was identified in a trial of screening with ultrasound scanning. After initial screening, men were rescanned at 6- to 12-month intervals. CRP levels were measured at the first follow-up visit. Rates of expansion and risk factors for expansion were assessed with the use of data from 545 men who attended for at least 1 scan after CRP levels were measured. These men were followed for a median of 48 (range, 5 to 69) months. The mean annual rate of expansion was 1.6 mm. The median CRP level was 2.6 mg/L in men with the smaller AAAs (30 to 39 mm, n=433) compared with 3.5 mg/L in men with larger AAAs (40 to 54 mm, n=112) (P=0.007). The multivariate age-adjusted logistic model confirmed initial aortic diameter to be the only factor associated with rapid expansion with an odds ratio of 7.2 (95% CI, 4.3,12.2) for an initial diameter of 40 to 54 mm relative to one of 30 to 39 mm. Conclusions-Most small aneurysms expand slowly. CRP levels are elevated in larger aneurysms but do not appear to be associated with rapid expansion. The most useful predictor of aneurysmal expansion in men is aortic diameter.

On parameter estimation in population models

We describe methods for estimating the parameters of Markovian population processes in continuous time, thus increasing their utility in modelling real biological systems. A general approach, applicable to any finite-state continuous-time Markovian model, is presented, and this is specialised to a computationally more efficient method applicable to a class of models called density-dependent Markov population processes. We illustrate the versatility of both approaches by estimating the parameters of the stochastic SIS logistic model from simulated data. This model is also fitted to data from a population of Bay checkerspot butterfly (Euphydryas editha bayensis), allowing us to assess the viability of this population. (c) 2006 Elsevier Inc. All rights reserved.

A landscape-scale test of the predictive ability of a spatially explicit model for population viability analysis

1. Although population viability analysis (PVA) is widely employed, forecasts from PVA models are rarely tested. This study in a fragmented forest in southern Australia contrasted field data on patch occupancy and abundance for the arboreal marsupial greater glider Petauroides volans with predictions from a generic spatially explicit PVA model. This work represents one of the first landscape-scale tests of its type. 2. Initially we contrasted field data from a set of eucalypt forest patches totalling 437 ha with a naive null model in which forecasts of patch occupancy were made, assuming no fragmentation effects and based simply on remnant area and measured densities derived from nearby unfragmented forest. The naive null model predicted an average total of approximately 170 greater gliders, considerably greater than the true count (n = 81). 3. Congruence was examined between field data and predictions from PVA under several metapopulation modelling scenarios. The metapopulation models performed better than the naive null model. Logistic regression showed highly significant positive relationships between predicted and actual patch occupancy for the four scenarios (P = 0.001-0.006). When the model-derived probability of patch occupancy was high (0.50-0.75, 0.75-1.00), there was greater congruence between actual patch occupancy and the predicted probability of occupancy. 4. For many patches, probability distribution functions indicated that model predictions for animal abundance in a given patch were not outside those expected by chance. However, for some patches the model either substantially over-predicted or under-predicted actual abundance. Some important processes, such as inter-patch dispersal, that influence the distribution and abundance of the greater glider may not have been adequately modelled. 5. Additional landscape-scale tests of PVA models, on a wider range of species, are required to assess further predictions made using these tools. This will help determine those taxa for which predictions are and are not accurate and give insights for improving models for applied conservation management.

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.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

Optimal crossover designs for logistic regression models in pharmacodynamics

Pharmacodynamics (PD) is the study of the biochemical and physiological effects of drugs. The construction of optimal designs for dose-ranging trials with multiple periods is considered in this paper, where the outcome of the trial (the effect of the drug) is considered to be a binary response: the success or failure of a drug to bring about a particular change in the subject after a given amount of time. The carryover effect of each dose from one period to the next is assumed to be proportional to the direct effect. It is shown for a logistic regression model that the efficiency of optimal parallel (single-period) or crossover (two-period) design is substantially greater than a balanced design. The optimal designs are also shown to be robust to misspecification of the value of the parameters. Finally, the parallel and crossover designs are combined to provide the experimenter with greater flexibility.

Simulation of air traffic controllers' behaviour using the operator choice model

The Operator Choice Model (OCM) was developed to model the behaviour of operators attending to complex tasks involving interdependent concurrent activities, such as in Air Traffic Control (ATC). The purpose of the OCM is to provide a flexible framework for modelling and simulation that can be used for quantitative analyses in human reliability assessment, comparison between human computer interaction (HCI) designs, and analysis of operator workload. The OCM virtual operator is essentially a cycle of four processes: Scan Classify Decide Action Perform Action. Once a cycle is complete, the operator will return to the Scan process. It is also possible to truncate a cycle and return to Scan after each of the processes. These processes are described using Continuous Time Probabilistic Automata (CTPA). The details of the probability and timing models are specific to the domain of application, and need to be specified using domain experts. We are building an application of the OCM for use in ATC. In order to develop a realistic model we are calibrating the probability and timing models that comprise each process using experimental data from a series of experiments conducted with student subjects. These experiments have identified the factors that influence perception and decision making in simplified conflict detection and resolution tasks. This paper presents an application of the OCM approach to a simple ATC conflict detection experiment. The aim is to calibrate the OCM so that its behaviour resembles that of the experimental subjects when it is challenged with the same task. Its behaviour should also interpolate when challenged with scenarios similar to those used to calibrate it. The approach illustrated here uses logistic regression to model the classifications made by the subjects. This model is fitted to the calibration data, and provides an extrapolation to classifications in scenarios outside of the calibration data. A simple strategy is used to calibrate the timing component of the model, and the results for reaction times are compared between the OCM and the student subjects. While this approach to timing does not capture the full complexity of the reaction time distribution seen in the data from the student subjects, the mean and the tail of the distributions are similar.

Making Fedora easier to implement with Fez: A free open source content model and workflow management front-end to Fedora

The University of Queensland, Australia has developed Fez, a world-leading user-interface and management system for Fedora-based institutional repositories, which bridges the gap between a repository and users. Christiaan Kortekaas, Andrew Bennett and Keith Webster will review this open source software that gives institutions the power to create a comprehensive repository solution without the hassle..

A modified discrete random pore model allowing for different initial surface reactivity

We investigate here a modification of the discrete random pore model [Bhatia SK, Vartak BJ, Carbon 1996;34:1383], by including an additional rate constant which takes into account the different reactivity of the initial pore surface having attached functional groups and hydrogens, relative to the subsequently exposed surface. It is observed that the relative initial reactivity has a significant effect on the conversion and structural evolution, underscoring the importance of initial surface chemistry. The model is tested against experimental data on chemically controlled char oxidation and steam gasification at various temperatures. It is seen that the variations of the reaction rate and surface area with conversion are better represented by the present approach than earlier random pore models. The results clearly indicate the improvement of model predictions in the low conversion region, where the effect of the initially attached functional groups and hydrogens is more significant, particularly for char oxidation. It is also seen that, for the data examined, the initial surface chemistry is less important for steam gasification as compared to the oxidation reaction. Further development of the approach must also incorporate the dynamics of surface complexation, which is not considered here.

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 Nonstationary Model of Newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and non-stationary nature. The model consists of background and seizure sub-models. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models has a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively).