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.

Is the increase in coronary events on Mondays an artifact?

Background: The aim of this article was to investigate the size and possible causes of the reported excess in coronary events on Mondays. Methods: We conducted a metaanalysis of data from the World Health Organization (WHO) MONICA Project, which monitored trends and determinants in cardiovascular disease. The MONICA Project was undertaken in 21 countries from 1980 to 1995. Results: We found a small overall excess rate of coronary events on Mondays. In a population experiencing 100 events per week, we estimate there would be approximately I more event on Monday than on any other day. Hierarchical logistic regression showed that the Monday excess was greater in centers with less thorough data collection procedures. Conclusions: The excess of coronary events on Mondays is probably an artifact resulting from events with uncertain dates being coded as taking place on Mondays.

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.

Goal orientation, ability and task performance: A moderated analysis

Achievement goal orientation represents an individual's general approach to an achievement situation, and has important implications for how individuals react to novel, challenging tasks. However, theorists such as Yeo and Neal (2004) have suggested that the effects of goal orientation may emerge over time. Bell and Kozlowski (2002) have further argued that these effects may be moderated by individual ability. The current study tested the dynamic effects of a new 2x2 model of goal orientation (mastery/performance x approach/avoidance) on performance on a simulated air traffic control (ATC) task, as moderated by dynamic spatial ability. One hundred and one first-year participants completed a self-report goal orientation measure and computerbased dynamic spatial ability test and performed 30 trials of an ATC task. Hypotheses were tested using a two-level hierarchical linear model. Mastery-approach orientation was positively related to task performance, although no interaction with ability was observed. Performance-avoidance orientation was negatively related to task performance; this association was weaker at high levels of ability. Theoretical and practical implications will be discussed.

A Bayesian hierarchical model for categorical longitudinal data from a social survey of immigrants

The paper investigates a Bayesian hierarchical model for the analysis of categorical longitudinal data from a large social survey of immigrants to Australia. Data for each subject are observed on three separate occasions, or waves, of the survey. One of the features of the data set is that observations for some variables are missing for at least one wave. A model for the employment status of immigrants is developed by introducing, at the first stage of a hierarchical model, a multinomial model for the response and then subsequent terms are introduced to explain wave and subject effects. To estimate the model, we use the Gibbs sampler, which allows missing data for both the response and the explanatory variables to be imputed at each iteration of the algorithm, given some appropriate prior distributions. After accounting for significant covariate effects in the model, results show that the relative probability of remaining unemployed diminished with time following arrival in Australia.

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.

Adjustment of homeless adolescents to a crisis shelter: Application of a stress and coping model

The present study examined the utility of a stress and coping model of adaptation to a homeless shelter among homeless adolescents. Seventy-eight homeless adolescents were interviewed and completed self-administered scales at Time 1 (day of shelter entry) and Time 2 (day of discharge). The mean duration of stay at the shelter was 7.23 days (SD = 7.01). Predictors included appraisal (threat and self-efficacy), coping resources, and coping strategies (productive, nonproductive, and reference to others coping). Adjustment outcomes were Time I measures of global distress, physical health, clinician-and youthworker- rated social adjustment, and externalizing behavior and Time 2 youthworker-rated social adjustment and goal achievement. Results of hierarchical regression analyses indicated that after controlling for the effects of relevant background variables (number of other shelters visited, sexual, emotional, and physical abuse), measures of coping resources, appraisal, and coping strategies evidenced distinct relations with measures of adjustment in ways consistent with the model's predictions with few exceptions. In cross-sectional analyses better Time I adjustment was related to reports of higher levels of coping resources, self-efficacy beliefs, and productive coping strategies, and reports of lower levels of threat appraisal and nonproductive coping strategies. Prospective analyses showed a link between reports of higher levels of reference to others coping strategies and greater goal achievement and, unexpectedly, an association between lower self-efficacy beliefs and better Time 2 youthworker-rated social adjustment. Hence, whereas prospective analyses provide only limited support for the use of a stress and coping model in explaining the adjustment of homeless adolescents to a crisis shelter, cross-sectional findings provide stronger support.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

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.

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.