A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

Testing the niche apportionment hypothesis with parasite communities: is random assortment always the rule?

Niche apportionment models have only been applied once to parasite communities. Only the random assortment model (RA), which indicates that species abundances are independent from each other and that interspecific competition is unimportant, provided a good fit to 3 out of 6 parasite communities investigated. The generality of this result needs to be validated, however. In this study we apply 5 niche apportionment models to the parasite communities of 14 fish species from the Great Barrier Reef. We determined which model fitted the data when using either numerical abundance or biomass as an estimate of parasite abundance, and whether the fit of niche apportionment models depends on how the parasite community is defined (e.g. ecto, endoparasites or all parasites considered together). The RA model provided a good fit for the whole community of parasites in 7 fish species when using biovolume (as a surrogate of biomass) as a measure of species abundance. The RA model also fitted observed data when ecto- and endoparasites were considered separately, using abundance or biovolume, but less frequently. Variation in fish sizes among species was not associated with the probability of a model fitting the data. Total numerical abundance and biovolume of parasites were not related across host species, suggesting that they capture different aspects of abundance. Biovolume is not only a better measurement to use with niche-orientated models, it should also be the preferred descriptor to analyse parasite community structure in other contexts. Most of the biological assumptions behind the RA model, i.e. randomness in apportioning niche space, lack of interspecific competition, independence of abundance among different species, and species with variable niches in changeable environments, are in accordance with some previous findings on parasite communities. Thus, parasite communities may generally be unsaturated with species, with empty niches, and interspecific interactions may generally be unimportant in determining parasite community structure.

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models-a fixed effects model and a random effects model-are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed. (c) 2004 Elsevier B.V. All rights reserved.

Increasing uncertainty: A definition

We present a definition of increasing uncertainty, in which an elementary increase in the uncertainty of any act corresponds to the addition of an 'elementary bet' that increases consumption by a fixed amount in (relatively) 'good' states and decreases consumption by a fixed (and possibly different) amount in (relatively) 'bad' states. This definition naturally gives rise to a dual definition of comparative aversion to uncertainty. We characterize this definition for a popular class of generalized models of choice under uncertainty.

Characteristics and benefits of professional work - Assessment of their importance over a 30-year career

The Professions in Australia Study is the first longitudinal investigation of the professions in Australia; it spans 33 years. Self-administered questionnaires were distributed on at least eight occasions between 1965 and 1998 to cohorts of students and later practitioners from the professions of engineering, law and medicine. The longitudinal design of this study has allowed for an investigation of individual change over time of three archetypal characteristics of the professions, service, knowledge and autonomy and two of the benefits of professional work, financial rewards and prestige. A cumulative logit random effects model was used to statistically assess changes in the ordinal response scores for measuring importance of the characteristics and benefits through stages of the career path. Individuals were also classified by average trends in response scores over time and hence professions are described through their members' tendency to follow a particular path in attitudes either of change or constancy, in relation to the importance of the five elements (characteristics and benefits). Comparisons in trends are also made between the three professions.

Methods for Categorical Longitudinal Survey Data: Understanding Employment Status of Australian Women

Many variables that are of interest in social science research are nominal variables with two or more categories, such as employment status, occupation, political preference, or self-reported health status. With longitudinal survey data it is possible to analyse the transitions of individuals between different employment states or occupations (for example). In the statistical literature, models for analysing categorical dependent variables with repeated observations belong to the family of models known as generalized linear mixed models (GLMMs). The specific GLMM for a dependent variable with three or more categories is the multinomial logit random effects model. For these models, the marginal distribution of the response does not have a closed form solution and hence numerical integration must be used to obtain maximum likelihood estimates for the model parameters. Techniques for implementing the numerical integration are available but are computationally intensive requiring a large amount of computer processing time that increases with the number of clusters (or individuals) in the data and are not always readily accessible to the practitioner in standard software. For the purposes of analysing categorical response data from a longitudinal social survey, there is clearly a need to evaluate the existing procedures for estimating multinomial logit random effects model in terms of accuracy, efficiency and computing time. The computational time will have significant implications as to the preferred approach by researchers. In this paper we evaluate statistical software procedures that utilise adaptive Gaussian quadrature and MCMC methods, with specific application to modeling employment status of women using a GLMM, over three waves of the HILDA survey.

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.

Referral to rehabilitation following traumatic brain injury: a model for understanding inequities in access

Identifying inequities in access to health care requires critical scrutiny of the patterns and processes of care decisions. This paper describes a conceptual model. derived from social problems theory. which is proposed as a useful framework for explaining patterns of post-acute care referral and in particular, individual variations in referral to rehabilitation after traumatic brain injury (TBI). The model is based on three main components: (1) characteristics of the individual with TBI, (2) activities of health care professionals and the processes of referral. and (3) the contexts of care. The central argument is that access to rehabilitation following TBI is a dynamic phenomenon concerning the interpretations and negotiations of health care professionals. which in turn are shaped by the organisational and broader health care contexts. The model developed in this paper provides opportunity to develop a complex analysis of post-acute care referral based on patient factors, contextual factors and decision-making processes. It is anticipated that this framework will have utility in other areas examining and understanding patterns of access to health care. (C) 2002 Elsevier Science Ltd. All rights reserved.

Utility of cotyledon and detached leaf assays for assessing root reactions of lucerne to Phytophthora root rot caused by Phytophthora medicaginis

Phytophthora root rot, caused by Phytophthora medicaginis, is a major limitation to lucerne production but it can be managed through the use of resistant cultivars. Current resistance screening methods, using mature plants or post-emergence seedling assays, are costly and time consuming. The use of zoospore inoculum on detached leaves and intact cotyledons as an assay for plant resistance was assessed using genetically defined segregating populations. The detached leaf assay was a reproducible test, but this test could not be used for accurately predicting root ratings. The cotyledon tests using zoospores gave results at the population level that were indicative of the root responses of 19 cultivars and lines tested. The cotyledon reaction of individual plants also showed a strong association with root response. The cotyledon test, while not completely predictive of mature root responses, allowed the selection of Phytophthora resistant plants at a higher frequency than could be achieved by random selection.

Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Using the effect size to model change in preference values from descriptive health status

Objectives: This pilot study describes a modelling approach to translate group-level changes in health status into changes in preference values, by using the effect size (ES) to summarize group-level improvement. Methods: ESs are the standardized mean difference between treatment groups in standard deviation (SD) units. Vignettes depicting varying severity in SD decrements on the SF-12 mental health summary scale, with corresponding symptom severity profiles, were valued by a convenience sample of general practitioners (n = 42) using the rating scale (RS) and time trade-off methods. Translation factors between ES differences and change in preference value were developed for five mental disorders, such that ES from published meta-analyses could be transformed into predicted changes in preference values. Results: An ES difference in health status was associated with an average 0.171-0.204 difference in preference value using the RS, and 0.104-0.158 using the time trade off. Conclusions: This observed relationship may be particular to the specific versions of the measures employed in the present study. With further development using different raters and preference measures, this approach may expand the evidence base available for modelling preference change for economic analyses from existing data.

Equity weights in the allocation of health care: the rank-dependent QALY model

This paper introduces the rank-dependent quality-adjusted life-years (QALY) model, a new method to aggregate QALYs in economic evaluations of health care. The rank-dependent QALY model permits the formalization of influential concepts of equity in the allocation of health care, such as the fair innings approach, and it includes as special cases many of the social welfare functions that have been proposed in the literature. An important advantage of the rank-dependent QALY model is that it offers a straightforward procedure to estimate equity weights for QALYs. We characterize the rank-dependent QALY model and argue that its central condition has normative appeal. (C) 2003 Elsevier B.V. All rights reserved.

Adaptation to being at-risk for Huntington's disease and the availability of genetic testing: Application of a stress and coping model

This study examined the utility of a stress/coping model in explaining adaptation in two groups of people at-risk for Huntington's Disease (HD): those who have not approached genetic testing services (non-testees) and those who have engaged a testing service (testees). The aims were (1) to compare testees and non-testees on stress/coping variables, (2) to examine relations between adjustment and the stress/coping predictors in the two groups, and (3) to examine relations between the stress/coping variables and testees' satisfaction with their first counselling session. Participants were 44 testees and 40 non-testees who completed questionnaires which measured the stress/coping variables: adjustment (global distress, depression, health anxiety, social and dyadic adjustment), genetic testing concerns, testing context (HD contact, experience, knowledge), appraisal (control, threat, self-efficacy), coping strategies (avoidance, self-blame, wishful thinking, seeking support, problem solving), social support and locus of control. Testees also completed a genetic counselling session satisfaction scale. As expected, non-testees reported lower self-efficacy and control appraisals, higher threat and passive avoidant coping than testees. Overall, results supported the hypothesis that within each group poorer adjustment would be related to higher genetic testing concerns, contact with HD, threat appraisals, passive avoidant coping and external locus of control, and lower levels of positive experiences with HD, social support, internal locus of control, self-efficacy, control appraisals, problem solving, emotional approach and seeking social support coping. Session satisfaction scores were positively correlated with dyadic adjustment, problem solving and positive experience with HD, and inversely related to testing concerns, and threat and control appraisals. Findings support the utility of the stress/coping model in explaining adaptation in people who have decided not to seek genetic testing for HD and those who have decided to engage a genetic testing service.