Gaussian Mixed Model Research Articles

Minimising Immunohistochemical False Negative ER Classification Using a Complementary 23 Gene Expression Signature of ER Status

BackgroundExpression of the oestrogen receptor (ER) in breast cancer predicts benefit from endocrine therapy. Minimising the frequency of false negative ER status classification is essential to identify all patients with ER positive breast cancers who should be offered endocrine therapies in order to improve clinical outcome. In routine oncological practice ER status is determined by semi-quantitative methods such as immunohistochemistry (IHC) or other immunoassays in which the ER expression level is compared to an empirical threshold[1], [2]. The clinical relevance of gene expression-based ER subtypes as compared to IHC-based determination has not been systematically evaluated. Here we attempt to reduce the frequency of false negative ER status classification using two gene expression approaches and compare these methods to IHC based ER status in terms of predictive and prognostic concordance with clinical outcome.Methodology/Principal FindingsFirstly, ER status was discriminated by fitting the bimodal expression of ESR1 to a mixed Gaussian model. The discriminative power of ESR1 suggested bimodal expression as an efficient way to stratify breast cancer; therefore we identified a set of genes whose expression was both strongly bimodal, mimicking ESR expression status, and highly expressed in breast epithelial cell lines, to derive a 23-gene ER expression signature-based classifier. We assessed our classifiers in seven published breast cancer cohorts by comparing the gene expression-based ER status to IHC-based ER status as a predictor of clinical outcome in both untreated and tamoxifen treated cohorts. In untreated breast cancer cohorts, the 23 gene signature-based ER status provided significantly improved prognostic power compared to IHC-based ER status (P = 0.006). In tamoxifen-treated cohorts, the 23 gene ER expression signature predicted clinical outcome (HR = 2.20, P = 0.00035). These complementary ER signature-based strategies estimated that between 15.1% and 21.8% patients of IHC-based negative ER status would be classified with ER positive breast cancer.Conclusion/SignificanceExpression-based ER status classification may complement IHC to minimise false negative ER status classification and optimise patient stratification for endocrine therapies.

A Gaussian mixed model for learning discrete Bayesian networks

In this paper, we address the problem of learning discrete Bayesian networks from noisy data. A graphical model based on a mixture of Gaussian distributions with categorical mixing structure coming from a discrete Bayesian network is considered. The network learning is formulated as a maximum likelihood estimation problem and performed by employing an EM algorithm. The proposed approach is relevant to a variety of statistical problems for which Bayesian network models are suitable—from simple regression analysis to learning gene/protein regulatory networks from microarray data.

Semi‐parametric latent process model for longitudinal ordinal data: Application to cognitive decline

Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi-parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non-parametric function of time, f(t), to model the expected change over time. This model includes random-effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f(t) and all the model parameters are estimated by penalized likelihood using a cubic-spline approximation for f(t). The smoothing parameter is estimated by an approximate cross-validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time-course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects.

Estimating the returns to schooling: a likelihood approach based on normal mixtures

In this paper we develop likelihood-based methods for statistical inference in a joint system of equations for the choice of length of schooling and earnings. The model for schooling choice is assumed to be an ordered probit model, whereas the earnings equation contains variables that are flexible transformations of schooling and experience, with corresponding coefficients that are allowed to be heterogeneous across individuals. Under the assumption that the distribution of the random terms of the model can be expressed as a finite mixture of multinormal distributions, we show that the joint probability distribution for schooling and earnings can be expressed on closed form. In an application of our method on Norwegian data, we find that the mixed Gaussian model offers a substantial improvement in fit to the (heavy-tailed) empirical distribution of log-earnings compared to a multinormal benchmark model. Copyright © 2010 John Wiley & Sons, Ltd.

Colonyzer: automated quantification of micro-organism growth characteristics on solid agar

BackgroundHigh-throughput screens comparing growth rates of arrays of distinct micro-organism cultures on solid agar are useful, rapid methods of quantifying genetic interactions. Growth rate is an informative phenotype which can be estimated by measuring cell densities at one or more times after inoculation. Precise estimates can be made by inoculating cultures onto agar and capturing cell density frequently by plate-scanning or photography, especially throughout the exponential growth phase, and summarising growth with a simple dynamic model (e.g. the logistic growth model). In order to parametrize such a model, a robust image analysis tool capable of capturing a wide range of cell densities from plate photographs is required.ResultsColonyzer is a collection of image analysis algorithms for automatic quantification of the size, granularity, colour and location of micro-organism cultures grown on solid agar. Colonyzer is uniquely sensitive to extremely low cell densities photographed after dilute liquid culture inoculation (spotting) due to image segmentation using a mixed Gaussian model for plate-wide thresholding based on pixel intensity. Colonyzer is robust to slight experimental imperfections and corrects for lighting gradients which would otherwise introduce spatial bias to cell density estimates without the need for imaging dummy plates. Colonyzer is general enough to quantify cultures growing in any rectangular array format, either growing after pinning with a dense inoculum or growing with the irregular morphology characteristic of spotted cultures. Colonyzer was developed using the open source packages: Python, RPy and the Python Imaging Library and its source code and documentation are available on SourceForge under GNU General Public License. Colonyzer is adaptable to suit specific requirements: e.g. automatic detection of cultures at irregular locations on streaked plates for robotic picking, or decreasing analysis time by disabling components such as lighting correction or colour measures.ConclusionColonyzer can automatically quantify culture growth from large batches of captured images of microbial cultures grown during genome-wide scans over the wide range of cell densities observable after highly dilute liquid spot inoculation, as well as after more concentrated pinning inoculation. Colonyzer is open-source, allowing users to assess it, adapt it to particular research requirements and to contribute to its development.

Prosodic boundaries in German: Final lengthening in spontaneous speech.

Most theories of prosodic structure postulate at least two phrasal categories above the word level, a minor and a major one. One correlate of phrasal boundary marking is lengthening on the right edge of a phrase. To gain a theory neutral understanding of the nature of prosodic boundaries, a Gaussian mixed model (GMM) was applied to durational data, estimating the underlying clusters of a continuous distribution. Spontaneous speech data were collected with standardized interviews from 19 adolescent speakers of a multi-ethnolect (Kiezdeutsch, Hood German) spoken in Berlin, orthographically transcribed and added to a database that allowed for searches of the particle “so”(so or like) in different conditions. Acoustic durations of /z/ and /o/ of so in phrase final position (as determined by orthographical markings or by following pauses) were labeled and z-transformed per speaker. The results show that a model including two clusters accounts best for the data. Nevertheless, there is an overlap between the two distributions supporting the gradient nature of boundaries. Further analyses with more tokens of so including word level junctures are currently under way. The impact of our data-driven results on theoretical models of prosodic boundaries is discussed. [Supported by a grant from BMBF.]

형상 형성 제어를 이용한 어휘인식 공유 모델의 가우시안 최적화

연속 어휘 인식 확률 분포의 공유 방법에서는 사용될 모델 파라미터들의 초기 추정치를 생성하기 위한 각 문맥들에 대한 음소 데이터가 반드시 필요하지만 이들 음소 데이터에 대한 모델을 구성할 수 없는 단점으로 가우시안 모델의 정확성을 확보하지 못한다는 단점이 있다. 이를 개선하기 위하여 확률 분포의 혼합 가우시안 모델을 최적화하고, 음소 단위로 데이터를 탐색을 지원하는 형상 형성 시스템을 제안한다. 본 논문의 형상 형성 시스템은 확장 facet 분류를 이용하여 사용자에게 음소 단위의 형상 형성 정보를 제공하므로 가우시안 모델의 정확성을 제공한다. 본 논문에서 제안한 시스템을 적용한 결과 시스템 성능에서 어휘 종속 인식률은 98.31%, 어휘 독립 인식률은 97.63%의 인식률을 나타내었다. In continuous vocabulary recognition system by probability distribution of clustering method has used model parameters of an advance estimate to generated each contexts for phoneme data surely needed but it has it's bad points of gaussian model the accuracy unsecure of composed model for phoneme data. To improve suggested probability distribution mixed gaussian model to optimized that phoneme data search supported configuration thread system. This paper of configuration thread system has used extension facet classification user phoneme configuration thread information offered gaussian model the accuracy secure. System performance as a result of represent vocabulary dependence recognition rate of 98.31%, vocabulary independence recognition rate of 97.63%.

공유모델 인식 성능 향상을 위한 효율적인 연속 어휘 군집화 모델링

연속 어휘 인식 시스템에서는 통계적 방법에 의한 어휘 인식을 수행하기 위하여 확률분포를 이용하며 이는 음소 단위의클러스터링을사용하여모델링하여샘플들을기반으로 확률 파라미터를 추정한다. 어휘 검색 시 추정된 확률 파라미터로부터 인식 결과를 나타내는데 미리 정의되지 않은 음소와 추가되어진 음소로부터 인식률이 저하되는 문제점이 발생하며, 하나의 클러스터링으로 모델링하므로 가우시안 모델이 정확성을 확보하지 못한다는 단점이 있다. 이를 개선하기 위하여 확률 분포의 혼합 가우시안 모델을 최적화하여 유사도를 기반으로 Euclidean과 Bhattacharyya 거리 측정 방법을 혼합한 군집화 모델을 제안하고, 군집화된 모델에서 음소 단위로 확률 모델을 탐색할 수 있는 시스템을 모델링하였다. 본 논문에서 제안한 시스템을 적용한 결과 시스템 성능에서 어휘 종속 인식률은 98.63%, 어휘 독립 인식률은 97.91%의 인식률을 나타내었다. In continuous vocabulary recognition system by statistical method vocabulary recognition to be performed using probability distribution it also modeling using phoneme clustering for based sample probability parameter presume. When vocabulary search that low recognition rate problem happened in express vocabulary result from presumed probability parameter by not defined phoneme and insert phoneme and it has it's bad points of gaussian model the accuracy unsecure for one clustering modeling. To improve suggested probability distribution mixed gaussian model to optimized for based resemble Euclidean and Bhattacharyya distance measurement method mixed clustering modeling that system modeling for be searching phoneme probability model in clustered model. System performance as a result of represent vocabulary dependence recognition rate of 98.63%, vocabulary independence recognition rate of 97.91%.

Optical Degradation of CdSe/ZnS Quantum Dots upon Gamma-Ray Irradiation

We report quantitative changes to the fluorescent characteristics of quantum dots (QDs) following gamma irradiation. One CdSe/ZnS QD ensemble synthesized via a wet-chemistry approach was dispersed in hexane. Six identical dispersions were prepared, three of which were unexposed controls, whereas the other three were irradiated by a Co-60 source, incrementally to doses of 0.1, 1.0, 10, and 100 Gy. Fluorescence spectra were immediately collected after each irradiation. Emission spectra were fit to a three-component mixed Gaussian model, which included CENTRE, SHOULDER, and BACKGROUND Gaussians. For all of the irradiated samples, the CENTRE and SHOULDER Gaussian amplitude decreased with increased irradiation dose. The BACKGROUND Gaussian exhibited increased amplitude, blue-shift, and widening. The three control samples exhibited consistent unchanged fluorescent spectra during our experimental time scale. The fluorescent response of QDs to radiation provides the proof of concept for use of quantum dots as nov...

Bayes factor between Student t and Gaussian mixed models within an animal breeding context

The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The twomodels can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model). The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC) as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months), both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.

Bayes factor between Student t and Gaussian mixed models within an animal breeding context

The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The twomodels can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model). The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC) as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months), both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.

Estudo de simulação de modelos lineares mistos com distribuição normal contaminada no melhoramento genético animal

Objetivou-se com esse trabalho comparar estimativas de componentes de variâncias obtidas por meio de modelos lineares mistos Gaussianos e Robustos, via Amostrador de Gibbs, em dados simulados. Foram simulados 50 arquivos de dados com 1.000 animais cada um, distribuídos em cinco gerações, em dois níveis de efeito fixo e três valores fenotípicos distintos para uma característica hipotética, com diferentes níveis de contaminação. Exceto para os dados sem contaminação, quando os modelos foram iguais, o modelo Robusto apresentou melhores estimativas da variância residual. As estimativas de herdabilidade foram semelhantes em todos os modelos, mas as análises de regressão mostraram que os valores genéticos preditos com uso do modelo Robusto foram mais próximos dos valores genéticos verdadeiros. Esses resultados sugerem que o modelo linear normal contaminado oferece uma alternativa flexível para estimação robusta em melhoramento genético animal.

Estimation of soil salinity in semi‐arid land using a geostatistical model

AbstractSoil salinity is one of the great problems in arid and semi‐arid environments. The estimation and prediction of spatial soil salinity may be considered as a stochastic process, observed at irregular locations in space. Environmental variables usually show spatial dependence among observations which is an important drawback to traditional statistical methods. Geostatistical techniques that analyse and describe the spatial dependence and quantify the scale and intensity of the spatial variation, provides spatial information for local estimation of soil salinity. In this paper we propose a Gaussian Spatial Linear Mixed Model (GSLMM), which involves a non‐parametric term, accounting for a deterministic trend given by exogenous variables, and a parametric component defining the purely spatial random variation, possibly due to latent spatial processes. We focus here on the analysis of the relationship between soil electrical conductivity as a parameter related directly to soil salinity as well as sodium content (sodicity) to identify spatial variations in these parameters. This kind of methodology is demonstrated as a useful tool for environmental land management. Copyright © 2007 John Wiley & Sons, Ltd.

Combination Tetrathiomolybdate and Radiation Therapy in a Mouse Model of Head and Neck Squamous Cell Carcinoma

To assess the effect of combining tetrathiomolybdate therapy and radiation treatment (RT) on tumor growth in the mouse head and neck squamous cell carcinoma (HNSCC) model. One million HNSCC cells were injected subcutaneously into the flanks of C3H/HeJ mice and the tumors grown to an average of 301 mm3 (day 0). Mice were randomized into 4 groups: (a) no therapy, (b) tetrathiomolybdate alone, (c) RT alone, or (d) tetrathiomolybdate + RT. Data from 3 experiments with these 4 groups were analyzed. A gaussian mixed model was fit to the initialized logarithm of the tumor size counts between days 7 and 16 (linear component), and growth rates were compared. Assays using 3-(4,5-dimethylthiazol-2yl)-2,5 diphenyltetrazolium bromide (MTT) were conducted on HNSCC cells in culture with varying doses of tetrathiomolybdate. Treated mice were given tetrathiomolybdate in their water and observed for clinical evidence of toxic effects associated with copper depletion as measured by ceruloplasmin assay. When tumor sizes reached an average of 535 mm(3), mice receiving RT were given a single fraction of 750 rad (7.5 Gy), a dose determined in previous experiments to slow but not cure tumor growth, permitting an examination of interaction of radiation with tetrathiomolybdate. Data from 3 separate experiments were analyzed. There were a total of 37 mice in the untreated group, 32 mice in the tetrathiomolybdate alone group, 38 mice in the RT alone group, and 46 mice in the tetrathiomolybdate + RT group. Ceruloplasmin assays showed that we had obtained adequate copper reduction throughout the experiments to inhibit angiogenesis with minimal toxic effects. The tetrathiomolybdate + RT combined therapy group of mice showed a statistically significant decrease in tumor growth compared with both the tetrathiomolybdate alone (P = .001) and RT alone groups (P<.001). The combination of the anti-angiogenic copper chelating agent tetrathiomolybdate with RT improved local control of HNSCC in an isogenic mouse model compared with either therapy alone.

Equivalence of conditional and marginal regression models for clustered and longitudinal data

Certain statistical models specify a conditional mean function, given a random effect and covariates of interest. On the other hand, one may instead model a marginal mean only in terms of the covariates. We discuss some common situations where conditional and marginal means coincide. In a Gaussian linear mixed effects model we have equivalent interpretations of the conditional and marginal regression parameter estimates. Similar results exist for more general link functions. In this paper we give a short overview of some models, where conditional and marginal results are equivalent and we illustrate this with some examples. When the conditional mean is additive in a random effect on the log scale, it is seen that the marginal mean equals the conditional mean plus a constant, such that slope parameters have the same interpretation in both formulations. No further distributional assumptions are needed in either of these cases. With a logit link and a double exponential random effect, a closed form marginal link function is derived from the conditional model. When a logit or probit link is used with a normal random effect, the marginal mean parameters become attenuated by a factor which depends on parameters of the distribution of the covariates. In a conditional Weibull proportional hazards model with a positive stable frailty, the marginal hazards are again Weibull but with slope parameters attenuated towards zero.

Spatio-temporal modeling of benthic biological species

The spatial and temporal distribution of the number of benthic species located in an important area under ecological stress (Puerto CALICA, Quintana Roo, Mexico) is analyzed by means of Gaussian Spatial Linear Mixed Models. Following a model-based approach we derive spatial predictions taking into account temporal variations between May 1996 and June 1999. The proposed models were evaluated in terms of their ability to detect the underlying spatial structure for further interpolation. Uncertainty in the prediction could be evaluated by using the Bayesian paradigm. The results can be used as a guide for further environmental management policies in the region.

Longitudinal data analysis using t-type regression

We consider a robust estimator of linear regression for longitudinal data by maximizing marginal likelihood of a scaled t-type error distribution. The marginal likelihood can also be applied to the de-correlated response when the within-subject correlation can be consistently estimated from an initial estimate of the model based on the working assumption of independence. While the t-distributed errors can be motivated from a latent hierarchical model as an extension of Gaussian mixed models, our estimators have asymptotic normal distributions for a wider class of error distributions. The estimators have bounded influence functions and can achieve positive breakdown points regardless of the dimension of the covariates.

Prediction error variance and expected response to selection, when selection is based on the best predictor - for Gaussian and threshold characters, traits following a Poisson mixed model and survival traits.

In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found – otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits – and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.

Prediction error variance and expected response to selection, when selection is based on the best predictor - for Gaussian and threshold characters, traits following a Poisson mixed model and survival traits

In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found – otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits – and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.

LAN, LAM and convergence of Iterative ML estimates; optimal design in Gaussian one-way mixed model

For a one-way mixed Gaussian ANOVA model we prove local asymptotic normality and local asymptotic minimaxity of maximum likelihood estimates (MLE) and of its certain iterative approximations. A geometric rate of convergence in probability is proved for these iterative estimates to MLE. Asymptotically optimal designs for large samples are studied.