Selection of Log-Linear Models with Orthonormal Basis for Contingency Tables

A model selection criterion for log-linear models with orthonormal basis for contingency tables is developed using the Gauss discrepancy between the logarithms of the frequencies. The contribution of each parameter to the criterion may be determined separately. A test for the hypothesis that the use of a certain parameter increases the expected discrepancy is given.     

Evaluation of community-intervention trials via generalized linear mixed models

In community-intervention trials, communities, rather than individuals, are randomized to experimental arms. Generalized linear mixed models offer a flexible parametric framework for the evaluation of community-intervention trials, incorporating both systematic and random variations at the community and individual levels. We propose here a simple two-stage inference method for generalized linear mixed models, specifically tailored to the analysis of community-intervention trials. In the first stage, community-specific random effects are estimated from individual-level data, adjusting for the effects of individual-level covariates. This reduces the model approximately to a linear mixed model with the unit of analysis being community. Because the number of communities is typically small in community-intervention studies, we apply the small-sample inference method of Kenward and Roger (1997, Biometrics53, 983-997) to the linear mixed model of second stage. We show by simulation that, under typical settings of community-intervention studies, the proposed approach improves the inference on the intervention-effect parameter uniformly over both the linearized mixed-effect approach and the adaptive Gaussian quadrature approach for generalized linear mixed models. This work is motivated by a series of large randomized trials that test community interventions for promoting cancer preventive lifestyles and behaviors.     

Nonparametric mixed effects models for unequally sampled noisy curves

We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low-rank, low-frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as best linear unbiased predictor (BLUP) estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques--Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross-validation--to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis.     

A Bayesian Hierarchical Model for Classification with Selection of Functional Predictors

Summary In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample‐related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fluorescence spectroscopy to detect cervical precancer. In this article, we propose a Bayesian hierarchical model that takes into account random batch effects and selects effective functions among multiple functional predictors. Fixed effects or predictors in nonfunctional form are also included in the model. The dimension of the functional data is reduced through orthonormal basis expansion or functional principal components. For posterior sampling, we use a hybrid Metropolis–Hastings/Gibbs sampler, which suffers slow mixing. An evolutionary Monte Carlo algorithm is applied to improve the mixing. Simulation and real data application show that the proposed model provides accurate selection of functional predictors as well as good classification.     

Conditional Akaike information under generalized linear and proportional hazards mixed models

We study model selection for clustered data, when the focus is on cluster specific inference. Such data are often modelled using random effects, and conditional Akaike information was proposed in Vaida & Blanchard (2005) and used to derive an information criterion under linear mixed models. Here we extend the approach to generalized linear and proportional hazards mixed models. Outside the normal linear mixed models, exact calculations are not available and we resort to asymptotic approximations. In the presence of nuisance parameters, a profile conditional Akaike information is proposed. Bootstrap methods are considered for their potential advantage in finite samples. Simulations show that the performance of the bootstrap and the analytic criteria are comparable, with bootstrap demonstrating some advantages for larger cluster sizes. The proposed criteria are applied to two cancer datasets to select models when the cluster-specific inference is of interest.     

A note on joint versus gene-specific mixed model analysis of microarray gene expression data

Currently, linear mixed model analyses of expression microarray experiments are performed either in a gene-specific or global mode. The joint analysis provides more flexibility in terms of how parameters are fitted and estimated and tends to be more powerful than the gene-specific analysis. Here we show how to implement the gene-specific linear mixed model analysis as an exact algorithm for the joint linear mixed model analysis. The gene-specific algorithm is exact, when the mixed model equations can be partitioned into unrelated components: One for all global fixed and random effects and the others for the gene-specific fixed and random effects for each gene separately. This unrelatedness holds under three conditions: (1) any gene must have the same number of replicates or probes on all arrays, but these numbers can differ among genes; (2) the residual variance of the (transformed) expression data must be homogeneous or constant across genes (other variance components need not be homogeneous) and (3) the number of genes in the experiment is large. When these conditions are violated, the gene-specific algorithm is expected to be nearly exact.     

How quantitative measures unravel design principles in multi-stage phosphorylation cascades

We investigate design principles of linear multi-stage phosphorylation cascades by using quantitative measures for signaling time, signal duration and signal amplitude. We compare alternative pathway structures by varying the number of phosphorylations and the length of the cascade. We show that a model for a weakly activated pathway does not reflect the biological context well, unless it is restricted to certain parameter combinations. Focusing therefore on a more general model, we compare alternative structures with respect to a multivariate optimization criterion. We test the hypothesis that the structure of a linear multi-stage phosphorylation cascade is the result of an optimization process aiming for a fast response, defined by the minimum of the product of signaling time and signal duration. It is then shown that certain pathway structures minimize this criterion. Several popular models of MAPK cascades form the basis of our study. These models represent different levels of approximation, which we compare and discuss with respect to the quantitative measures.     

Planning incomplete block experiments when treatments are genetically related

Selection trials in plant and animal breeding, in incomplete blocks, are described by linear models with random effect parameters associated with treatments with known genetic covariance structure. It is now well known that the information on relatives can improve the analysis and many extensions of this model have been proposed, but no studies have been done on the consequences of this genetical relatedness among treatments for the optimality of block designs. Using a suitable optimality criterion, we show that the knowledge on relatedness may imply that the optimal design is not in the class of designs which are optimal for unrelated treatments. Implications for practical applications are discussed.     

Linear Mixed-Effects Models to Describe Individual Tree Crown Width for China-Fir in Fujian Province,Southeast China

A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike’s information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R ²). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.     

Testing for cubic smoothing splines under dependent data

Summary In most research on smoothing splines the focus has been on estimation, while inference, especially hypothesis testing, has received less attention. By defining design matrices for fixed and random effects and the structure of the covariance matrices of random errors in an appropriate way, the cubic smoothing spline admits a mixed model formulation, which places this nonparametric smoother firmly in a parametric setting. Thus nonlinear curves can be included with random effects and random coefficients. The smoothing parameter is the ratio of the random‐coefficient and error variances and tests for linear regression reduce to tests for zero random‐coefficient variances. We propose an exact F‐test for the situation and investigate its performance in a real pine stem data set and by simulation experiments. Under certain conditions the suggested methods can also be applied when the data are dependent.     

Theory relating in vitro and in vivo microdialysis with one or two probes

In this paper, we further develop the general theory of microdialysis by extending the linear model of Bungay et al. to provide a theoretical basis for in vitro and in vivo microdialysis. Specifically, we considered the effect of active clearance processes on in vivo microdialysis, and thereby elaborated the theory of Benveniste et al. to endogenous compounds. We examined the use of steady state tissue diffusion resistance with negligible clearance processes to interpret microdialysis data. The influence of the tissue properties on the in vitro and in vivo recoveries in dual-probe microdialysis was analyzed and we simulated the effect of the operating parameters on dual probe microdialysis performance. We estimated that the minimum clearance rate constant detectable by microdialysis in a quasi-steady state is about 5.5 x 10(-5) s(-1). This minimum rate constant establishes a criterion, below which inhibition of the active clearance processes does not show detectable influences on the microdialysis extraction efficiency.     

A continuum theoretical model and finite elements simulation of bacterial flagellar filament phase transition

The Bacterial flagellar filament can undergo a polymorphic phase transition in response to both mechanical and chemical variations in vitro and in vivo environments. Under mechanical stimuli, such as viscous flow or forces induced by motor rotation, the filament changes its phase from left-handed normal (N) to right-handed semi-coiled (SC) via phase nucleation and growth. Our detailed mechanical analysis of existing experiments shows that both torque and bending moment contribute to the filament phase transition. In this paper, we establish a non-convex and non-local continuum model based on the Ginzburg-Landau theory to describe main characteristics of the filament phase transition such as new-phase nucleation, growth, propagation and the merging of neighboring interfaces. The finite element method (FEM) is adopted to simulate the phase transition under a displacement-controlled loading condition (rotation angle and bending deflection). We show that new-phase nucleation corresponds to the maximum torque and bending moment at the stuck end of the filament. The hysteresis loop in the loading and unloading curves indicates energy dissipation. When the new phase grows and propagates, torque and bending moment remain static. We also find that there is a drop in load when the two interfaces merge, indicating a concomitant reduction in the interfacial energy. Finally, the interface thickness is governed by the coefficients of the gradient of order parameters in the non-local interface energy. Our continuum theory and the finite element method provide a method to study the mechanical behavior of such biomaterials.     

Representing three-dimensional objects by sets of activities of receptive fields

Idealized models of receptive fields (RFs) can be used as building blocks for the creation of powerful distributed computation systems. The present report concentrates on investigating the utility of collections of RFs in representing three-dimensional objects under changing viewing conditions. The main requirement in this task is that the pattern of activity of RFs vary as little as possible when the object and the camera move relative to each other. I propose a method for representing objects by RF activities, based on the observation that, in the case of rotation around a fixed axis, differences of activities of RFs that are properly situated with respect to that axis remain invariant. Results of computational experiments suggest that a representation scheme based on this algorithm for the choice of stable pairs of RFs would perform consistently better than a scheme involving random sets of RFs. The proposed scheme may be useful under object or camera rotation, both for ideal lambertian objects, and for real-world objects such as human faces.     

Identification of protein complexes from multi-relationship protein interaction networks

Background

Protein complexes play an important role in biological processes. Recent developments in experiments have resulted in the publication of many high-quality, large-scale protein-protein interaction (PPI) datasets, which provide abundant data for computational approaches to the prediction of protein complexes. However, the precision of protein complex prediction still needs to be improved due to the incompletion and noise in PPI networks.

Results

There exist complex and diverse relationships among proteins after integrating multiple sources of biological information. Considering that the influences of different types of interactions are not the same weight for protein complex prediction, we construct a multi-relationship protein interaction network (MPIN) by integrating PPI network topology with gene ontology annotation information. Then, we design a novel algorithm named MINE (identifying protein complexes based on Multi-relationship protein Interaction NEtwork) to predict protein complexes with high cohesion and low coupling from MPIN.

Conclusions

The experiments on yeast data show that MINE outperforms the current methods in terms of both accuracy and statistical significance.

     

Linear Mixed Model Selection for False Discovery Rate Control in Microarray Data Analysis

Summary In a microarray experiment, one experimental design is used to obtain expression measures for all genes. One popular analysis method involves fitting the same linear mixed model for each gene, obtaining gene‐specific p‐values for tests of interest involving fixed effects, and then choosing a threshold for significance that is intended to control false discovery rate (FDR) at a desired level. When one or more random factors have zero variance components for some genes, the standard practice of fitting the same full linear mixed model for all genes can result in failure to control FDR. We propose a new method that combines results from the fit of full and selected linear mixed models to identify differentially expressed genes and provide FDR control at target levels when the true underlying random effects structure varies across genes.     

Botanical ratchets

Ratcheting surfaces are a common motif in nature and appear in plant awns and grasses. They are known to proffer selective advantages for seed dispersion and burial. In two simple model experiments, we show that these anisotropically toothed surfaces naturally serve as motion rectifiers and generically move in a unidirectional manner, when subjected to temporally and spatially symmetric excitations of various origins. Using a combination of theory and experiment, we show that a linear relationship between awn length and ratchet efficiency holds under biologically relevant conditions. Grass awns can thus efficiently transform non-equilibrium environmental stresses from such sources as humidity variations into useful work and directed motion using their length as a fluctuation amplifier, yielding a selective advantage to these organelles in many plant species.     

Clustering in linear‐mixed models with a group fused lasso penalty

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear‐mixed models that are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose, an EM algorithm‐based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.     

Integrative approach for inference of gene regulatory networks using lasso-based random featuring and application to psychiatric disorders

Background

Inferring gene regulatory networks is one of the most interesting research areas in the systems biology. Many inference methods have been developed by using a variety of computational models and approaches. However, there are two issues to solve. First, depending on the structural or computational model of inference method, the results tend to be inconsistent due to innately different advantages and limitations of the methods. Therefore the combination of dissimilar approaches is demanded as an alternative way in order to overcome the limitations of standalone methods through complementary integration. Second, sparse linear regression that is penalized by the regularization parameter (lasso) and bootstrapping-based sparse linear regression methods were suggested in state of the art methods for network inference but they are not effective for a small sample size data and also a true regulator could be missed if the target gene is strongly affected by an indirect regulator with high correlation or another true regulator.

Results

We present two novel network inference methods based on the integration of three different criteria, (i) z-score to measure the variation of gene expression from knockout data, (ii) mutual information for the dependency between two genes, and (iii) linear regression-based feature selection.Based on these criterion, we propose a lasso-based random feature selection algorithm (LARF) to achieve better performance overcoming the limitations of bootstrapping as mentioned above.

Conclusions

In this work, there are three main contributions. First, our z score-based method to measure gene expression variations from knockout data is more effective than similar criteria of related works. Second, we confirmed that the true regulator selection can be effectively improved by LARF. Lastly, we verified that an integrative approach can clearly outperform a single method when two different methods are effectively jointed. In the experiments, our methods were validated by outperforming the state of the art methods on DREAM challenge data, and then LARF was applied to inferences of gene regulatory network associated with psychiatric disorders.

     

Relationships between geometry and kinematic characteristics in the temporomandibular joint

Motions of the temporomandibular joint (TMJ) involve both translation and rotation; however, there may be substantial variations from one human to another, and these variations present significant difficulties when designing TMJ prostheses. The disc–condyle glides along the temporal bone and the condyle centre describe a curve that depends on the individual morphology.

This study analyses disc–condyle rotatory and translatory displacements moving all along the temporal bone facets which are mainly composed of two areas: the articular tubercle slope (ATS) and the preglenoid plane separated by the articular tubercle crest. Displacements were quantified using 3D video analysis, and this technique was computer-assisted.

From a population of 32 volunteers, we were able to establish a correlation between the kinematic characteristics of the joint and the disc–condyle trajectories. This study quantifies the geometrical characteristics of the ATS and their inter-individual variations, which are useful in TMJ prosthesis design.