Graphical Methods for Analysing Combination Effects in Dose-Response Experiments

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.     

Simulation of hyper-inverse Wishart distributions in graphical models

We introduce and exemplify an efficient method for direct samplingfrom hyper-inverse Wishart distributions. The method reliesvery naturally on the use of standard junction-tree representationof graphs, and couples these with matrix results for inverseWishart distributions. We describe the theory and resultingcomputational algorithms for both decomposable and nondecomposablegraphical models. An example drawn from financial time seriesdemonstrates application in a context where inferences on astructured covariance model are required. We discuss and investigatequestions of scalability of the simulation methods to higher-dimensionaldistributions. The paper concludes with general comments aboutthe approach, including its use in connection with existingMarkov chain Monte Carlo methods that deal with uncertaintyabout the graphical model structure.     

Estimates of mean alveolar PCO2 during steady-state exercise in man: a theoretical study.

The partial pressure of carbon dioxide in arterial blood is an important operator in the control of breathing, by actions on peripheral and central chemoreceptors. In experiments on man we must often assume that lung alveolar PCO2 equals arterial PCO2 and obtain estimates of the former derived from measurements in expired gas sampled at the mouth. This paper explores the potential errors of such estimates, which are magnified during exercise. We used a published model of the cardiopulmonary system to simulate various levels of exercise up to 300 W. We tested three methods of estimating mean alveolar PCO2 (PACO2) against the true value derived from a time average of the within-breath oscillation in steady-state exercise. We used both sinusoidal and square-wave ventilatory flow wave forms. Over the range 33-133 W end-tidal PCO2 (P(et)CO2) overestimated PACO2 progressively with increasing workload, by about 4 mmHg at 133 W with normal respiratory rate for that load. PCO2 by a graphical approximation technique (PgCO2; "graphical method") underestimated PACO2 by 1-2 mmHg. PCO2 from an experimentally obtained empirical equation (PnjCO2; "empirical method") overestimated PACO2 by 0.5-1.0 mmHg. Graphical and empirical methods were insensitive to alterations in cardiac output or respiratory rate. End-tidal PCO2 was markedly affected by respiratory rate during exercise, the overestimate of PACO2 increasing if respiratory rate was slowed. An increase in anatomical dead space with exercise tends to decrease the error in P(et)CO2 and increase the error in the graphical method. Changes in the proportion of each breath taken up by inspiration make no important difference, and changes in functional residual capacity, while important in principle, are too small to have any major effect on the estimates. Changes in overall alveolar ventilation which alter steady-state PACO2 over a range of 30-50 mmHg have no important effect. At heavy work loads (200-300 W), P(et)CO2 grossly overestimates by 6-9 mmHg. The graphical method progressively underestimates, by about 5 mmHg at 300 W. A simulated CO2 response (the relation between ventilation and increasing PCO2) performed at 100 W suggests that a response slope close to the true one can be obtained by using any of the three methods. The graphical method gave results closest to the true absolute values. Either graphical or empirical methods should be satisfactory for detecting experimentally produced changes in PACO2 during steady-state exercise, to make comparisons between different steady-state exercise loads, and to assess CO2 response in exercise.(ABSTRACT TRUNCATED AT 400 WORDS)     

The role of extrafloral nectaries in the herbivore defence of Cassia fasiculata

Abstract. 1. An experiment is presented that tests the hypothesis that the extrafloral nectaries of Chssia fasiculata reduce herbivory by attracting pugnacious ants that deter herbivores, and tests the equivalence of two methods of ant exclusion: treatment with Tanglefoot, and nectary excision.
2. The protectionist hypothesis is not supported; treatment plants produced as many pods as did control plants.
3. Treatment with Tanglefoot is equivalent to nectary excision in terms of pod production
4. A graphical model is presented that relates the efficacy of ant protection to plant density and ant activity.     

Evaluation of exact and asymptotic interval estimators in logistic analysis of matched case-control studies.

We compare six methods for constructing confidence intervals for a single parameter in stratified logistic regression. Three of these are based on inversion of standard asymptotic tests--namely, the Wald, the score, and the likelihood ratio tests. The other three are based on the exact distribution of the sufficient statistic for the parameter of interest. These include the traditional exact method of constructing confidence intervals, and two others, the mid-P and mean-P methods, which are modifications of this procedure that aim at reducing the conservative bias of the exact method. Using efficient algorithms, the six methods are compared by determination of their exact coverage levels in a series of conditional sample spaces. An incident case-control study of lung cancer in women is used to further illustrate the differences among the various methods. Computation of coverage functions is seen as a useful graphical diagnostic tool for assessing the appropriateness of different methods. The mid-P and the score methods are seen to have better coverage properties than the other four.     

Cultural evolution and perpetuation of arbitrary communicative conventions in experimental microsocieties

Previous studies have shown that iconic graphical signs can evolve into symbols through repeated usage within dyads and interacting communities. Here we investigate the evolution of graphical signs over chains of participants. In these chains (or “replacement microsocieties”), membership of an interacting group changed repeatedly such that the most experienced members were continually replaced by naïve participants. Signs rapidly became symbolic, such that they were mutually incomprehensible across experienced members of different chains, and new entrants needed to learn conventionalised meanings. An objective measure of graphical complexity (perimetric complexity) showed that the signs used within the microsocieties were becoming progressively simplified over successive usage. This is the first study to show that the signs that evolve in graphical communication experiments can be transmitted to, and spontaneously adopted by, naïve participants. This provides critical support for the view that human communicative symbols could have evolved culturally from iconic representations.     

PermutMatrix: a graphical environment to arrange gene expression profiles in optimal linear order

PermutMatrix is a work space designed to graphically explore gene expression data. It relies on the graphical approach introduced by Eisen and also offers several methods for the optimal reorganization of rows and columns of a numerical dataset. For example, several methods are proposed for optimal reorganization of the leaves of a hierarchical clustering tree, along with several seriation or unidimensional scaling methods that do not require any preliminary hierarchical clustering. This program, developed for MS Windows, with MS-Visual C++, has a clear and efficient graphical interface. Large datasets can be thoroughly and quickly analyzed.     

Linear selection indices for non-linear profit functions

Summary Two methods of deriving linear selection indices for non-linear profit functions have been proposed. One is by linear approximation of profit, and another is the graphical method of Moav and Hill (1966). When profit is defined as the function of population means, the graphical method is optimal. In this paper, profit is defined as the function of the phenotypic values of individual animals; it is then shown that the graphical method is not generally optimal. We propose new methods for constructing selection indices. First, a numerical method equivalent to the graphical method is proposed. Furthermore, we propose two other methods using quadratic approximation of profit: one is based on Taylor series about means before selection, and the other is based on Tayler series about means after selection. Among these different methods, it is shown that the method using quadratic approximation based on Taylor series about means after selection is the most efficient.     

Semiparametric analysis of recurrent events data in the presence of dependent censoring

Dependent censoring occurs in longitudinal studies of recurrent events when the censoring time depends on the potentially unobserved recurrent event times. To perform regression analysis in this setting, we propose a semiparametric joint model that formulates the marginal distributions of the recurrent event process and dependent censoring time through scale-change models, while leaving the distributional form and dependence structure unspecified. We derive consistent and asymptotically normal estimators for the regression parameters. We also develop graphical and numerical methods for assessing the adequacy of the proposed model. The finite-sample behavior of the new inference procedures is evaluated through simulation studies. An application to recurrent hospitalization data taken from a study of intravenous drug users is provided.     

Virtual Reality in Chemistry

With the advent of ever more powerful computer graphics hardware and visualization packages, new graphical methods of scientific visualization and data exploration are beginning to be explored. This includes fully immersive environments where the chemist is surrounded by data objects in 3D space. New models of animation and interactive manipulation of graphical entities are developed to help the chemist in gaining insight from or navigating in large amounts of data. This review discusses some representative approaches and systems which demonstrate where chemistry-related visualization and data management is headed.     

Bayesian analysis of matrix normal graphical models

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Extensions to matrix-variate time series embed matrix normal graphs in dynamic models. Examples highlight questions of graphical model uncertainty, search and comparison in matrix data contexts. These models may be applied in a number of areas of multivariate analysis, time series and also spatial modelling.     

Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

Robust Gaussian Graphical Modeling Via l1 Penalization

Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l₁ penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified‐likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re‐estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso.     

DAnTE: a statistical tool for quantitative analysis of -omics data

Data Analysis Tool Extension (DAnTE) is a statistical tool designed to address challenges associated with quantitative bottom-up, shotgun proteomics data. This tool has also been demonstrated for microarray data and can easily be extended to other high-throughput data types. DAnTE features selected normalization methods, missing value imputation algorithms, peptide-to-protein rollup methods, an extensive array of plotting functions and a comprehensive hypothesis-testing scheme that can handle unbalanced data and random effects. The graphical user interface (GUI) is designed to be very intuitive and user friendly. AVAILABILITY: DAnTE may be downloaded free of charge at http://omics.pnl.gov/software/. SUPPLEMENTARY INFORMATION: An example dataset with instructions on how to perform a series of analysis steps is available at http://omics.pnl.gov/software/     

Machine learning in bioinformatics

This article reviews machine learning methods for bioinformatics. It presents modelling methods, such as supervised classification, clustering and probabilistic graphical models for knowledge discovery, as well as deterministic and stochastic heuristics for optimization. Applications in genomics, proteomics, systems biology, evolution and text mining are also shown.     

Reducing modeling error of graphical methods for estimating volume of distribution measurements in PIB-PET study

Graphical analysis methods are widely used in positron emission tomography quantification because of their simplicity and model independence. But they may, particularly for reversible kinetics, lead to bias in the estimated parameters. The source of the bias is commonly attributed to noise in the data. Assuming a two-tissue compartmental model, we investigate the bias that originates from modeling error. This bias is an intrinsic property of the simplified linear models used for limited scan durations, and it is exaggerated by random noise and numerical quadrature error. Conditions are derived under which Logan’s graphical method either over-or under-estimates the distribution volume in the noise-free case. The bias caused by modeling error is quantified analytically. The presented analysis shows that the bias of graphical methods is inversely proportional to the dissociation rate. Furthermore, visual examination of the linearity of the Logan plot is not sufficient for guaranteeing that equilibrium has been reached. A new model which retains the elegant properties of graphical analysis methods is presented, along with a numerical algorithm for its solution. We perform simulations with the fibrillar amyloid β radioligand [11C] benzothiazole-aniline using published data from the University of Pittsburgh and Rotterdam groups. The results show that the proposed method significantly reduces the bias due to modeling error. Moreover, the results for data acquired over a 70 min scan duration are at least as good as those obtained using existing methods for data acquired over a 90 min scan duration.     

Graphical rules for non-steady state enzyme kinetic

The exiting graphical methods in enzyme kinetics can be used only within the scope of steady state reactions. In this paper, two graphical rules are presented to deal with the non-steady state enzyme catalysed reaction systems. According to Rule 1 we can immediately write out the phase concentration of enzyme species. The calculation work such as setting up differential equations, making Laplace transformation, expanding determinants, which are both tedious and liable to error, are completely saved. By means of Rule 2 the secular equations for the consecutive first-order reactions can be written out directly without need of setting up differential equations, expanding determinants, etc., that would otherwise be laborious and prone to errors. In addition, two check formulae are also presented for these two graphical methods, respectively. They are useful in order for avoiding the omission of terms during calculations, especially, for complicated mechanisms.     

Microbial Interaction Network Estimation via Bias-Corrected Graphical Lasso

With the increasing availability of microbiome 16S data, network estimation has become a useful approach to studying the interactions between microbial taxa. Network estimation on a set of variables is frequently explored using graphical models, in which the relationship between two variables is modeled via their conditional dependency given the other variables. Various methods for sparse inverse covariance estimation have been proposed to estimate graphical models in the high-dimensional setting, including graphical lasso. However, current methods do not address the compositional count nature of microbiome data, where abundances of microbial taxa are not directly measured, but are reflected by the observed counts in an error-prone manner. Adding to the challenge is that the sum of the counts within each sample, termed “sequencing depth,” is an experimental technicality that carries no biological information but can vary drastically across samples. To address these issues, we develop a new approach to network estimation, called BC-GLASSO (bias-corrected graphical lasso), which models the microbiome data using a logistic normal multinomial distribution with the sequencing depths explicitly incorporated, corrects the bias of the naive empirical covariance estimator arising from the heterogeneity in sequencing depths, and builds the inverse covariance estimator via graphical lasso. We demonstrate the advantage of BC-GLASSO over current approaches to microbial interaction network estimation under a variety of simulation scenarios. We also illustrate the efficacy of our method in an application to a human microbiome data set.

     

A kinetic method for the simultaneous determination of isoenzymes activities in mixture. Application to A2 and A3 horseradish peroxidases

A graphical method for the simultaneous determination of the activity of two isoenzymes in a mixture, is presented. The method is based on the different kinetic behaviour of the isoenzymes to the changes in the substrate concentrations. Having determined the reaction rates for the enzyme mixture at different substrate concentrations, the activity of both isoenzymes can be derived graphically. An algebraic method for two or more isoenzymes is mentioned, as well. The applications of the graphical and the algebraic method to A2 and A3 horseradish isoperoxidases demonstrated that the difference between the actual activities of the two isoperoxidases and those determined by the proposed method was around 5% of the actual activities. The scope of application of this method could be extended to isoenzymes of clinical importance.