analysis of embryonic development with a model for under or overdispersion relative to binomial variation summary observations from a study of the development of ovulations into embryos for texel sheep are analysed with a model for count data that are under or overdispersed relative to binomial variation the analysis is based on maximum quasi likelihood mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall following an approach suggested by williams 1982 applied statistics 31 144 148 the dispersion parameter is developed as a combination of a variance component representing shared maternal effects and a correlation typically negative between ovulations within ewes the number of ovulations the binomial denominator is included as an explanatory variable

an evaluation of some methods for fitting dose response models to quantal response developmental toxicology data the analysis of quantal response developmental toxicology data by dose response modeling is discussed with emphasis on methods that avoid exact distributional assumptions these methods quasi likelihood bootstrapping and jackknifing are contrasted with analyses based on the beta binomial distribution for the resampling procedures dose response models are fit under a binomial likelihood a justification for this choice of estimator in resampling plans is given based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators this justification depends only on the true distribution of the data having the usual binomial expectation a quasi likelihood approach is also considered in which simple assumptions about the intralitter correlation structure are made quasi likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure the practical implications of these asymptotic results are evaluated in a simulation study

optimization of spatial complex networks abstract first we estimate the connectivity properties of a predefined fixed node locations spatial network which optimizes a connectivity functional that balances construction and transportation costs in this case we obtain a gaussian distribution for the connectivity however when we consider these spatial networks in a growing process we obtain a power law distribution for the connectivity if the transportation costs in the functional involve the shortest geometrical path we obtain a scaling exponent 2 5 however if the transportation costs in the functional involve just the shortest path we obtain 2 2 both cases may be useful to analyze in some real networks

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

true scale invariant random spatial networks some aspects of real world road networks seem to have an approximate scale invariance property motivating study of mathematical models of random networks whose distributions are exactly invariant under euclidean scaling this requires working in the continuum plane so making a precise definition is not trivial we introduce an axiomatization of a class of processes we call scale invariant random spatial networks whose primitives are routes between each pair of points in the plane one concrete model based on minimum time routes in a binary hierarchy of roads with different speed limits has been shown to satisfy the axioms and two other constructions based on poisson line processes and on dynamic proximity graphs are expected also to do so we initiate study of structure theory and summary statistics for general processes in the class many questions arise in this setting via analogies with diverse existing topics from geodesics in first passage percolation to transit node based route finding algorithms

interval estimation of risk difference for data sampled from clusters risk difference rd is an important measure in epidemiological studies where the probability of developing a disease for individuals in an exposed group for example is compared with that in a control group there are varying cluster sizes in each group and the binary responses within each cluster cannot be assumed independent under the cluster sampling scenario lui statistical estimation of epidemiological risk wiley ca 2004 7 27 discusses four methods for the construction of a confidence interval for the rd in this paper we introduce two very simple methods one method is based on an estimator of the variance of a ratio estimator sampling techniques 3rd edn wiley new york 1977 30 67 and the other method is based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations approach of zeger and liang biometrics 1986 42 121 130 these two methods are then compared by simulation in terms of maintaining nominal coverage probability and average coverage length with the four methods discussed by lui statistical estimation of epidemiological risk wiley ca 2004 7 27 simulations show at least as good properties of these two methods as those of the others the method based on an estimate of the variance of a ratio estimator performs best overall it involves a very simple variance expression and can be implemented with a very few computer codes therefore it can be considered as an easily implementable alternative

transport and diffusion of material quantities on propagating interfaces via level set methods we develop theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework level set methods are computational techniques for tracking moving interfaces they work by embedding the propagating interface as the zero level set of a higher dimensional function and then approximate the solution of the resulting initial value partial differential equation using upwind finite difference schemes the traditional level set method works in the trace space of the evolving interface and hence disregards any parameterization in the interface description consequently material quantities on the interface which themselves are transported under the interface motion are not easily handled in this framework we develop model equations and algorithmic techniques to extend the level set method to include these problems we demonstrate the accuracy of our approach through a series of test examples and convergence studies

solving eigenvalue problems on curved surfaces using the closest point method eigenvalue problems are fundamental to mathematics and science we present a simple algorithm for determining eigenvalues and eigenfunctions of the laplace beltrami operator on rather general curved surfaces our algorithm which is based on the closest point method relies on an embedding of the surface in a higher dimensional space where standard cartesian finite difference and interpolation schemes can be easily applied we show that there is a one to one correspondence between a problem defined in the embedding space and the original surface problem for open surfaces we present a simple way to impose dirichlet and neumann boundary conditions while maintaining second order accuracy convergence studies and a series of examples demonstrate the effectiveness and generality of our approach

on the metric topological and functional structures of urban networks abstract axial graphs are networks whose nodes are linear axes in urban space and whose edges represent intersections of such axes these graphs are used in urban planning and urban morphology studies in this paper we analyse distance distributions between nodes in axial graphs and show that these distributions are well approximated by rescaled poisson distributions we then demonstrate a correlation between the parameters governing the distance distribution and the degree of the polynomial distribution of metric lengths of linear axes in cities this correlation provides topological support to the metrically based categorisation of cities proposed in r carvalho a penn scaling and universality in the micro structure of urban space physica a 332 2004 539 547 finally we attempt to explain this topologico metric categorisation in functional terms to this end we introduce a notion of attraction cores defined in terms of aggregations of random walk agents we demonstrate that the number of attraction cores in cities correlates with the parameters governing their distance and line length distributions the intersection of all the three points of view topological metric and agent based yields a descriptive model of the structure of urban networks

a cell based particle method for modeling dynamic interfaces abstract we propose several modifications to the grid based particle method gbpm 21 for moving interface modeling there are several nice features of the proposed algorithm the new method can significantly improve the distribution of sampling particles on the evolving interface unlike the original gbpm where footpoints sampling points tend to cluster to each other the sampling points in the new method tend to be better separated on the interface moreover by replacing the grid based discretization using the cell based discretization we naturally decompose the interface into segments so that we can easily approximate surface integrals as a possible alternative to the local polynomial least square approximation we also study a geometric basis for local reconstruction in the resampling step we will show that such modification can simplify the overall implementations numerical examples in two and three dimensions will show that the algorithm is computationally efficient and accurate

the impact of litter effects on dose response modeling in teratology the fitting of dose response models to teratology data involving littermates in order to generate estimates of teratogenic risk is receiving increasing attention as a potential alternative to the safety factor approach to risk estimation in this paper we utilize the beta binomial distribution to introduce varying degrees of intralitter correlation and for purposes of illustration consider a logistic dose response model that describes the logit of risk as a straight line function of ln dose the biases and exact and asymptotic variances of the maximum likelihood estimators of the intercept and slope are studied by simulation as a function of the intralitter correlation structure

unfolding kernel embeddings of graphs in this paper we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels the idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels the resulting data tends to be clustered along a curve that wraps around the embedding space a behavior that suggests that long range distances are not estimated accurately resulting in an increased curvature of the embedding space hence we propose to use a number of manifold learning techniques to compute a low dimensional embedding of the graphs in an attempt to unfold the embedding manifold and increase the class separation we perform an extensive experimental evaluation on a number of standard graph datasets using the shortest path borgwardt and kriegel 2005 graphlet shervashidze et al 2009 random walk kashima et al 2003 and weisfeiler lehman shervashidze et al 2011 kernels we observe the most significant improvement in the case of the graphlet kernel which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold on the other hand the weisfeiler lehman kernel partially mitigates the locality problem by using the node labels information and thus does not clearly benefit from the manifold learning interestingly our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels highlightswe use manifold learning techniques to enhance the performance of graph kernels we try to increase the class separation by unfolding the embedding manifold we propose a procedure to find the optimal embedding of the data the kernels which neglect the locational information show the largest improvement the unfolding of the space helps to reduce the performance gap between the kernels

a grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion we develop numerical methods for solving partial differential equations pde defined on an evolving interface represented by the grid based particle method gbpm recently proposed in s leung h k zhao a grid based particle method for moving interface problems j comput phys 228 2009 7706 7728 in particular we develop implicit time discretization methods for the advection diffusion equation where the time step is restricted solely by the advection part of the equation we also generalize the gbpm to solve high order geometrical flows including surface diffusion and willmore type flows the resulting algorithm can be easily implemented since the method is based on meshless particles quasi uniformly sampled on the interface furthermore without any computational mesh or triangulation defined on the interface we do not require remeshing or reparametrization in the case of highly distorted motion or when there are topological changes as an interesting application we study locally inextensible flows governed by energy minimization we introduce tension force via a lagrange multiplier determined by the solution to a helmholtz equation defined on the evolving interface extensive numerical examples are also given to demonstrate the efficiency of the proposed approach

estimation bias using the beta binomial distribution in teratology kupper et al 1986 biometrics 42 85 98 considered the fitting of dose response regressions to litter proportions in teratology experiments they found that the estimators which maximise the beta binomial likelihood become biased when the intralitter correlation is incorrectly assumed to be homogeneous this paper considers the nature of this bias and its implications for the analysis of litter proportions in toxicology

on the use of stochastic ordering to test for trend with clustered binary data we introduce the use of stochastic ordering for defining treatment related trend in clustered exchangeable binary data for both when cluster sizes are fixed and when they vary randomly in the latter case there is a well documented tendency for such data to be sparse a problem we address by making an assumption of interpretability or equivalently marginal compatibility our procedures are based on a representation of the joint distribution of binary exchangeable random variables by a saturated model and may hence be considered nonparametric the definition of trend by stochastic ordering is proposed to ensure a flexibility that allows for various forms of monotone increases in response to the cluster as a whole to be included in the evaluation of the trend we obtain maximum likelihood estimates of probability functions under stochastic ordering using mixture likelihood based algorithms since the data are sparse we avoid the use of asymptotic results and obtain p values of the likelihood ratio procedures by permutation resampling we demonstrate how the proposed framework can be used in risk assessment and provide comparisons with existing procedures

profile likelihood based confidence interval of the intraclass correlation for binary outcome data sampled from clusters the intraclass correlation in binary outcome data sampled from clusters is an important and versatile measure in many biological and biomedical investigations properties of the different estimators of the intraclass correlation based on the parametric semi parametric and nonparametric approaches have been studied extensively mainly in terms of bias and efficiency see for example ridout et al biometrics 1999 55 137 148 paul et al journal of statistical computation and simulation 2003 73 507 523 and lee statistical modelling 2004 4 113 126 but little attention has been paid to extending these results to the problem of the confidence intervals in this article we generalize the results of the four point estimators by constructing asymptotic confidence intervals obtaining closed form asymptotic and sandwich variance expressions of those four point estimators it appears from simulation results that the asymptotic confidence intervals based on these four estimators have serious under coverage to remedy this we introduce the fisher s z transformation approach on the intraclass correlation coefficient the profile likelihood approach based on the beta binomial model and the hybrid profile variance approach based on the quadratic estimating equation for constructing the confidence intervals of the intraclass correlation for binary outcome data as assessed by monte carlo simulations these confidence interval approaches show significant improvement in the coverage probabilities moreover the profile likelihood approach performs quite well by providing coverage levels close to nominal over a wide range of parameter combinations we provide applications to biological data to illustrate the methods copyright 2012 john wiley sons ltd

an rbf fd closest point method for solving pdes on surfaces abstract partial differential equations pdes on surfaces appear in many applications throughout the natural and applied sciences the classical closest point method ruuth and merriman 2008 17 is an embedding method for solving pdes on surfaces using standard finite difference schemes in this paper we formulate an explicit closest point method using finite difference schemes derived from radial basis functions rbf fd unlike the orthogonal gradients method piret 2012 22 our proposed method uses rbf centers on regular grid nodes this formulation not only reduces the computational cost but also avoids the ill conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm leung and zhao 2009 26 when compared to the standard finite difference discretization of the closest point method the proposed method requires a smaller computational domain surrounding the surface resulting in a decrease in the number of sampling points on the surface in addition higher order schemes can easily be constructed by increasing the number of points in the rbf fd stencil applications to a variety of examples are provided to illustrate the numerical convergence of the method

scale invariance in road networks we study the topological and geographic structure of the national road networks of the united states england and denmark by transforming these networks into their dual representation where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect we show that they exhibit both topological and geographic scale invariance that is we show that for sufficiently large geographic areas the dual degree distribution follows a power law with exponent 2 2 or alpha or 2 4 and that journeys regardless of their length have a largely identical structure to explain these properties we introduce and analyze a simple fractal model of road placement that reproduces the observed structure and suggests a testable connection between the scaling exponent and the fractal dimensions governing the placement of roads and intersections

quantitative risk assessment for teratological effects abstract this article presents a quantitative procedure for using a benchmark dose to obtain low dose risk estimates for reproductive and developmental toxic effects this procedure combines the best features of the previously proposed methods for handling litter effects for teratology data and the currently used methods for quantitative risk assessment the beta binomial distribution is used to account for litter effects and the weibull dose response model is used for modeling teratogenic effects a benchmark dose defined to be the lowest dose at which the excess risk does not exceed 1 with 95 confidence is proposed to replace the no observed effect level noel the noel is generally the highest experimental dose that is not statistically different from the control the noel approach does not use experimental data effectively for quantitative risk estimation in this article a lower limit on the safe dose is estimated by linearly extrapolating downward from the benchmark dose this procedure is

extended generalized estimating equations for clustered data abstract typically analysis of data consisting of multiple observations on a cluster is complicated by within cluster correlation estimating equations for generalized linear modeling of clustered data have recently received much attention this article proposes an extension to the generalized estimating equation method proposed by liang and zeger which treats within cluster correlations as nuisance parameters using ideas from extended quasi likelihood estimating equations for regression and association parameters are provided simultaneously the resulting estimators are proven to be asymptotically normal and consistent under certain conditions the consistency of regression estimators allows incorrect modeling of the correlation among repeated responses the method is illustrated with an analysis of data from a developmental toxicity study

characterization of spatial networklike patterns from junction geometry we propose a method for quantitative characterization of spatial networklike patterns with loops such as surface fracture patterns leaf vein networks and patterns of urban streets such patterns are not well characterized by purely topological estimators also patterns that both look different and result from different morphogenetic processes can have similar topology a local geometric cue the angles formed by the different branches at junctions can complement topological information and allow the quantification of the large scale spatial coherence of the pattern for patterns that grow over time such as fracture lines on the surface of ceramics the rank assigned by our method to each individual segment of the pattern approximates the order of appearance of that segment we apply the method to various networklike patterns and find a continuous but sharp dichotomy between two classes of spatial networks hierarchical and homogeneous the former class results from a sequential growth process and presents large scale organization and the latter presents local but not global organization

estimating logistic regression parameters for bivariate binary data summary consider bivariate binary data with possibly different covariates for each marginal binary observation suppose that the correlation between paired observations is a nuisance and the interest lies in estimating logistic regression parameters associated with the covariates we consider the estimator obtained by using the independence estimating equation with corrected variance this estimator can be very efficient and robust compared with maximum likelihood or the estimator of liang and zeger some comments are made concerning higher dimensional multivariate data

confidence intervals for the risk ratio under cluster sampling based on the beta binomial model in cohort studies the risk ratio rr is one of the most commonly used epidemiologic indices to quantify the effect of a suspected risk factor on the probability of developing a disease when we employ cluster sampling to collect data an interval estimator that does not account for the intraclass correlation between subjects within clusters is likely inappropriate in application of the beta binomial model to account for the intraclass correlation we develop four asymptotic interval estimators of the rr which are direct extensions of some recently developed estimators for independent binomial sampling we then use monte carlo simulation to evaluate the finite sample performance of these four interval estimators in a variety of situations we find that the estimator using the logarithmic transformation generally performs well and is preferable to the other three estimators in most of the situations considered here finally we include an example from a study of an educational intervention with emphasis on behaviour change to illustrate the use of the estimators developed in this paper

modeling and computation of two phase geometric biomembranes using surface finite elements biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions the modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces this leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints in this paper we propose a new computational tool for computing equilibria based on an l 2 relaxation flow for the total energy in which the line energy is approximated by a surface ginzburg landau phase field functional the relaxation dynamics couple a nonlinear fourth order geometric evolution equation of willmore flow type for the membrane with a surface allen cahn equation describing the lateral decomposition a novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface the mean curvature vector and the surface phase field function the resulting variational formulation uses h 1 spaces and we employ triangulated surfaces and h 1 conforming quadratic surface finite elements for approximating solutions together with a semi implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells discocytes and starfishes with lateral phase separation

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

scale free network on euclidean space optimized by rewiring of links a barabasi albert scale free network is constructed whose nodes are the poisson distributed random points within a unit square and links are the straight line connections among the nodes the cost function which is the total wiring length associated with such a network defined on a two dimensional plane is optimized the optimization process consists of random selection of a pair of links and rewiring them to reduce the total length of the pair but with the constraint that the degree as well as the out degree and in degree of each node are precisely maintained the resulting optimized network has a small diameter as well as high clustering and the link length distribution has a stretched exponential tail

a grid based particle method for moving interface problems we propose a novel algorithm for modeling interface motions the interface is represented and is tracked using quasi uniform meshless particles these particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface the underlying grid provides an eulerian reference and local sampling rate for particles on the interface it also renders neighborhood information among the meshless particles for local reconstruction of the interface the resulting algorithm which is based on lagrangian tracking using meshless particles with eulerian reference grid can naturally handle control topological changes moreover adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad oct tree data structure extensive numerical examples are presented to demonstrate the capability of our new algorithm

further results on a multiple testing procedure for clinical trials o brien and fleming 1979 biometrics 35 549 556 proposed a procedure for multiple testing in clinical trials for acute disease we evaluated their procedure for chronic disease models and found that it can be used without modification type i errors are unaltered and no loss of power is seen in comparison with single sample procedures however average savings in sample size are less for the chronic disease models than for the acute model finally it is shown that for any specific disease model and fixed maximum number of inspections of the data the percentage reduction in sample size can be readily predicted from the power

two random effects models for multivariate binary data we consider two regression models for multivariate binary data in the case that the marginal success probabilities are unequal the first model is based on an additive random effect operating on the probability scale the second model assumes a discrete random effect operates on the logit scale consequently the interpretation of the regression parameters differs for the two models their use is illustrated by application to some dental data

schwarz solvers and preconditioners for the closest point method the discretization of surface intrinsic elliptic partial differential equations pdes poses interesting challenges not seen in flat spaces the discretization of these pdes typically proceeds by e

the performance of the o brien fleming multiple testing procedure in the presence of intraclass correlation assuming that all subject responses were independent o brien and fleming 1979 biometrics 35 549 556 proposed a simple and useful multiple testing procedure for clinical trials for comparing two treatments with dichotomous data differences in the methods of evaluating subject responses at each evaluation time however may induce an intraclass correlation among these responses used in calculating the o brien fleming multiple testing procedure on the basis of monte carlo simulations we note that even a small intraclass correlation among subject responses in the same analysis can substantially inflate the type i error of the o brien fleming multiple testing procedure furthermore this inflation generally increases as either the number of analyses or the underlying response probability increases we also have demonstrated that if we were able to maintain a uniform medical test procedure between the two treatments for each analysis the actual type i error of the o brien fleming multiple testing procedure may conversely become conservative

interval estimation for the intraclass correlation in dirichlet multinomial data when the underlying distribution is discrete with a limited number of categories methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use on the basis of large sample theory this paper develops an asymptotic closed form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category this paper employs monte carlo simulation to demonstrate that when the underlying intraclass correlation is large the traditional interval estimator which assumes normality can be misleading we find that when the number of classes is 20 the interval estimator proposed here can generally perform reasonably well in a variety of situations this paper further notes that the proposed interval estimator is invariant with respect to a linear transformation when the data are on a nominal scale an extension of the proposed method to account for this case as well as a discussion on the relationship between the intraclass correlation and a kappa type measure defined here and on the limitation of the corresponding kappa type estimator are given

interval estimation of generalized odds ratio in data with repeated measurements when the underlying responses are on an ordinal scale the generalized odds ratio gor defined as the ratio of the proportions of concordant and discordant pairs is a useful index to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable we discuss interval estimation of the gor for ordinal data with repeated measurements on the basis of the dirichlet multinomial model we develop three asymptotic interval estimators of the gor using wald s test statistic a logarithmic transformation and a method analogous to fieller s theorem respectively to evaluate and compare the finite sample performance of these estimators we apply monte carlo simulation we find that when the number of subjects per group is not large the coverage probability of interval estimator using wald s test statistic is likely to be less than the desired confidence level by contrast the coverage probability of the other two estimators are approximately equal to or larger than the desired confidence level when the number of subjects per group is small and the intraclass correlation between repeated measurements within subjects is large we note that applying the interval estimator derived from a method analogous to fieller s theorem can lose efficiency we also note that the interval estimator using the logarithmic transformation is generally preferable to the other two estimators with respect to both the coverage probability and the average length finally on the basis of a few preliminary simulations we do find some robustness for all the estimators developed here we include an example comparing the inflammation grade after lung transplant between surgeries to illustrate the use of the proposed interval estimators

models for quantal response experiments over time response carter and hubert 1984 biometrics 40 699 706 propose and apply an approach based on multivariate growth curve theory to quantal bioassay over time their experimental data are reanalyzed using a fairly standard approach based on models for grouped response time data this alternate approach is considerably more direct and theoretically more satisfactory practical advantages include direct assessment of model adequacy and parsimonious modelling of extra multinomial variation

combinatorial and approximative analyses in a spatially random division process for a spatial characteristic there exist commonly fat tail frequency distributions of fragment size and mass of glass areas enclosed by city roads and pore size volume in random packings in order to give a new analytical approach for the distributions we consider a simple model which constructs a fractal like hierarchical network based on random divisions of rectangles the stochastic process makes a markov chain and corresponds to directional random walks with splitting into four particles we derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions

procedures for testing the homogeneity of relative difference in sparse data to quantify the excess effect of an experimental treatment over a placebo group in clinical trials we often consider use of the relative difference defined as the proportion of patients who would respond to the experimental treatment among those who would not otherwise if they were assigned to the placebo group to control the effects due to confounders on the response of interest we frequently employ stratified analysis in practice before obtaining a summary estimate of the relative difference it is desirable to assess whether this measure is constant across strata based on the beta binomial model we develop simple procedures for testing the homogeneity of relative difference for sparse data in which we have many strata but few patients per stratum using monte carlo simulations we demonstrate that the proposed test procedures can generally perform well with respect to type i error in a variety of situations we further evaluate and study the power of these test procedures finally we note some robustness in using the test procedures proposed here

the evaluation of integrals of the form f t exp t 2 dt application to logistic normal models abstract logistic normal distributions and related functions arise in a variety of statistical applications of current interest including binary measurement error models and the analysis of teratogenicity experiments analytic intractability has led to the development of numerous approximations to the desired forms often with consequences that have not been well studied a method is developed to compute these forms to arbitrary accuracy and comparative calculations are made that show when the common numerical alternative 20 point gaussian quadrature begins to fail by using a simple matrix transformation this method can be used with multiple covariate regression models of the logistic normal form we conducted a simulation study that compares the ability of 20 point gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic normal measurement error model using standard subroutines to maximize the likelihood equations 27 of 50 trials failed to

a discussion on the conventional estimator of sensitivity and specificity in multiple tests both the variation of positive responses negative responses among individuals and the internal correlation among responses for the same individual affect the precision of the estimate of sensitivity specificity to estimate the sensitivity specificity of a medical diagnostic test this paper proposes a bayesian approach with a simple markov model to evaluate the performance of the conventional estimator under different situations on the basis of the assumed model we derive a general formula for the variance of the conventional estimator regarding multiple tests and present a quantitative discussion on the limitations of this estimator

on the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems this paper considers the asymptotic distribution of the likelihood ratio statistic t for testing a subset of parameter of interest h 0 0 based on the pseudolikelihood l where is a consistent estimator of the nuisance parameter we show that the asymptotic distribution of t under h 0 is a weighted sum of independent chi squared variables some sufficient conditions are provided for the limiting distribution to be a chi squared variable when the true value of the parameter of interest 0 or the true value of the nuisance parameter 0 lies on the boundary of parameter space the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix or from a mixture of multivariate normal distributions a variety of examples are provided for which the limiting distributions of t may be mixtures of chi squared variables we conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments

measuring graph similarity through continuous time quantum walks and the quantum jensen shannon divergence in this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs we design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous time quantum walks in order to analyze the behavior of the walks without causing wave function collapse we base our analysis on the recently introduced quantum jensen shannon divergence in particular we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic we also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the hamiltonians associated with the two original graphs have an empty intersection

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

a localized meshless method for diffusion on folded surfaces partial differential equations pdes on surfaces arise in a variety of application areas including biological systems medical imaging fluid dynamics mathematical physics image processing and computer graphics in this paper we propose a radial basis function rbf discretization of the closest point method the corresponding localized meshless method may be used to approximate diffusion on smooth or folded surfaces our method has the benefit of having an a priori error bound in terms of percentage of the norm of the solution a stable solver is used to avoid the ill conditioning that arises when the radial basis functions rbfs become flat

a grid based particle method for evolution of open curves and surfaces we propose a new numerical method for modeling motion of open curves in two dimensions and open surfaces in three dimensions following the grid based particle method we proposed in s leung h k zhao a grid based particle method for moving interface problems j comput phys 228 2009 2993 3024 we represent the open curve or the open surface by meshless lagrangian particles sampled according to an underlying fixed eulerian mesh the underlying grid is used to provide a quasi uniform sampling and neighboring information for meshless particles the key idea in the current paper is to represent and to track end points of the open curve and boundary points of the open surface explicitly and consistently with interior particles we apply our algorithms to several applications including spiral crystal growth modeling and image segmentation using active contours

estimating the number of clusters for the analysis of correlated binary response variables from unbalanced data dominating the literature on sample size determination are papers concerned with observations collected from independent responses we discuss in this paper under the common correlation model for binary responses the issue of estimating the number of groups when the sampling units are clusters of variable sizes

an interval estimate for the interclass correlation in beta binomial sampling the beta binomial distribution has been frequently applied to model intraclass correlation among dichotomous responses in cluster sampling to avoid using sophisticated numerical procedures to calculate maximum likelihood estimates many authors have proposed different moment estimators most of them focused their discussion however on point estimation only in this paper we have developed a closed form interval estimate for the intraclass correlation and have shown it has asymptotically correct coverage we have further used a monte carlo simulation to evaluate the performance of the proposed interval estimation in a variety of situations we have found that when the number of clusters is moderate 50 the proposed interval estimation performs reasonably well except for the situation where the intraclass correlation is large and the underlying mean response probability is small even when the number of clusters is as small as 20 the proposed interval estimation may still be useful in the situation where the intraclass correlation is small we have also extended the proposed interval estimate to accommodate stratified sampling in which each stratum has a different mean response probability but has a common intraclass correlation

pdes on moving surfaces via the closest point method and a modified grid based particle method partial differential equations pdes on surfaces arise in a wide range of applications the closest point method ruuth and merriman 2008 20 is a recent embedding method that has been used to solve a variety of pdes on smooth surfaces using a closest point representation of the surface and standard cartesian grid methods in the embedding space the original closest point method cpm was designed for problems posed on static surfaces however the solution of pdes on moving surfaces is of considerable interest as well here we propose solving pdes on moving surfaces using a combination of the cpm and a modification of the grid based particle method leung and zhao 2009 12 the grid based particle method gbpm represents and tracks surfaces using meshless particles and an eulerian reference grid our modification of the gbpm introduces a reconstruction step into the original method to ensure that all the grid points within a computational tube surrounding the surface are active we present a number of examples to illustrate the numerical convergence properties of our combined method experiments for advection diffusion equations that are strongly coupled to the velocity of the surface are also presented

the implicit closest point method for the numerical solution of partial differential equations on surfaces many applications in the natural and applied sciences require the solutions of partial differential equations pdes on surfaces or more general manifolds the closest point method is a simple and accurate embedding method for numerically approximating pdes on rather general smooth surfaces however the original formulation is designed to use explicit time stepping this may lead to a strict time step restriction for some important pdes such as those involving the laplace beltrami operator or higher order derivative operators to achieve improved stability and efficiency we introduce a new implicit closest point method for surface pdes the method allows for large stable time steps while retaining the principal benefits of the original method in particular it maintains the order of accuracy of the discretization of the underlying embedding pde it works on sharply defined bands without degrading the accuracy of the method and it applies to general smooth surfaces it also is very simple and may be applied to a rather general class of surface pdes convergence studies for the in surface heat equation and a fourth order biharmonic problem are given to illustrate the accuracy of the method we demonstrate the flexibility and generality of the method by treating flows involving diffusion reaction diffusion and fourth order spatial derivatives on a variety of interesting surfaces including surfaces of mixed codimension

estimation and testing with overdispersed proportions using the beta logistic regression model of heckman and willis summary methods are presented for modeling dose related effects in proportion data when extra binomial variability is a concern motivation is taken from experiments in developmental toxicology where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions appeal is made to the well known beta binomial distribution to represent the overdispersion from this an exponential function of the linear predictor is used to model the dose response relationship the specification was introduced previously for econometric applications by heckman and willis it induces a form of logistic regression for the mean response together with a reciprocal biexponential model for the intralitter correlation large sample likelihood based methods for estimating and testing the joint proportion correlation response are studied a developmental toxicity data set illustrates the methods

a random effects model for ordered categorical data abstract this article presents a random effects model for multivariate and grouped univariate ordered categorical data the assumed family of distributions for the random effects adopts a wide variety of forms and shapes the model s likelihood has a closed expression and can be computed without recourse to numerical integration or gaussian quadrature a bivariate and a grouped univariate example are used to illustrate the proposed model

a note on the effect of the intraclass correlation in the multiple reading procedure with a unanimity rule the use of multiple reading procedures to improve the performance of a diagnostic test occurs often in practice evaluation of the utility of multiple reading procedures however usually ignores the effect of the intraclass correlation this paper provides a quantitative assessment of this effect in the multiple reading procedure with a unanimity rule with respect to sensitivity specificity positive and negative predictive values we have found that when the disease prevalence is rare or moderate less than or equal to 0 20 use of the multiple reading procedure with a unanimity rule is effective in increasing the positive predictive value of a single reading procedure for the situation in which the variation of responses among different subjects and the intraclass correlation among repeated tests are small this is however not true for the situation in which the disease is rare and the variation of responses among different subjects is large even when the intraclass correlation is small or 0 furthermore when the disease is rare and the variation of responses among subjects is small a small or moderate intraclass correlation can substantially decrease the positive predictive value that one calculates under the assumption that the intraclass correlation is equal to 0 in general when the disease is rare or moderate less than or equal to 0 20 the intraclass correlation between repeated tests and the variation of responses among subjects have little effect on the negative predictive value

the analysis of binary longitudinal data with time independent covariates summary this paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject we propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject s data the efficiency of the proposed estimators is examined an analysis of stress in mothers with infants is presented to illustrate the proposed method

tree structured logistic model for over dispersed binomial data with application to modeling developmental effects this article proposes tree structured logistic regression modeling for over dispersed binomial data recursive partitioning is performed using a combination of statistical tests and residual analysis the splitting criterion in cross validation is based on the deviance function a nested grid algorithm to estimate the bootstrap parameters is developed the regression tree procedure provides a new approach for exploring in detail the relationship between the binomial response and explanatory variables the proposed procedure is used to model the relationship between the incidence of malformation and dose and fetal weight using data from a developmental experiment conducted at the national center for toxicological research a conditional gaussian chain model is used to account for the effect of fetal weight by dose

the effect of retaining probability variation on sample size calculations for normal variates skalski 1992 biometrics 48 877 882 assumed a constant retaining probability p for all experimental units and found that the traditional ad hoc procedure of escalating sample size by the multiplicative factor ilp tends to underestimate the required sample size when p is small because this retaining probability p often depends on characteristics of different experimental units however p may vary from one unit to another in this report we have allowed p to vary among different experimental units we have noted that when the retaining probability p has a small mean but a large variance the underestimation of the required sample size for a desired precision by use of the traditional adjusted sample size formula can be even more serious than that demonstrated by skalski

a parametric model for cluster correlated categorical data summary a fully parametric copula model for symmetric dependent clustered categorical data is discussed the model accommodates any marginal regression models of interest and admits a broad range of within cluster association the form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes the model contains an association parameter that is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence two examples are given to illustrate the methods

a revisit on tests for homogeneity of the risk difference lipsitz et al 1998 biometrics 54 148 160 discussed testing the homogeneity of the risk difference for a series of 2 x 2 tables they proposed and evaluated several weighted test statistics including the commonly used weighted least squares test statistic here we suggest various important improvements on these test statistics first we propose using the one sided analogues of the test procedures proposed by lipsitz et al because we should only reject the null hypothesis of homogeneity when the variation of the estimated risk differences between centers is large second we generalize their study by redesigning the simulations to include the situations considered by lipsitz et al 1998 as special cases third we consider a logarithmic transformation of the weighted least squares test statistic to improve the normal approximation of its sampling distribution on the basis of monte carlo simulations we note that as long as the mean treatment group size per table is moderate or large or 16 this simple test statistic in conjunction with the commonly used adjustment procedure for sparse data can be useful when the number of 2 x 2 tables is small or moderate or 32 in these situations in fact we find that our proposed method generally outperforms all the statistics considered by lipsitz et al finally we include a general guideline about which test statistic should be used in a variety of situations

confidence interval estimation of the intraclass correlation coefficient for binary outcome data we obtain closed form asymptotic variance formulae for three point estimators of the intraclass correlation coefficient that may be applied to binary outcome data arising in clusters of variable size our results include as special cases those that have previously appeared in the literature fleiss and cuzick 1979 applied psychological measurement 3 537 542 bloch and kraemer 1989 biometrics 45 269 287 altaye donner and klar 2001 biometrics 57 584 588 simulation results indicate that confidence intervals based on the estimator proposed by fleiss and cuzick provide coverage levels close to nominal over a wide range of parameter combinations two examples are presented

multiple reading procedures the performance of diagnostic tests this paper examines the effects on sensitivity and specificity of various multiple reading procedures multiple reading procedures entail the performance of a diagnostic test several times and consequent assignment of the subject to an affected or unaffected group a unanimity rule that is all tests must be positive leads to the largest predictive value positive but may have unacceptably low sensitivity the rule which classifies the subject as positive based on the majority of the tests increases both the sensitivity and specificity of the individual test variability of subjects sensitivity and specificity that is case of correct diagnosis on a test affects the performance of these rules we also study alternative procedures in which the final test is a better but more expensive test

an exact trend test for correlated binary data the problem of testing a dose response relationship in the presence of exchangeably correlated binary data has been addressed using a variety of models most commonly used approaches are derived from likelihood or generalized estimating equations and rely on large sample theory to justify their inferences however while earlier work has determined that these methods may perform poorly for small or sparse samples there are few alternatives available to those faced with such data we propose an exact trend test for exchangeably correlated binary data when groups of correlated observations are ordered this exact approach is based on an exponential model derived by molenberghs and ryan 1999 and ryan and molenberghs 1999 and provides natural analogues to fisher s exact test and the binomial trend test when the data are correlated we use a graphical method with which one can efficiently compute the exact tail distribution and apply the test to two examples

hypothesis testing for proportions with overdispersion summary the properties of likelihood ratio tests and simpler t tests are investigated by simulation under an assumed beta binomial model for parameter values typically found in toxicological studies it is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

preferential attachment in randomly grown networks abstract we reintroduce the model of callaway et al 2001 as a special case of a more general model for random network growth vertices are added to the graph at a rate of 1 while edges are introduced at rate rather than edges being introduced at random we allow for a degree of preferential attachment with a linear attachment kernel parametrised by m the original model is recovered in the limit of no preferential attachment m as expected even weak preferential attachment introduces a power law tail to the degree distribution additionally this generalisation retains a great deal of the tractability of the original along with a surprising range of behaviour although key mathematical features are modified for finite m in particular the critical edge density c which marks the onset of a giant network component is reduced with increasing tendency for preferential attachment the positive degree degree correlation introduced by the unbiased growth process is offset by the skewed degree distribution reducing the network assortativity

local polynomial estimation in multiparameter likelihood models abstract the nonparametric regression technique of local polynomial fitting is extended to multiparameter likelihood models some well known appealing features of local polynomial smoothers such as the behavior at the boundary are shown to carry over to the multiparameter case asymptotic consistency and normality of the resulting estimators are derived under suitable regularity conditions this work is motivated by the need for a nonparametric alternative to parametric dose response models for clustered binary data probability models for clustered binary response data include a success probability parameter and one or more correlation parameters the proposed local polynomial estimators can play an important role as a diagnostic tool or to suggest the form of the functional relationships in parametric likelihood models as an illustration it is shown how the local likelihood estimation procedure can be implemented for fitting a dose response curve based on the beta binomial model a data example and

bias corrected maximum likelihood estimator of the intraclass correlation parameter for binary data a popular model to analyse over under dispersed proportions is to assume the extended beta binomial model with dispersion intraclass correlation parameter phi and then to estimate this parameter by maximum likelihood however it is well known that maximum likelihood estimate mle may be biased when the sample size n or the total fisher information is small in this paper we obtain a bias corrected maximum likelihood bcml estimator of the intraclass correlation parameter and compare it by simulation in terms of bias and efficiency with the mle an estimator q 2 based on optimal quadratic estimating equations of crowder and recommended by paul et al and a double extended quasi likelihood deql estimator proposed by lee the bcml estimator has superior bias and efficiency properties in most instances analyses of a set of toxicological data from paul and a set of medical data pertaining to chromosomal abnormalities among survivors of the atomic bomb in hiroshima from otake and prentice show in general much improvement in standard errors of the bcml estimates over the other three estimates

on the use of the quasi likelihood method in teratological experiments this paper concerns the impact of litter effects on the inference of dose response relationships in teratological experiments with binary response kupper et al 1986 biometrics 42 85 98 concluded that when intra litter correlations are dose dependent the use of a common intra litter correlation likelihood based on the beta binomial distribution could lead to severe bias in estimation of the parameter beta which characterizes the dose response relationship we show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra litter correlations we then examine through a simulation study the performance of the quasi likelihood method wedderburn 1974 biometrika 61 439 447 and recommend that this method with a common intra litter correlation parameter be used when the number of litters is small or modest

cluster sampling techniques in quantal response teratology and developmental toxicity studies summary this paper presents a model free approach for evaluating teratology and developmental toxicity data involving clustered binary responses in teratology studies a major statistical problem arises from the effect of intralitter correlation or the potential for littermates to respond similarly some statistical methods impose strict distributional assumptions to account for extra binomial variation while others rely on nonparametric resampling and empirical variance estimation techniques quasi likelihood methods and generalized estimating equations gee which model the marginal mean variance relationship also avoid strict distributional assumptions the proposed approach often used to analyze complex sample survey data is based on a first order taylor series approximation and a between cluster variance estimation procedure yielding consistent variance estimates for binomial based proportions and regression coefficients from dose response models the cluster sample technique presented here in the context of a logistic dose response model incorporates many of the advantages of quasi likelihood methods are valid for any underlying nested correlation structure and are adaptable to a variety of analytical settings the results of a simulation study show the cluster sample technique to be a viable competitor to gee methods currently receiving attention

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

a study on some urban bus transport networks abstract in this paper we present the empirical investigation results on the urban bus transport networks btns of four major cities in china in btn nodes are bus stops two nodes are connected by an edge when the stops are serviced by a common bus route the empirical results show that the degree distributions of btns take exponential function forms other two statistical properties of btns are also considered and they are suggested as the distributions of so called the number of stops in a bus route represented by s and the number of bus routes a stop joins by r the distributions of r also show exponential function forms while the distributions of s follow asymmetric unimodal functions to explain these empirical results and attempt to simulate a possible evolution process of btn we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts finally we also discuss some other possible evolution cases where the degree distribution shows a power law or an interpolation between the power law and the exponential decay

numerical simulation of dealloying by surface dissolution via the evolving surface finite element method in this article we formulate a numerical method for the simulation of dealloying of a binary alloy by the selective removal of one component via electrochemical dissolution such that there is phase separation of the other component at the solid electrolyte interface the evolution of the interface is modelled by a forced mean curvature flow strongly coupled to the solution of a cahn hilliard equation modelling surface phase separation the method is based on a triangulated hypersurface whose evolution is calculated as well as the solution of the cahn hilliard equation by the evolving surface finite element method esfem the numerical experiments simulate complex morphology and concentration patterns providing evidence that the mathematical model may describe the formation of nanoporosity

design effects for binary regression models fitted to dependent data dependent data such as arise with cluster sampling typically yield variances of parameter estimates which are larger than would be provided by a simple random sample of the same size this variance inflation factor is called the design effect of the estimator design effects have been derived for cluster sampling designs using simple estimators such as means and proportions and also for linear regression coefficient estimators in this paper we show that a method to derive design effects for linear regression estimators extends to generalized linear models for binary responses in particular some simple expressions for design effects in the linear regression model provide accurate approximations for binary regression models such as those based on the logistic probit and complementary log log links we corroborate our findings with two examples and some simulation studies

a stabilized moment estimator for the beta binomial distribution the beta binomial distribution has been proposed as a model for the incorporation of historical control data in the analysis of rodent carcinogenesis bioassays low spontaneous tumor incidences along with the small number and sizes of historical control groups combine to make the moment and maximum likelihood estimates of the beta binomial parameters deficient we therefore propose a stabilized moment estimator for one of the parameters the stabilized moment estimator is similar to the ridge regression estimator and introduces a shrinkage parameter computer simulations were run to examine the behavior of the stabilized moment estimator the effect of the stabilized moment estimator on the score test for dose related trend is considered both on simulated data and on an example from the literature