choice of column scores for testing independence in ordered 2 x k contingency tables the numerous statistical methods for testing no association between a binary response rows and k ordered categories columns group naturally into two classes those that require preassigned numerical column scores and those that do not an example of the former would be a logistic regression analysis and of the latter would be a wilcoxon rank sum test in this paper we demonstrate that the perceived advantage of not preassigning scores is illusory we do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate our recommendations are to assign reasonable column scores whenever possible and to consider equally spaced scores when the choice is not apparent midranks as scores should always be examined for their appropriateness before a rank test is applied

analysis of rank measures of association for ordinal data from longitudinal studies abstract consideration is given to longitudinal data settings in which an ordinal response variable is observed at two or more visits for each subject in two or more ordered groups with at least moderately large sample sizes e g overall n 40 rank measures of association between group and response are constructed at each time and the covariance matrix of these measures is also estimated variation among the rank measures of association is then analyzed through weighted least squares methods with weights based on the estimated covariance matrix such methods permit evaluation of group visit interaction as well as other effects of interest extensions of this type of analysis to situations with stratification or concomitant variables or missing data are also considered examples are provided for illustrative purposes

nonparametric two sample comparisons of changes on ordinal responses abstract we discuss two armed clinical trials in which an ordinal response is observed on entry and at follow up in certain subject areas such data are often reduced to the counts of patients who have deteriorated remained the same or improved we develop asymptotic distribution theory to compare this approach to the use of nonparametric tests based on poststratification of the follow up responses according to the entry levels the theory for the latter approach is established by a general result for two sample u statistics based on bivariate data application to data from clinical trials and evaluation of asymptotic relative efficiencies and powers for a variety of contexts illustrate the increased sensitivity of poststratified wilcoxon tests

multivariate non parametric methods for mann whitney statistics to analyse cross over studies with two treatment sequences a non parametric strategy for the analysis of ordinal data from cross over studies with two treatment sequences and d or 2 periods is examined through mann whitney rank measures of association for each period these statistics estimate the probability of larger response for a randomly selected patient in one group relative to a randomly selected patient in the other group such estimates are as well formed for comparisons between groups for u pairs of periods with the same treatment methods for u statistics are used to produce a consistent estimate of the covariance matrix for the d u mann whitney estimates the effects of periods and treatments on the respective mann whitney estimates are evaluated through linear or log linear models for estimation of the parameters in these models a modified weighted least squares method is applied through a 2d 1 or d u dimensional basis which effectively addresses potentially near singularities in the estimated covariance matrix of the mann whitney estimates the proposed methods are applicable to response variables with an interval or an ordered categorical scale their scope additionally has capabilities for controlling strata in the design of a cross over study or concomitant variables for which covariance adjustment is of interest for reduction of variance applications of the methods are illustrated through three cross over studies with different specifications for the two sequences of two treatments during two to four periods

probabilistic index an intuitive non parametric approach to measuring the size of treatment effects effect sizes es tell the magnitude of the difference between treatments and ideally should tell clinicians how likely their patients will benefit from the treatment currently used es are expressed in statistical rather than in clinically useful terms and may not give clinicians the appropriate information we restrict our discussion to studies with two groups one with n patients receiving a new treatment and the other with m patients receiving the usual or no treatment the standardized mean difference e g cohen s d is a well known index for continuous outcomes there is some intuitive value to d but measuring improvement in standard deviations sd is a statistical concept that may not help a clinician how much improvement is a half sd a more intuitive and simple to calculate es is the probability that the response of a patient given the new treatment x is better than the one for a randomly chosen patient given the old or no treatment y i e p x y larger values meaning better outcomes this probability has an immediate identity with the area under the curve auc measure in procedures for receiver operator characteristic roc curve comparing responses to two treatments it also can be easily calculated from the mann whitney u wilcoxon or kendall statistics we describe the characteristics of an ideal es we propose p x y as an alternative index summarize its correspondence with well known non parametric statistics compare it to the standardized mean difference index and illustrate with clinical data copyright 2005 john wiley sons ltd

probabilistic index an intuitive non parametric approach to measuring the size of the treatment effects by l acion j j peterson s temple and s arndt statistics in medicine 2006 25 4 591 602

temporal evolution of the domain structure in a poisson voronoi nucleation and growth transformation results for one and three dimensions the distribution of spatial domain structures originated during one and three dimensional poisson voronoi transformations are computed analytically extending the recently obtained results for the two dimensional case the presented method gives a full description of the developed microstructure and is valid for tessellations of any dimensionality the temporal and spatial dependences of the domain structure are completely discriminated and separated showing the existence of geometric configurations independent of time a single computation of the probability distribution of these geometric configurations allows us to calculate the total free boundary and size probability distributions at any desired time the obtained results show full agreement with stochastic simulations and reproduce completely the previously existing partial results a discussion about the potential applications of the method to the calculation of other geometrical properties and the characteristics of the final static structure leading to a gamma distribution of sizes is also presented

anisotropic goal oriented mesh adaptivity for elliptic problems we propose in this paper an anisotropic adaptive finite element algorithm for steady linear advection diffusion reaction problems with strong anisotropic features the error analysis is based on the dual weighted residual methodology allowing us to perform goal oriented adaptation of a certain functional j u of the solution and derive an optimal metric tensor for local mesh adaptation with linear and quadratic finite elements as a novelty and to evaluate the weights of the error estimator on unstructured meshes composed of anisotropic triangles we make use of a patchwise higher order interpolation recovery readily extendable to finite elements of arbitrary order we carry out a number of numerical experiments in two dimensions so as to prove the capabilities of the goal oriented adaptive method we compute the convergence rate and the effectivity index for a series of output functionals of the solution the results show the good performance of the algorithm with linear as well as quadratic

cell size distribution in random tessellations of space random subdivisions in a d dimensional euclidean space are commonly observed in many scientific fields such as metallurgy geology biology and even in the case of large d in subjects related to information codification this paper presents an analytical approximation of the size probability distribution in space subdivisions generated by random point processes which include the well known cases of the poisson voronoi and the johnson mehl cellular structures based on the calculations of gilbert ann math stat 33 958 1962 and an assumption for the distribution shape the cell size distributions are obtained in a general way for a very wide range of random space subdivisions

an anisotropic fully adaptive algorithm for the solution of convection dominated equations with semi lagrangian schemes abstract we present in this paper an anisotropic fully adaptive spatial temporal algorithm for the solution of convection dominated equations in the context of semi lagrangian schemes we devise the algorithm within a finite element framework suitable for higher order finite elements and derive a newly proposed a posteriori error indicator which allows us to control the local or truncation error in the l 2 norm at each time step this a posteriori error is split into temporal and spatial contributions leading us to define an optimal time step size and an optimal triangulation respectively as regards the spatial adaptation anisotropic unstructured triangular meshes are used to capture the distinctive features of the evolving discrete solution of the governing equations for solutions exhibiting strong anisotropies the orientation shape and size of the mesh triangles are provided by a metric tensor valid for linear and quadratic finite elements finally we show the capabilities of the algorithm for linear and quadratic finite elements by a series of two and three dimensional benchmarks taken from the literature involving purely convective as well as convection dominated problems

a nearly conservative high order lagrange galerkin method for the resolution of scalar convection dominated equations in non divergence free velocity fields abstract in this work we present a novel lagrange galerkin method for the resolution of the scalar pure convection and convection dominated diffusion equations in non divergence free velocity fields the scheme has been formulated so that i time integration is carried out by means of an arbitrary order backward differentiation formula ii finite element space discretizations of any order can be employed and iii it satisfies a discrete mass balance equation at each simulation instant and preserves mass in those cases in which no fluid enters nor leaves the control domain as long as the integrals involved are computed exactly these properties are achieved by posing a conservation law for a weighted mass from which the standard mass can be seen as a particular case that can be easily discretized in time and in space with any order of accuracy numerical experiments which include a three dimensional test show that the method is as accurate in time as the employed time marching formula as accurate in space as the finite element discretization and generally more accurate especially in terms of mass conservation errors and efficient than the classic non conservative lagrange galerkin method to the best of our knowledge this is the first conservative lagrange galerkin method for convection dominated equations that considers both non divergence free velocity fields and time and space discretizations of any order

robust rank procedures for the behrens fisher problem abstract the problem of testing for equality of the medians of two populations is considered the standard distribution free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis a method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations the method is demonstrated using the mann whitney wilcoxon statistic

boundaries kinetic properties and final domain structure of plane discrete uniform poisson voronoi tessellations with von neumann neighborhoods discrete random tessellations appear not infrequently in describing nucleation and growth transformations generally several non euclidean metrics are possible in this case previously a korobov phys rev b 76 085430 2007 continual analogs of such tessellations have been studied here one of the simplest discrete varieties of the kolmogorov johnson mehl avrami model namely the model with von neumann neighborhoods has been examined per se i e without continualization the tessellation is uniform in the sense that domain boundaries consist of tiles similarities and distinctions between discrete and continual models are discussed

a local anisotropic adaptive algorithm for the solution of low mach transient combustion problems a novel numerical algorithm for the simulation of transient combustion problems at low mach and moderately high reynolds numbers is presented these problems are often characterized by the existence of a large disparity of length and time scales resulting in the development of directional flow features such as slender jets boundary layers mixing layers or flame fronts this makes local anisotropic adaptive techniques quite advantageous computationally in this work we propose a local anisotropic refinement algorithm using for the spatial discretization unstructured triangular elements in a finite element framework for the time integration the problem is formulated in the context of semi lagrangian schemes introducing the semi lagrange galerkin slg technique as a better alternative to the classical semi lagrangian sl interpolation the good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem the flame vortex interaction first a premixed methane air flame vortex interaction with simplified transport and chemistry description test i is considered results are found to be in excellent agreement with those in the literature proving the superior performance of the slg scheme when compared with the classical sl technique and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement as a more realistic example we then conduct simulations of non premixed hydrogen air flame vortex interactions test ii using a more complex combustion model which involves state of the art transport and chemical kinetics in addition to the analysis of the numerical features this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature

a new nonparametric approach for baseline covariate adjustment for two group comparative studies we consider two armed clinical trials in which the response and or the covariates are observed on either a binary ordinal or continuous scale a new general nonparametric np approach for covariate adjustment is presented using the notion of a relative effect to describe treatment effects the relative effect is defined by the probability of observing a higher response in the experimental than in the control arm the notion is invariant under monotone transformations of the data and is therefore especially suitable for ordinal data for a normal or binary distributed response the relative effect is the transformed effect size or the difference of response probability respectively an unbiased and consistent np estimator for the relative effect is presented further we suggest a np procedure for correcting the relative effect for covariate imbalance and random covariate imbalance yielding a consistent estimator for the adjusted relative effect asymptotic theory has been developed to derive test statistics and confidence intervals the test statistic is based on the joint behavior of the estimated relative effect for the response and the covariates it is shown that the test statistic can be used to evaluate the treatment effect in the presence of random covariate imbalance approximations for small sample sizes are considered as well the sampling behavior of the estimator of the adjusted relative effect is examined we also compare the probability of a type i error and the power of our approach to standard covariate adjustment methods by means of a simulation study finally our approach is illustrated on three studies involving ordinal responses and covariates

issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non parametric strategies for addressing them analysis of covariance is an effective method for addressing two considerations for randomized clinical trials one is reduction of variance for estimates of treatment effects and thereby the production of narrower confidence intervals and more powerful statistical tests the other is the clarification of the magnitude of treatment effects through adjustment of corresponding estimates for any random imbalances between the treatment groups with respect to the covariables the statistical basis of covariance analysis can be either non parametric with reliance only on the randomization in the study design or parametric through a statistical model for a postulated sampling process for non parametric methods there are no formal assumptions for how a response variable is related to the covariables but strong correlation between response and covariables is necessary for variance reduction computations for these methods are straightforward through the application of weighted least squares to fit linear models to the differences between treatment groups for the means of the response variable and the covariables jointly with a specification that has null values for the differences that correspond to the covariables moreover such analysis is similarly applicable to dichotomous indicators ranks or integers for ordered categories and continuous measurements since non parametric covariance analysis can have many forms the ones which are planned for a clinical trial need careful specification in its protocol a limitation of non parametric analysis is that it does not directly address the magnitude of treatment effects within subgroups based on the covariables or the homogeneity of such effects for this purpose a statistical model is needed when the response criterion is dichotomous or has ordered categories such a model may have a non linear nature which determines how covariance adjustment modifies results for treatment effects insight concerning such modifications can be gained through their evaluation relative to non parametric counterparts such evaluation usually indicates that alternative ways to compare treatments for a response criterion with adjustment for a set of covariables mutually support the same conclusion about the strength of treatment effects this robustness is noteworthy since the alternative methods for covariance analysis have substantially different rationales and assumptions since findings can differ in important ways across alternative choices for covariables as opposed to methods for covariance adjustment the critical consideration for studies with covariance analyses planned as the primary method for comparing treatments is the specification of the covariables in the protocol or in an amendment or formal plan prior to any unmasking of the study

a goal oriented anisotropic hp mesh adaptation method for linear convection diffusion reaction problems abstract we deal with the numerical solution of linear convection diffusion reaction equations using the h p variant of the discontinuous galerkin method on triangular grids we develop a mesh adaptive algorithm which modifies the size and shape of mesh elements and the corresponding polynomial approximation degrees in order to decrease the error in a target functional under the given tolerance we recall some theoretical results and describe in detail several technical aspects of this approach numerical experiments demonstrating the accuracy efficiency and robustness of the algorithm are presented

variational localizations of the dual weighted residual estimator the dual weighted residual method dwr and its localization for mesh adaptivity applied to elliptic partial differential equations are investigated the contribution of this paper is twofold first we introduce a novel localization technique based on the introduction of a partition of unity this new technique is very easy to apply as neither strong residuals nor jumps over element edges are required second we compare and analyze theoretically and numerically different localization techniques used for mesh adaptivity with respect to their effectivity here we focus on localizations in variational formulations that do not require the evaluation of the corresponding differential operator in the classical strong formulation in our mathematical analysis we show for different localization techniques established methods and our new approach that the local error indicators used for mesh adaptivity converge with proper order in the error functional several numerical tests substantiate our theoretical investigations

new monte carlo method for planar poisson voronoi cells by a new monte carlo algorithm we evaluate the sidedness probability pn of a planar poisson voronoi cell in the range 3 n 1600 the algorithm is developed on the basis of earlier theoretical work it exploits in particular the known asymptotic behaviour of pn as n our pn values all have between four and six significant digits accurate n dependent averages second moments and variances are obtained for the cell area and the cell perimeter the numerical large n behaviour of these quantities is analysed in terms of an asymptotic power series in n 1 snapshots are shown of typical occurrences of extremely rare events implicating cells of up to n 1600 sides embedded in an ordinary poisson voronoi diagram we reveal and discuss the characteristic features of such many sided cells and their immediate environment their relevance for observable properties is stressed

domain size distribution in a poisson voronoi nucleation and growth transformation we present an analytical result for the evolution of the domain size distribution during the growth of simultaneously nucleated domains the final stage of this transformation is the well known poisson voronoi tessellation the method can be easily extended to the calculation of the probability distribution of any other geometric characteristic as far as we know it is the first time that an exact result is given for this classic system