the standard error of cohen s kappa this paper gives a standard error for cohen s kappa conditional on the margins of the observed r x r table an explicit formula is given for the 2 x 2 table and a procedure for the more general situation a parsimonious log linear model is suggested for the general case and an approximate confidence interval for kappa is based on that model numerical illustrations are given comparing the standard results with exact conditional results and those of the present paper the conclusions are first that the standard error of kappa under the null hypothesis that kappa is zero should not be used except when the null is plausible secondly that the usual formula for the standard error appears appropriate except in the unusual circumstance of kappa taking large negative values and thirdly in small samples the distribution of the estimate of kappa appears very non symmetric and it is preferable to base confidence intervals on transformations of kappa a pc program with source code implementing the suggested procedures is available from the author

exact approaches for testing hypotheses based on the intra class kappa coefficient testing involving the intra class kappa coefficient is commonly performed in order to assess agreement involving categorical ratings a number of procedures have been proposed which make use of the limiting null distribution as the sample size goes to infinity in order to compute the observed significance as with many tests based on asymptotic null distributions these tests are associated with problematic type i error control for selected sample sizes and points in the parameter space we propose and study a collection of exact testing approaches for both the one sample and k sample scenarios for the one sample case p values are obtained using the exact distribution of the test statistic conditional on a sufficient statistic in addition unconditional approaches are considered on the basis of maximization across the nuisance parameter space numerical evaluation reveals advantages with the exact unconditional procedures copyright 2014 john wiley sons ltd

on similarity coefficients for 2 2 tables and correction for chance this paper studies correction for chance in coefficients that are linear functions of the observed proportion of agreement the paper unifies and extends various results on correction for chance in the literature a specific class of coefficients is used to illustrate the results derived in this paper coefficients in this class e g the simple matching coefficient and the dice sorenson coefficient become equivalent after correction for chance irrespective of what expectation is used the coefficients become either cohen s kappa scott s pi mak s rho goodman and kruskal s lambda or hamann s eta depending on what expectation is considered appropriate both a multicategorical generalization and a multivariate generalization are discussed

a goodness of fit approach to inference procedures for the kappa statistic confidence interval construction significance testing and sample size estimation we propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome the procedure is based on a chi square goodness of fit test as applied to a model frequently used for clustered binary data the procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures the procedure also has use for significance testing and the planning of corresponding sample size requirements

combinatorial decompositions of a class of rings in this paper we introduce some combinatorial methods for the study of graded rings and use these methods to analyze a class of rings that are of importance in combinatorics our methods are based on a unique representation theorem which is shown section 2 to hold for any graded algebra and which in a sense is an extension of the direct sum decomposition for cohen macaulay algebras this unique representation is reminiscent of a similar result obtained by rees 20 both results yield a decomposition of the algebra however our result differs from that of rees in that it carries more information about the algebra our main results are concerned with a class of rings see section 3 for the definition associated to simplicial complexes there are several natural operations that can be performed on simplicial complexes to obtain new complexes which in turn have an interpretation for the corresponding rings we show sections 4 5 and 6 that our basic decompositions can be transferred during these operations from the original rings to the newly constructed ones the operations studied here are the chain transform or barycentric subdivision section 4 rank selection both for partially ordered sets and for simplicial complexes section s and localization section 6 as we develop these tools we give some applications in section 5 we give a new topological characterization of the cohen macaulay property for partially ordered sets an immediate consequence of which is the rankselection theorem baclawski 2 this characterization is closely related to those obtained by garsia in 14

a measure of 2 x 2 association with stable variance and approximately normal small sample distribution planning cost effective studies a measure of 2 x 2 association z is developed having the property that n z z has approximately a standard normal distribution even for quite small sample size examples of the use of this variance stabilizing and normalizing transformation in planning studies of 2 x 2 association are presented studies of the association between coronary artery disease and exercise stress test results are used to illustrate these methods

maximum likelihood estimation of the kappa coefficient from models of matched binary responses we present an estimate of the kappa coefficient of agreement between two methods of rating based on matched pairs of binary responses and show that the estimate depends on the common intraclass correlation coefficient between the pairs via monte carlo simulation we investigate power of the test of significance on kappa and the large sample bias and variance of its maximum likelihood estimator

estimating equations for kappa statistics kappa statistics are often used for measuring agreement or association the original measure suggested by cohen for use with nominal data has since been generalized in a number of ways including the incorporation of weights adaptation for use with more than one rater and the application to bivariate data each modification requires a new approximation to the standard error and these have usually been derived by the delta method this paper illustrates the use of estimating equations for kappa which offer a unified approach to many previously considered situations and which is also applicable to more complex designs

assessment on homogeneity tests for kappa statistics under equal prevalence across studies in reliability in this paper we assess the performance of homogeneity tests for two or more kappa statistics when prevalence rates across reliability studies are assumed to be equal the likelihood score method and the chi square goodness of fit gof test provide type 1 error rates that are satisfactorily close to the nominal level but a fleiss like test is not satisfactory for small or moderate sample sizes simulations show that the score test is more powerful than the chi square gof test and the approximate sample size required for a specific power of the former is substantially smaller than the latter in addition the score test is robust to deviations from the equal prevalence assumption while the gof test is highly sensitive and it may give a grossly misleading type 1 error rate when the assumption of equal prevalence is violated we conclude that the homogeneity score test is the preferred method

modelling patterns of agreement for nominal scales the measurement of agreement of repeat rating is the usual method of assessing the reliability of categorical scales measurement of agreement is also important in genetic twin studies based on categorical scales one of the most commonly used methods of analysis for both types of study is the kappa coefficient for scales with more than two categories one approach is to use a single summary kappa coefficient while this may be sufficient for many studies in some instances investigation of heterogeneity in the pattern of agreement may give additional insights as there may be greater agreement for some pairs of categories than for others in this paper kappa type coefficients are used to model heterogeneity in the pattern of agreement constraints are added to the heterogeneous model to obtain simplified models procedures for estimation confidence intervals and inference for these coefficients are described for the case of two ratings per subject for a single sample and for the comparison of two independent samples formulae for sample size and power calculation are derived using the non central chi squared distribution two simulation studies are carried out to check the empirical test size and power methods are illustrated by two examples involving nominal scales with three categories

the combinatorics of twisted involutions in coxeter groups the open intervals in the bruhat order on twisted involutions in a coxeter group are shown to be pl spheres this implies results conjectured by f incitti and sharpens the known fact that these posets are gorenstein over z 2 we also introduce a boolean cell complex which is an analogue for twisted involutions of the coxeter complex several classical coxeter complex properties are shared by our complex when the group is finite it is a shellable sphere shelling orders being given by the linear extensions of the weak order on twisted involutions furthermore the h polynomial of the complex coincides with the polynomial counting twisted involutions by descents in particular this gives a type independent proof that the latter is symmetric

statistical implications of the choice between a dichotomous or continuous trait in studies of interobserver agreement summary a frequently occurring question in the planning of studies is whether to measure the trait of interest on a continuous or dichotomous scale an issue potentially relevant to this question centers around the resulting reliability of the measure assuming the continuous trait has a normal distribution we quantify the effect of this decision on the overall number of subjects required to test whether a population reliability coefficient equals a specified criterion value two distinct cases are explored the choice between a continuous response and a truly dichotomous response and the case in which an inherently continuous response is dichotomized in both cases and particularly in the second the loss of power associated with measuring the trait on a dichotomous scale is shown to be always severe and frequently prohibitive

interval estimation for a difference between intraclass kappa statistics summary model based inference procedures for the kappa statistic have developed rapidly over the last decade however no method has yet been developed for constructing a confidence interval about a difference between independent kappa statistics that is valid in samples of small to moderate size in this article we propose and evaluate two such methods based on an idea proposed by newcombe 1998 statistics in medicine 17 873 890 for constructing a confidence interval for a difference between independent proportions the methods are shown to provide very satisfactory results in sample sizes as small as 25 subjects per group sample size requirements that achieve a prespecified expected width for a confidence interval about a difference of kappa statistic are also presented

group actions on stanley reisner rings and invariants of permutation groups abstract let h be a group of permutations of x 1 x n and let q h x 1 x 2 x n denote the ring of h invariant polynomials in x 1 x 2 x n with rational coefficients combinatorial methods for the explicit construction of free bases for q h x 1 x 2 x n as a module over the symmetric polynomials are developed the methods are developed by studying the action of the symmetric group on the stanley reisner ring of the subset lattice some general results are also obtained by studying the action of a coxeter group on the stanley reisner ring of the corresponding coxeter complex in the case of a weyl group a purely combinatorial construction of certain invariants first considered by r steinberg topology 14 1975 173 177 is obtained some applications to representation theory are also included

kappa coefficients in medical research kappa coefficients are measures of correlation between categorical variables often used as reliability or validity coefficients we recapitulate development and definitions of the k categories by m ratings kappas k x m discuss what they are well or ill designed to do and summarize where kappas now stand with regard to their application in medical research the 2 x m m 2 intraclass kappa seems the ideal measure of binary reliability a 2 x 2 weighted kappa is an excellent choice though not a unique one as a validity measure for both the intraclass and weighted kappas we address continuing problems with kappas there are serious problems with using the k x m intraclass k 2 or the various k x m weighted kappas for k 2 or m 2 in any context either because they convey incomplete and possibly misleading information or because other approaches are preferable to their use we illustrate the use of the recommended kappas with applications in medical research

continuous transforming the btw to the manna model abstract in this paper we define some stochastic perturbations of the btw model which make it into manna model these models have a continuous parameter p where p 0 and 1 correspond to the btw and manna models respectively we have investigated the properties of the statistical observables of the waves of avalanches for various values of p our data supports the expectation of a crossover in such systems at large scales manna model is dominant therefore we find strong evidence in favor of the universality classes being distinct also it is observed that the btw fixed point is unstable when manna type perturbation is added to the model

interlacing polynomials and the veronese construction for rational formal power series fixing a positive integer r and define for every formal power series f as jochemko recently showed that the polynomial has only non positive zeros for any and any positive integer n as a consequence jochemko confirmed a conjecture of beck and stapledon on the ehrhart polynomial of a lattice polytope of dimension n which states that has only negative real zeros whenever in this paper we provide an alternative approach to beck and stapledon s conjecture by proving the following general result if the polynomial sequence is interlacing so is our result has many other interesting applications in particular this enables us to give a new proof of savage and visontai s result on the interlacing property of some refinements of the descent generating functions for coloured permutations besides we derive a carlitz identity for refined coloured permutations

coxeter cones and their h vectors coxeter cones are formed by intersecting the nonnegative sides of a collection of root hyperplanes in some root system they are shellable subcomplexes of the coxeter complex and their h vectors record the distribution of descents among their chambers we identify a natural class of graded coxeter cones with the property that their h vectors are symmetric and unimodal thereby generalizing recent theorems of reiner welker and branden about the eulerian polynomials of graded partially ordered sets

modelling covariate effects in observer agreement studies the case of nominal scale agreement correction for chance expected agreement has become an accepted technique in the analysis of observer agreement data and may be particularly useful when the level of agreement achieved in different populations is compared however formal methods for making comparisons of chance corrected agreement or more generally for studying the effects of covariates on chance corrected agreement have not received much attention for nominal scale agreement data we show how tanner and young s model for observer agreement can be applied to this problem the models discussed can be fitted using existing software and certain model parameters have interpretations in terms of positive and negative agreement odds ratios the proposed methodology facilitates investigation of issues such as confounding of covariate effects and interaction between covariates in their effect on chance corrected agreement the methods outlined therefore allow observer agreement data to be analyzed in a manner strongly analogous to the logistic modelling of the association between disease and suspected risk factors the methods are illustrated using data on the comparability of primary and proxy respondent reports of the primary respondents participation in physically vigorous leisure time activity

power and sample size evaluation for the mcnemar test with application to matched case control studies various expressions have appeared for sample size calculation based on the power function of mcnemar s test for paired or matched proportions especially with reference to a matched case control study these differ principally with respect to the expression for the variance of the statistic under the alternative hypothesis in addition to the conditional power function i identify and compare four distinct unconditional expressions i show that the unconditional calculation of schlesselman for the matched case control study can be expressed as a first order unconditional calculation as described by miettinen corrections to schlesselman s unconditional expression presented by fleiss and levin and by dupont which use different models to describe exposure association among matched cases and controls are also equivalent to a first order unconditional calculation i present a simplification of these corrections that directly provides the underlying table of cell probabilities from which one can perform any of the alternative sample size calculations also i compare the four unconditional sample size expressions relative to the exact power function the conclusion is that miettinen s first order expression tends to underestimate sample size while his second order expression is usually fairly accurate though possibly slightly anti conservative a multinomial based expression presented by connor among others is also fairly accurate and is usually slightly conservative finally a local unconditional expression of mitra among others tends to be excessively conservative

a general goodness of fit approach for inference procedures concerning the kappa statistic the kappa statistic is frequently used as a measure of agreement among two or more raters although considerable research on statistical inferences for this statistic has been published for the case of two raters and a binary outcome relatively little work has appeared on inference problems for the case of multiple raters and or polytomous nominal outcome categories in this paper we propose a new procedure for constructing inferences for the kappa statistic that may be applied to this general case the procedure is based on a chi square goodness of fit test as applied to the dirichlet multinomial model and is a natural extension of previously proposed procedures that apply to more restricted cases a simulation study shows that the new procedure provides confidence interval coverage levels and type i error rates close to nominal over a wide range of parameter combinations we also present a sample size formula which may be used to determine the required number of subjects and raters for a given number of outcome categories

measurement of interrater agreement with adjustment for covariates summary the kappa coefficient measures chance corrected agreement between two observers in the dichotomous classification of subjects the marginal probability of classification by each rater may depend on one or more confounding variables however failure to account for these confounders may lead to inflated estimates of agreement a multinomial model is used that assumes both raters have the same marginal probability of classification but this probability may depend on one or more covariates the model may be fit using software for conditional logistic regression additionally likelihood based confidence intervals for the parameter representing agreement may be computed a simple example is discussed to illustrate model fitting and application of the technique

the cohomology of period domains for reductive groups over local fields we compute the etale cohomology of period domains over local fields in the case of a basic isocrystal for quasi split reductive groups period domains which have been introduced by rapoport and zink rz are open admissible rigid analytic subsets of generalized flag varieties they parametrize weakly admissible filtrations of a given isocrystal with additional structure of a reductive group

higher order kappa type statistics for a dichotomous attribute in multiple ratings we introduce a sequence of parameters called canonical moments to characterize the predictive value of the pattern of consensus among kappa 1 ratings to an additional rating the usual kappa coefficient of agreement among ratings two or more is just the second canonical moment by using the higher canonical moments we can evaluate the consensus of multiple binary ratings

the signature of a toric variety we identify a combinatorial quantity the alternating sum of the h vector defined for any simple polytope as the signature of a toric variety this quantity was introduced by r charney and m davis in their work which in particular showed that its nonnegativity is closely related to a conjecture of h hopf on the euler characteristic of a nonpositively curved manifold we prove positive or nonnegative lower bounds for this quantity under geometric hypotheses on the polytope and in particular resolve a special case of their conjecture these hypotheses lead to ampleness or weaker conditions for certain line bundles on toric divisors and then the lower bounds follow from calculations using the hirzebruch signature formula moreover we show that under these hypotheses on the polytope the ith l class of the corresponding toric variety is 1 i times an effective class for any i

extensions of cocycles cohen macaulay geometries and a vanishing theorem for cohomology of alternating groups abstract a new approach to the computation of the cohomology of groups acting on buekenhout geometries is described it is shown that in many cases including bn pairs and groups acting on dimensional linear spaces to compute the kth cohomology group hk g m it is sufficient roughly speaking to consider only parabolic subgroups of rank k 1 as an application it is shown that h k a n f p 0 for k 1 p k 2 where an is the alternating group

on decomposition of modular representations from cohen macaulay geometries abstract chain spaces for a cohen macaulay complex split into subspaces corresponding to cycles for truncations of the complex precisely when the cycles are non degenerate in the natural bilinear form application to the tits building provides a simple geometric approach to the well known splitting of ind g b 1 for a lie type group g in natural characteristic an application to a sporadic geometry is also indicated

interval estimation under two study designs for kappa with binary classifications cornfield s test based method of setting a confidence interval on a parameter associated with a two by two contingency table is adapted for use with the measure of agreement kappa one sided confidence intervals derived in this way are compared to other intervals proposed for kappa under two study designs both designs involve two ratings per subject on a dichotomous scale in one design the same two raters make all evaluations in the other possibly different pairs of raters evaluate different subjects or the same rater carries out a pair of independent assessments for each subject it is shown through simulation that lower bounds based on cornfield s test based method attain the nominal coverage probability more often than other intervals proposed in the literature

shellable nonpure complexes and posets ii this is a direct continuation of shellable nonpure complexes and posets i which appeared in transactions of the american mathematical society 348 1996 1299 1327 8 interval generated lattices and dominance order in this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets let f i1 i2 in be a family of intervals of integers by which is meant sets of the form a b a a 1 b a b we assume that there are no containments among these intervals and that they are ordered so that their left and right endpoints are increasing let l f be the lattice of all sets that are unions of subfamilies of f ordered by inclusion such interval generated lattices l f were introduced and studied by greene g define an edge labeling of l f as follows if a b is a covering and a max b a then a b a if a 1 a and a is the left endpoint of some i f

canonical modules of partially ordered sets in this brief note we show that the canonical module of the stanley reisner ring of a doubly cohen macaulay ordered set is isomorphic to a certain ideal of the same ring for a general finite partially ordered set the corresponding ideal is isomorphic to a submodule of the canonical module for an introduction to cohen macaulay ordered sets from the ringtheoretical point of view see garsia 4 and baclawski garsia 3 doubly cohen macaulay ordered sets were introduced in baclawski 2 let a be a finite simplicial complex of rank r dimension r 1 on vertex set v we write a for t e a 1 u 1 k we assume that a can be colored i e there exists a map c v r r 1 2 r such that for every u e a i c l i iu an d we fix a choice of coloring henceforth the most important example of a colored complex is the simplicial complex a p of chains of a partially ordered set poset p for example the map c p r given by

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

comparing two diagnostic tests against the same gold standard in the same sample methods are proposed for comparing two diagnostic tests for the same data where a threshold for positive for each test is specified one method contrasts the diagnostic tests estimated risks a second method compares the two tests kappa coefficients when thresholds for positive test results are specified a priori maximum likelihood estimators and their asymptotic variances are derived and test statistics are presented for both case control and naturalistic methods of sampling the bootstrap is proposed as a method to assess differences in risk estimators when thresholds for positive test results are chosen by scanning the data examples are given to illustrate the methods

how reliable are change corrected measures of agreement chance corrected measures of agreement are prone to exhibit paradoxical and counter intuitive results when used as measures of reliability it is demonstrated that these problems arise with cohen s kappa as well as with aickin s alpha they are the consequence of an analogy to simpson s paradox in mixed populations it is further shown that chance corrected measures of agreement may yield misleading values for binary ratings it is concluded that improvements in the design and the analysis of reliability studies are a pre requisite for valid and pertinent results

testing the equality of two dependent kappa statistics procedures are developed and compared for testing the equality of two dependent kappa statistics in the case of two raters and a dichotomous outcome variable such problems may arise when each of a sample of subjects are rated under two distinct settings and it is of interest to compare the observed levels of inter observer and intra observer agreement the procedures compared are extensions of previously developed procedures for comparing kappa statistics computed from independent samples the results of a monte carlo simulation show that adjusting for the dependency between samples tends to be worthwhile only if the between setting correlation is comparable in magnitude to the within setting correlations in this case a goodness of fit procedure that takes into account the dependency between samples is recommended

shelling coxeter like complexes and sorting on trees abstract in their work on coxeter like complexes babson and reiner introduced a simplicial complex t associated to each tree t on n nodes generalizing chessboard complexes and type a coxeter complexes they conjectured that t is n b 1 connected when the tree has b leaves we provide a shelling for the n b skeleton of t thereby proving this conjecture in the process we introduce notions of weak order and inversion functions on the labellings of a tree t which imply shellability of t and we construct such inversion functions for a large enough class of trees to deduce the aforementioned conjecture and also recover the shellability of chessboard complexes m m n with n 2 m 1 we also prove that the existence or nonexistence of an inversion function for a fixed tree governs which networks with a tree structure admit greedy sorting algorithms by inversion elimination and provide an inversion function for trees where each vertex has capacity at least its degree minus one

interval estimation for cohen s kappa as a measure of agreement cohen s kappa statistic is a very well known measure of agreement between two raters with respect to a dichotomous outcome several expressions for its asymptotic variance have been derived and the normal approximation to its distribution has been used to construct confidence intervals however information on the accuracy of these normal approximation confidence intervals is not comprehensive under the common correlation model for dichotomous data we evaluate 95 per cent lower confidence bounds constructed using four asymptotic variance expressions exact computation rather than simulation is employed specific conditions under which the use of asymptotic variance formulae is reasonable are determined

some results about the quillen complex ofsp2n q abstract the structure of the quillen complex ofsp2n q atp denoted a p sp2n q is known whenpis the characteristic prime in this paper it is shown that ifp q 1 then a p sp2n q is cohen macaulay of dimension n 1 furthermore ifd 3 is the order ofqin z p z anddis odd it is shown that a p sp2n q is simply connected whenevermp sp2n q 3 it is also shown that the order complex of proper nondegenerate subspaces of a 2n dimensional symplectic space over f q ordered by inclusion is cohen macaulay of dimension n 2 ifq 2

group actions on arrangements of linear subspaces and applications to configuration spaces for an arrangement of linear subspaces in ri that is invariant under a finite subgroup of the general linear group gin ir we develop a formula for the g module structure of the cohomology of the complement m a our formula specializes to the well known goresky macpherson theorem in case g 1 but for g 1 the formula shows that the g module structure of the complement is not a combinatorial invariant as an application we are able to describe the free part of the cohomology of the quotient space ma4ig our motivating examples are arrangements in cn that are invariant under the action of sn by permuting coordinates a particular case is the k equal arrangement first studied by bj6rner lovasz and yao motivated by questions in complexity theory in these cases ma4 and ma sn are spaces of ordered and unordered point configurations in cn many of whose properties are reduced by our formulas to combinatorial questions in partition lattices more generally we treat point configurations in rd and provide explicit results for the k equal and the k divisible cases

homogeneity score test for the intraclass version of the kappa statistics and sample size determination in multiple or stratified studies quand le coefficient de correlation intra classe ou sa version equivalente du coefficient d agrement kappa ont ete estimes a partir de plusieurs etudes independantes ou d une etude avec stratification nous nous trouvons devant le probleme de la comparaison de statistiques kappa et de la combinaison d information sur ces statistiques en un kappa commun quand leur supposition d homogeneite est satisfaite dans cet article en utilisant la theorie de vraisemblance du score etendue aux parametres de nuisance tarone 1988 nous presentons un test d homogeneite efficace pour comparer plusieurs statistiques kappa independantes et de surcroit nous donnons une methode du score d homogeneite modifiee en employant comme alternative un estimateur non iteratif et consistant nous fournissons la taille d echantillon en employant la methode du score d homogeneite modifiee et nous la comparons a celle de la qualite d ajustement gof donner eliasziw et klar 1996 une etude de simulation pour des tailles d echantillon faibles et moderes a montre que le niveau actuel du test du score d homogeneite employant les estimateurs du maximum de vraisemblance mles des parametres est de maniere satisfaisante proche du nominal et qu il est plus faible que ceux du score d homogeneite mortifiee et des tests de la qualite d ajustement nous etudions les proprietes statistiques de plusieurs estimateurs non iteratifs d un kappa commun l estimateur donner eliasziw et klar 1996 est essentiellement efficace et peut etre employe comme une alternative au mle iteratif nous presentons une estimation par intervalle efficace d un kappa commun en employant la methode de vraisemblance du score

measures of agreement between many raters for ordinal classifications screening and diagnostic procedures often require a physician s subjective interpretation of a patient s test result using an ordered categorical scale to define the patient s disease severity because of wide variability observed between physicians ratings many large scale studies have been conducted to quantify agreement between multiple experts ordinal classifications in common diagnostic procedures such as mammography however very few statistical approaches are available to assess agreement in these large scale settings many existing summary measures of agreement rely on extensions of cohen s kappa these are prone to prevalence and marginal distribution issues become increasingly complex for more than three experts or are not easily implemented here we propose a model based approach to assess agreement in large scale studies based upon a framework of ordinal generalized linear mixed models a summary measure of agreement is proposed for multiple experts assessing the same sample of patients test results according to an ordered categorical scale this measure avoids some of the key flaws associated with cohen s kappa and its extensions simulation studies are conducted to demonstrate the validity of the approach with comparison with commonly used agreement measures the proposed methods are easily implemented using the software package r and are applied to two large scale cancer agreement studies copyright 2015 john wiley sons ltd

testing the homogeneity of kappa statistics procedures are compared for testing the homogeneity of k or 2 independent kappa statistics in the case of two raters and a dichotomous outcome one of the procedures is based on the estimated large sample variance derived under a model frequently adopted for inferences concerning interobserver agreement the other is based on a goodness of fit approach to this model the results of a monte carlo simulation show that the two approaches have similar properties if the number of subjects in each sample is large 100 and the prevalence of the underlying trait of interest is not extreme while the goodness of fit approach is recommended for comparisons involving smaller numbers of subjects or in which the prevalence of the underlying trait is small 0 3

inference procedures for assessing interobserver agreement among multiple raters summary we propose a new procedure for constructing inferences about a measure of interobserver agreement in studies involving a binary outcome and multiple raters the proposed procedure based on a chi square goodness of fit test as applied to the correlated binomial model bahadur 1961 in studies in item analysis and prediction 158 176 is an extension of the goodness of fit procedure developed by donner and eliasziw 1992 statistics in medicine11 1511 1519 for the case of two raters the new procedure is shown to provide confidence interval coverage levels that are close to nominal over a wide range of parameter combinations the procedure also provides a sample size formula that may be used to determine the required number of subjects and raters for such studies

symmetries and fixed point stability of stochastic differential equations modeling self organized criticality a stochastic nonlinear partial differential equation is constructed for two different models exhibiting self organized criticality the bak tang wiesenfeld btw sandpile model phys rev lett 59 381 1987 phys rev a 38 364 1988 and the zhang model phys rev lett 63 470 1989 the dynamic renormalization group drg enables one to compute the critical exponents however the nontrivial stable fixed point of the drg transformation is unreachable for the original parameters of the models we introduce an alternative regularization of the step function involved in the threshold condition which breaks the symmetry of the btw model although the symmetry properties of the two models are different it is shown that they both belong to the same universality class in this case the drg procedure leads to a symmetric behavior for both models restoring the broken symmetry and makes accessible the nontrivial fixed point this technique could also be applied to other problems with threshold dynamics

a kraemer type rescaling that transforms the odds ratio into the weighted kappa coefficient this paper presents a simple rescaling of the odds ratio that transforms the association measure into the weighted kappa statistic for a 2 2 table

2 x 2 kappa coefficients measures of agreement or association summary two general but different contexts in which kappa might be used are defined agreement and association two models one for agreement and one for utility of association are defined yielding different kappa coefficients and different sampling theory asymptotic results are derived for both models small sample evaluations are presented for the model for agreement

comparison of several goodness of fit tests for the kappa statistic based on exact power and coverage probability we present a general approach based on chi square goodness of fit tests for performing tests of significance about the kappa statistic we make recommendations for the particular goodness of fit test to use under different situations we also compare the test statistics in terms of the generated confidence intervals about the kappa statistic

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

some combinatorial and algebraic properties of coxeter complexes and tits buildings a des groupes de coxeter et des groupes a bn paire sont associes certaines structures combinatoires les complexes de coxeter et les constructions de tits on etudie ces structures du point de vue des complexes de cohen macaulay et des complexes decorticables

edwards wilkinson equation from lattice transition rules continuum equations of motion for the height fluctuations of lattice growth models are derived from their transition rules by regularizing and coarse graining the associated discrete langevin equations for models with random deposition followed by instantaneous relaxation to a neighboring site based on identifying the local height minimum our methodology yields the edwards wilkinson equation the application of this procedure to other growth models is discussed

equivariant ehrhart theory abstract motivated by representation theory and geometry we introduce and develop an equivariant generalization of ehrhart theory the study of lattice points in dilations of lattice polytopes we prove representation theoretic analogues of numerous classical results and give applications to the ehrhart theory of rational polytopes and centrally symmetric polytopes we also recover a character formula of procesi dolgachev lunts and stembridge for the action of a weyl group on the cohomology of a toric variety associated to a root system