on simultaneous assessment of sensitivity and specificity when combining two diagnostic tests diagnostic tests are seldom adopted in isolation few tests have high sensitivity and specificity simultaneously in these cases one can increase either the sensitivity or the specificity by combining two component tests under either the either positive rule or the both positive rule however there is a tradeoff between sensitivity and specificity when these rules are applied we propose three statistical procedures to simultaneously assess the sensitivity and specificity when combining two component tests measurements of interest include rate difference and rate ratio our empirical results demonstrate that i the asymptotic test procedures for both measurements and approximate test procedure for rate difference possess inflated type i error rate ii the exact test procedures for both measurements possess deflated type i error rate and iii the approximate unconditional test procedure for rate ratio becomes an reliable alternative and nicely controls the actual type i error rate in small to moderate sample sizes moreover the approximate unconditional test procedure is computationally less intensive than the exact unconditional test procedure we illustrate our methodologies with a real example from a residual nasopharyngeal carcinoma rnp study

assessing proportionality in the proportional odds model for ordinal logistic regression the proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories the model may be represented by a series of logistic regressions for dependent binary variables with common regression parameters reflecting the proportional odds assumption key to the valid application of the model is the assessment of the proportionality assumption an approach is described arising from comparisons of the separate correlated fits to the binary logistic models underlying the overall model based on asymptotic distributional results formal goodness of fit measures are constructed to supplement informal comparisons of the different fits a number of proposals including application of bootstrap simulation are discussed and illustrated with a data example

robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials in clinical trials comparing two treatments ordinal scales of three four or five points are often used to assess severity both prior to and after treatment analysis of covariance is an attractive technique however the data clearly violate the normality assumption and in the presence of small samples and large sample theory may not apply the robustness and power of various versions of parametric analysis of covariance applied to small samples of ordinal scaled data are investigated through computer simulation subjects are randomized to one of two competing treatments and the pre treatment or baseline assessment is used as the covariate we compare two parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regressions slopes and the two independent samples t test on difference scores under the null hypothesis of no difference in adjusted treatment means we estimated actual significance levels by comparing observed test statistics to appropriate critical values from the f and t distributions for nominal significance levels of 0 10 0 05 0 02 and 0 01 we estimated power by similar comparisons under various alternative hypotheses the model which assumes homogeneous slopes and the t test on difference scores were robust in the presence of three four and five point ordinal scales the hierarchical approach which first tests for homogeneity of regression slopes and then fits separate slopes if there is significant non homogeneity produced significance levels that exceeded the nominal levels especially when the sample sizes were small the model which assumes homogeneous regression slopes produced the highest power among competing tests for all of the configurations investigated the t test on difference scores also produced good power in the presence of small samples

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

the borel conjecture for hyperbolic and cat 0 groups we prove the borel conjecture for a class of groups containing word hyperbolic groups and groups acting properly isometrically and cocompactly on a finite dimensional cat 0 space

an application of maximum likelihood and generalized estimating equations to the analysis of ordinal data from a longitudinal study with cases missing at random data are analysed from a longitudinal psychiatric study in which there are no dropouts that do not occur completely at random a marginal proportional odds model is fitted that relates the response severity of side effects to various covariates two methods of estimation are used generalized estimating equations gee and maximum likelihood ml both the complete set of data and the data from only those subjects completing the study are analysed for the completers only data the gee and ml analyses produce very similar results these results differ considerably from those obtained from the analyses of the full data set there are also marked differences between the results obtained from the gee and ml analysis of the full data set the occurrence of such differences is consistent with the presence of a non completely random dropout process and it can be concluded in this example that both the analyses of the completers only and the gee analysis of the full data set produce misleading conclusions about the relationships between the response and covariates

a noniterative sample size procedure for tests based on t distributions a noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending guenther s approach for the one sample and two sample t tests the generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance ancova and the mixed effects model for repeated measures in randomized clinical trials the sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms which are functions of the covariates in the model but it does not require specifying the covariate distribution the noniterative procedure is suitable for superiority tests noninferiority tests and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer the method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials we also derive accurate power formulae for ancova and mixed effects model for repeated measures and the formula for ancova is exact for normally distributed covariates numerical examples demonstrate the accuracy of the proposed methods particularly in small samples

robustness and power of analysis of covariance applied to data distorted from normality by floor effects homogeneous regression slopes we investigate through computer simulations the robustness and power of two group analysis of covariance test applied to small samples distorted normality by floor effects when the regression slopes are homogeneous we consider four parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regression slopes and two t tests on unadjusted means and on difference scores under the null hypothesis of no difference in means we estimated actual significance levels by comparing observed test statistics to appropriate values from the f and t distributions for nominal significance levels of 0 10 0 05 0 02 and 0 01 we estimated power by similar comparisons under various alternative hypothesis the hierarchical approach that adjusts for non homogeneous slopes if found significant the test that assumes homogeneous regression slopes and the test that estimates separate regression slopes in each treatment were robust in general each test produced power at least equal to that expected from normal theory the textbook approach which does not test for mean differences when there is significant non homogeneity was conservative but also had good power the t tests were robust but had poorer power properties than the above procedures

on the partitioning of goodness of fit statistics for multivariate categorical response models abstract numerical and asymptotic stochastic partitioning of goodness of fit statistics are considered for a broad class of simultaneous multivariate categorical response models these simultaneous models impose constraints on the joint and marginal distributions of categorical response variables under certain conditions the tenability of the corresponding simultaneous hypothesis can be assessed by separately testing the two subhypotheses one regarding the joint distributions and the other regarding the marginal distributions specifically easily verifiable sufficient conditions are introduced that allow us to partition the overall goodness of fit statistic into two interesting goodness of fit statistics one for testing whether the joint distribution model holds and the other for testing whether the marginal distribution model holds moreover it is proven that when the sufficient conditions hold and the simultaneous hypothesis is true the two component goodness of fit statistics are asymptotically

nonlinear schrodinger type equations from multiscale reduction of pdes ii necessary conditions of integrability for real pdes the multiscale method has been applied in j math phys 41 6399 2000 to evolution pdes to obtain various nonlinear schrodinger type equations here these results are exploited to derive necessary conditions of integrability for nonlinear real evolution pdes in 1 1 dimensions these conditions are given by explicit formulas and several examples are detailed

comparisons of two part models with competitors two part models arise when there is a clump of 0 observations in a distribution of continuous non negative responses several methods for comparing two such distributions are available these include the straightforward application of the z test or t test the wilcoxon mann whitney rank sum test the kolmogorov smirnov test and three tests that use a 2 degree of freedom chi 2 test based on the sum of the test for equality of proportions and a conditional chi 2 test for the continuous responses this conditional test may be the z test the rank sum test or the chi 2 corresponding to the kolmogorov smirnov test this study compares the size and power of several of these methods all tests have the appropriate distribution under the null hypothesis if the distribution of the continuous part has finite moments if it does not the z test has no power to detect any alternatives it is found that the 2 d f tests are superior to the others when the larger proportion of 0 values corresponds to the population with the larger mean if the reverse holds the difference in the proportion of zeros reinforces the difference in means and some single part models the rank sum or kolmogorov smirnov do best in those cases the two part models are not far behind although statistically significantly poorer with respect to power published in 2001 by john wiley sons ltd

large riemannian manifolds which are flexible for each k z we construct a uniformly contractible metric on euclidean space which is not mod k hypereuclidean we also construct a pair of uniformly contractible riemannian metrics on r n n 11 so that the resulting manifolds z and z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism we show that for these spaces the c algebra assembly map k lf z k c z from locally finite k homology to the k theory of the bounded propagation algebra is not a monomorphism this shows that an integral version of the coarse novikov conjecture fails for real operator algebras if we allow a single cone like singularity a similar construction yields a counterexample for complex c algebras

multiscale reduction of discrete korteweg de vries equations we show how through a multiscale reduction technique performing the analysis at orders beyond the nonlinear schrodinger equation one can effectively prove if some nonlinear partial difference equation is not integrable the example is carried out on a symmetric discretization of the kdv equation and is compared to a similar reduction performed on the integrable lattice potential kdv equation

power and sample size calculations for discrete bounded outcome scores we consider power and sample size calculations for randomized trials with a bounded outcome score bos as primary response adjusted for a priori chosen covariates we define bos to be a random variable restricted to a finite interval typically a bos has a j or u shaped distribution hindering traditional parametric methods of analysis when no adjustment for covariates is needed a non parametric test could be chosen however there is still a problem with calculating the power since the common location shift alternative does not hold in general for a bos in this paper we consider a parametric approach and assume that the observed bos is a coarsened version of a true bos which has a logit normal distribution in each treatment group allowing correction for covariates a two step procedure is used to calculate the power firstly the power function is defined conditionally on the covariate values secondly the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using monte carlo integration a simulation study evaluates the performance of our method which is also applied to the ecass 1 stroke study

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

a discrete linearizability test based on multiscale analysis in this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad graph by the multiple scale reduction around their harmonic solution we show that the a1 a2 and a3 linearizability conditions restrain the number of the parameters which enter into the equation a subclass of the equations which pass the a3 c integrability conditions can be linearized by a mobius transformation

on hyperbolic groups with spheres as boundary let g be a torsion free hyperbolic group and let n 6 be an integer we prove that g is the fundamental group of a closed aspherical manifold if the boundary of g is homeomorphic to an n 1 dimensional sphere

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

the structures and interactions of solitary waves in a 2 1 dimensional coupled nonlinear extension of the reaction diffusion equation the complete integrability of a 2 1 dimensional coupled nonlinear extension of the reaction diffusion cnlerd equation using the technique of painlev p analysis is investigated using the formalism of weiss et al 1983 j math phys 24 522 the arbitrariness of the expansion coefficients are proved besides following the hirota s formalism hirota r 1980 direct methods in soliton theory soliton berlin springer combined to weiss et al s methodology weiss et al 1984 j math phys 25 13 the consistency of the truncation is shown thus without the use of kruskal s simplification the bcklund transformation bt of the equations is obtained via the truncation procedure taking into account the arbitrariness of the expansion coefficients in the foregoing truncation a typical spectrum of localized coherent structures may be unearthed the scattering behavior of such structures is also investigated

robustness of the two independent samples t test when applied to ordinal scaled data one may encounter the application of the two independent samples t test to ordinal scaled data for example data that assume only the values 0 1 2 3 from small samples this situation clearly violates the underlying normality assumption for the t test and one cannot appeal to large sample theory for validity in this paper we report the results of an investigation of the t test s robustness when applied to data of this form for samples of sizes 5 to 20 our approach consists of complete enumeration of the sampling distributions and comparison of actual levels of significance with the significance level expected if the data followed a normal distribution we demonstrate under general conditions the robustness of the t test in that the maximum actual level of significance is close to the declared level

the k theoretic farrell jones conjecture for hyperbolic groups we prove the k theoretic farrell jones conjecture for hyperbolic groups with twisted coefficients in any associative ring with unit

a latent trait finite mixture model for the analysis of rating agreement this article presents a latent distribution model for the analysis of agreement on dichotomous or ordered category ratings the model includes parameters that characterize bias category definitions and measurement error for each rater or test parameter estimates can be used to evaluate rater performance and to improve classification or measurement with use of multiple ratings a simple maximum likelihood estimation procedure is described two examples illustrate the approach although considered in the context of analyzing rater agreement the model provides a general approach for mixture analysis using two or more ordered caregory measures

assessing interrater agreement from dependent data estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods we investigate the use of a latent model proposed by qu piedmonte and medendorp 1995 biomerics 51 268 275 to estimate the correlation between raters for each method and test for their equality for each of the assessment methods these correlations can be interpreted as the variance components of random effects representing subject and rater this method is applied to an hiv study in which the amount of ectopy on a woman s cervix is measured by both direct visual assessment and a computer planimetry method

performance of analytical methods for overdispersed counts in cluster randomized trials sample size degree of clustering and imbalance many different methods have been proposed for the analysis of cluster randomized trials crts over the last 30 years however the evaluation of methods on overdispersed count data has been based mostly on the comparison of results using empiric data i e when the true model parameters are not known in this study we assess via simulation the performance of five methods for the analysis of counts in situations similar to real community intervention trials we used the negative binomial distribution to simulate overdispersed counts of crts with two study arms allowing the period of time under observation to vary among individuals we assessed different sample sizes degrees of clustering and degrees of cluster size imbalance the compared methods are i the two sample t test of cluster level rates ii generalized estimating equations gee with empirical covariance estimators iii gee with model based covariance estimators iv generalized linear mixed models glmm and v bayesian hierarchical models bayes hm variation in sample size and clustering led to differences between the methods in terms of coverage significance power and random effects estimation glmm and bayes hm performed better in general with bayes hm producing less dispersed results for random effects estimates although upward biased when clustering was low gee showed higher power but anticonservative coverage and elevated type i error rates imbalance affected the overall performance of the cluster level t test and the gee s coverage in small samples important effects arising from accounting for overdispersion are illustrated through the analysis of a community intervention trial on solar water disinfection in rural bolivia

improved tests for comparing treatments against a control and other one sided problems abstract three multivariate one sided testing problems are studied all problems concern a independent normal populations with unknown means and common unknown variance for the first problem the null hypothesis is that all means are zero while the alternative is that each mean is nonnegative and at least one is positive for the second problem the null hypothesis is that all means are equal and the alternative is that all of the first k 1 means are greater than or equal to the mean of the last population with strict inequality for at least one the alternative for the second problem is called the tree top alternative for the third problem the null hypothesis is that all means are equal while the alternative is that the means are ordered say nonincreasing this latter alternative is called the simple order alternative all three of these problems are discussed extensively in the book by robertson wright and dykstra we will assume that random samples of size n are drawn from each population

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

methods for estimating the parameters of a linear model for ordered categorical data in many empirical analyses the response of interest is categorical with an ordinal scale attached many investigators prefer to formulate a linear model assigning scores to each category of the ordinal response and treating it as continuous when the covariates are categorical haber 1985 computational statistics and data analysis 3 1 10 has developed a method to obtain maximum likelihood ml estimates of the parameters of the linear model using lagrange multipliers however when the covariates are continuous the only method we found in the literature is ordinary least squares ols performed under the assumption of homogeneous variance the ols estimates are unbiased and consistent but since variance homogeneity is violated the ols estimates of variance can be biased and may not be consistent we discuss a variance estimate white 1980 econometrica 48 817 838 that is consistent for the true variance of the ols parameter estimates the possible bias encountered by using the naive ols variance estimate is discussed an estimated generalized least squares egls estimator is proposed and its efficiency relative to ols is discussed finally an empirical comparison of ols egls and ml estimators is made

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

non parametric two sample tests for repeated ordinal responses consider data on two groups of clusters where each cluster consists of many units that respond on an ordinal scale we develop a mann whitney type test to determine whether a typical response from the first group is larger or smaller than a typical response from the second group

the score test for independence in r x c contingency tables with missing data in this paper the score test statistic for testing independence in r x c contingency tables with missing data is proposed under the null hypothesis of independence the statistic has an approximate chi squared distribution with r 1 c 1 degrees of freedom the proposed test statistic is quite similar to the pearson chi squared statistic with complete data and unlike the likelihood ratio statistic for testing independence its computation is simple and noniterative in addition a score test statistic is proposed for testing independence when the rows and columns of the r x c table are ordinal finally extensions of the score statistics to test for conditional independence in a set of r x c contingency tables with missing data are described this yields score test statistics that are natural extensions of the mantel haenszel statistic an example using a subset of data from the six cities study is presented to illustrate the methods

nonlinear schrodinger type equations from multiscale reduction of pdes i systematic derivation in this article we begin a systematic investigation via multiscale expansions of nonlinear evolution pdes partial differential equations in this first article we restrict consideration to a single autonomous but otherwise generic pde in 1 1 variables space time of first order in time whose linear part is dispersive and to solutions dominated by a single plane wave satisfying the linear part of the pde the expansion parameter is an assumedly small coefficient multiplying this plane wave the main indeed asymptotically exact effect of the weak nonlinearity is then to cause a modulation of the amplitude of the plane wave and of its harmonics which is generally described in appropriately defined coarse grained time and space variables by evolution equations of nonlinear schrodinger type a systematic analysis of such equations is presented corresponding to various assumptions on the resonances occurring for the first few harmonics

a class of regression models for multivariate categorical responses summary when data composed of several categorical responses together with categorical or continuous predictors are observed it is often useful to relate the response probabilities to the predictors via a generalised linear model with a composite link function this paper discusses a class of link functions that lie between the two extremes of the multivariate logistic transform of mccullagh nelder 1989 and the log linear decomposition of contingency table analysis the models derived from these link functions are shown to inherit various desirable properties of both the multivariate logistic regression models and the log linear regression models a computational scheme for implementing these models is derived and they are demonstrated to be computationally more tractable than the multivariate logistic regression models their application is illustrated in a numerical example

some general methods for the analysis of categorical data in longitudinal studies this paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs an expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets appropriate large sample tests of these hypotheses are developed through the application of weighted least squares to generate wald statistics these procedures are illustrated with extensive analyses of one of these data sets in some situations the resulting cross classification of the response variables leads to extremely sparse frequency data especially when the number of subjects is not large for such repeated measurement designs in which a single variable is measured repeatedly over time this paper considers the use of a generalized mantel haenszel strategy for tests of marginal homogeneity symmetry these randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale this paper also focuses on the available computing software to implement these methods within the version 5 release of the sas system the randomization model approach can be implemented within the freq procedure and a broad range of models and hypotheses can be investigated within the catmod procedure

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

new integrable pdes of boomeronic type novel integrable systems of coupled first order autonomous pdes in 1 1 dimensions space x and time t are presented integrable covariant 2 vector and 3 vector pdes as well as higher order integrable pdes for a single or a couple of scalar dependent variables including an extension of the sine gordon equation and a remarkably neat highly nonlinear third order pde are also obtained by appropriate reductions of the basic matrix equations the lax pairs that characterize the integrable character of the basic matrix pdes are also exhibited as well as their single soliton solutions these solitons generally exhibit the boomeronic and less generically the trapponic phenomenology namely they do not move uniformly but rather in an appropriate reference system come in from one end in the remote past and boomerang back to that same end in the remote future boomerons or are trapped to oscillate around a value fixed by the initial data trappons

improving tests for superior treatment in contingency tables abstract when comparing two treatments on the basis of ordinal data a natural alternative is stochastic order as it implies that more favorable outcomes receive greater probability results of eaton can be used to provide a complete class of tests we find that many tests in current use are not in this class and hence are inadmissible more important we present methods of improving such tests often the increase in power is substantial although the size remains the same

distribution free fitting of logit models with random effects for repeated categorical responses this article discusses random effects models for within subject comparisons of repeated responses on the same categorical scale the models account for the correlation that normally occurs between repeated responses the standard way of fitting such models maximizes the marginal likelihood after integrating with respect to a distribution for the random effect an alternative non parametric approach does not assume a distributional form for the random effects recent literature shows that for certain simple logit models this approach yields essentially the same model parameter estimates as conditional maximum likelihood moreover these estimates also result from fitting corresponding quasi symmetric log linear models for simple data sets in which primary interest relates to subject specific comparisons of the repeated responses one can easily obtain the estimates with standard software for log linear models examples include data from crossover designs and from comparisons of treatment and control groups regarding the change between baseline and follow up observations

ordinal regression methodology for roc curves derived from correlated data we present an approach for the analysis of correlated roc data using ordinal regression models in conjunction with generalized estimating equations the approach applies to the analysis of degree of suspicion data derived from multiple interpretations of the same diagnostic study and from the examination of the same patients with multiple diagnostic modalities the regression models make it possible to incorporate patient and reader characteristics into the analysis without having to resort to stratification we illustrate the potential of the approach with analysis of data from two studies in diagnostic oncology

the use of bootstrap methods for estimating sample size and analysing health related quality of life outcomes health related quality of life hrqol measures are increasingly used in trials as primary outcome measures investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes hrqol outcomes like the sf 36 are usual measured on an ordinal scale although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes the ordered categories reflect contiguous intervals along this continuum the ordinal scaling of hrqol measures means they tend to generate data that have discrete bounded and skewed distributions thus standard methods of analysis that assume normality and constant variance may not be appropriate for this reason conventional statistical advice would suggest non parametric methods be used to analyse hrqol data the bootstrap is one such computer intensive non parametric method for estimating sample sizes and analysing data we describe three methods of estimating sample sizes for two group cross sectional comparisons of hrqol outcomes we then compared the power of the three methods for a two group cross sectional study design using bootstrap simulation the results showed that under the location shift alternative hypothesis conventional methods of sample size estimation performed well particularly whitehead s method whitehead s method is recommended if the hrqol outcome has a limited number of discrete values 7 and or the expected proportion of cases at either of the bounds is high if a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate than conventional methods finally we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters in an example data set we then compared and contrasted the bootstrap with standard methods of analysing hrqol outcomes in the data set studied with the sf 36 outcome the use of the bootstrap for estimating sample sizes and analysing hrqol data produces results similar to conventional statistical methods these results suggest that bootstrap methods are not more appropriate for analysing hrqol outcome data than standard methods

a loop theorem for duality spaces and fibred ribbon knots in this paper we prove a version of the loop theorem for surfaces in the boundary of a 3 dimensional duality space i e a space which resembles a 3manifold only in that it satisfies the appropriate form of poincar6 lefschetz duality over some field of untwisted coefficients our motivation comes from the fact that such spaces occur as the infinite cyclic coverings of certain 4manifolds which arise in the study of knot concordance and as the main application of our theorem we show that if a fibred knot in the 3 sphere is a ribbon knot then its monodromy extends over a handlebody we approach the loop theorem via the study of planar coverings of a surface as in the original paper of papakyriakopoulos 11 and the subsequent work of maskit 9 w contains a simple geometric treatment of these matters the main result of w is that a duality space actually satisfies duality with twisted coefficient module the quotient of the fundamental group ring by any power of the augmentation ideal in w 4 the results of w167 2 and 3 together with an algebraic lemma on the intersection of the powers of the augmentation ideal of a group ring are used to prove the loop theorem for 3 dimensional duality spaces for the reader s convenience a proof of the algebraic temma is included as an appendix w contains the application to fibred ribbon knots mentioned above in w the result of w is used to obtain a limited amount of information on some questions about knots in the boundaries of contractible 4 manifolds in w we apply our methods to another aspect of knot concordance and show that for any concordance with a rationally anisotropic fibred knot see 7 at one end the inclusion of the complement of the knot into the complement of the concordance induces an injection of fundamental groups for torus knots this question was raised by scharlemann 14

analyzing bivariate ordinal data using a global odds ratio abstract a moment method is proposed for regression analysis of bivariate ordered categorical data using the global odds ratio as the measure of association for modeling the margins this method utilizes the stochastic ordering implicit in the data this method allows for covariate effects in modeling the association between responses an application of the proposed model is illustrated using the ophthalmological data from the wisconsin epidemiologic study of diabetic retinopathy for identifying risk factors among younger onset diabetics this model is also extended to a longitudinal data setting with more than two repeated measures

population averaged and cluster specific models for clustered ordinal response data we compare population averaged and cluster specific models for clustered ordinal data we consider generalized estimating equations and constrained equations maximum likelihood estimation of population averaged cumulative logit regression models and mixed effects estimation of cluster specific cumulative logit regression models a previously reported relationship between population averaged and cluster specific parameters for the binary logistic link appears to hold for analogous parameters under the cumulative logit link we address these issues in the context of data from two cross over clinical trials

a likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

proper actions on cohomology manifolds essential results about actions of compact lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds slices are replaced by certain fiber bundle structures on orbit neighborhoods the group dimension is shown to be effectively finite the orbits of maximal dimension form a dense open connected subset if some orbit has codimension at most 2 then the group is effectively a lie group

some power considerations when deciding to use transformations conventional wisdom suggests that for small data sets having substantial skew one should attempt to determine the correct distributional form if possible and apply statistical methods appropriate for that distribution transformations such as the log or square root are often used if an appropriate distributional form cannot be determined a distribution free procedure such as a rank transformation or a randomization test procedure can be used to better appreciate the effect of such alternatives on both the type i error and power of detecting differences between treatment groups simulation studies were conducted for responses having specific gamma g r theta and log normal ln m v distributions the gamma and log normal distributions were selected so that they had the same first two moments a simple two group design was assumed the reference group always had an average disease level mu 3 0 mu r theta for gamma mu m for log normal and the treatment group always had means whose reductions ranged from 0 per cent to 50 per cent the effect of distributional type and the degree of skewness was investigated by varying the population parameter values six statistical test procedures were compared for the gamma distributions all test procedures were robust relative to the type i error the ump test based on a ratio of sample means produced the greatest power for all combinations of n r and rt the power losses associated with the randomization test the t test on original scale and the t test on the square root scale were very small 3 per cent to 6 per cent in absolute value for n 10 and 15 and less than 2 per cent for group sizes of 25 or more the power loss associated with the t test on the log scale was much larger ranging from 5 per cent to 10 per cent smaller power than the t test on original scale the wilcoxon rank test produced similar results to that of the log t test for small samples the power for the shifted log x c test increased monotonically to the asymptotic value of the orig t test the same five test procedures based on differences in sample means were then compared for the corresponding log normal distributions the ump test that is log x produced the highest power there was very little power lost for the sqrt t test the loss in power varied between 2 per cent and 5 per cent for the rank test abstract truncated at 400 words

topology of homology manifolds anr homology n manifolds are nite dimensional absolute neighborhood retracts x with the property that for every x 2 x hi x x fxg is 0 for i 6 n and z for i n topological manifolds are natural examples of such spaces to obtain nonmanifold examples we can take a manifold whose boundary consists of a union of integral homology spheres and glue on the cone on each one of the boundary components the resulting space is not a manifold if the fundamental group of any boundary component is a nontrivial perfect group it is a consequence of the double suspension theorem of cannon and edwards that as in the examples above the singularities of polyhedral anr homology manifolds are isolated there are however many examples of anr homology manifolds which have no manifold points whatever see 12 for a good exposition of the relevant theory the purpose of this paper is to begin a surgical classi cation of anr homology manifolds sometimes referred to in the sequel simply as homology manifolds one way to approach this circle of ideas is via the problem of characterizing topological manifolds among anr homology manifolds in cannon s work on the double suspension problem 6 it became clear that in dimensions greater than 4 the right transversality hypothesis is the following weak form of general position

modeling within subject dependencies in ordinal paired comparison data this paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments it is argued that a core assumption of latent class choice models independence of individual decisions may not be well suited for the analysis of paired comparison data instead the analysis and interpretation of paired comparison data may be much simplified by allowing for within person dependencies that result from repeated evaluations of the same options in different pairs moreover by relating dependencies among the individual level responses to in consistencies in the judgmental process we show that the proposed graded paired comparison models reduce to ranking models under certain conditions three applications are presented to illustrate the approach

maximum likelihood methods for a generalized class of log linear models we discuss maximum likelihood methods for fitting a broad class of multivariate categorical response data models in particular we derive the large sample distributions for maximum likelihood estimators of parameters of product multinomial generalized log linear models the large sample behavior of other relevant likelihood based statistics such as goodness of fit statistics and adjusted residuals is also described the asymptotic results are derived within the framework of the constraint specification rather than the more common freedom specification of the model we also outline an improved fitting algorithm for computing parameter maximum likelihood estimates and other relevant statistics the broad class of multivariate categorical response data models which are referred to as generalized log linear models can imply structure on several response configuration distributions e g joint and marginal distributions these models which include as special cases log linear logit and cumulative logit models enjoy a wide breadth of application including longitudinal rater agreement and crossover data analyses

homology manifold bordism the bryant ferry mio weinberger surgery exact sequence for compact anr homology manifolds of dimension 6 is used to obtain transversality splitting and bordism results for homology manifolds generalizing previous work of johnston first we establish homology manifold transversality for submanifolds of dimension 7 if f m p is a map from an m dimensional homology manifold m to a space p and q p is a subspace with a topological q block bundle neighborhood and m q 7 then f is homology manifold s cobordant to a map which is transverse to q with f 1 q m an m q dimensional homology submanifold second we obtain a codimension q splitting obstruction sq f lsm q in the wall ls group for a simple homotopy equivalence f m p from an m dimensional homology manifold m to an m dimensional poincare space p with a codimension q poincare subspace q p with a topological normal bundle such that sq f 0 if and for m q 7 only if f splits at q up to homology manifold s cobordism third we obtain the multiplicative structure of the homology manifold bordism groups top l0 z

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

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

quasi symmetric latent class models with application to rater agreement suppose we observe responses on several categorical variables having the same scale we consider latent class models for the joint classification that satisfy quasi symmetry the models apply when subject specific response distributions are such that i for a given subject responses on different variables are independent and ii odds ratios comparing marginal distributions of the variables are identical for each subject these assumptions are often reasonable in modeling multirater agreement when a sample of subjects is rated independently by different observers in this application the model parameters describe two components of agreement strength of association between classifications by pairs of observers and degree of heterogeneity among the observers marginal distributions we illustrate the models by analyzing a data set in which seven pathologists classified 118 subjects in terms of presence or absence of carcinoma yielding seven categorical classifications with the same binary scale a good fitting model has a latent classification that differentiates between subjects on whom there is agreement and subjects on whom there is disagreement

the multiscale expansions of difference equations in the small lattice spacing regime and a vicinity and integrability test i we propose an algorithmic procedure i to study the distance between an integrable pde and any discretization of it in the small lattice spacing regime and at the same time ii to test the asymptotic integrability properties of such discretization this method should provide in particular useful and concrete information on how good is any numerical scheme used to integrate a given integrable pde the procedure illustrated on a fairly general ten parameter family of discretizations of the nonlinear schr dinger equation consists of the following three steps i the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in following degasperis et al 1997 physica d 100 187 211 ii the application to such an expansion of the degasperis procesi dp integrability test degasperis a and procesi m 1999 asymptotic integrability symmetry and perturbation theory spt98 ed a degasperis and g gaeta singapore world scientific pp 23 37 degasperis a 2001 multiscale expansion and integrability of dispersive wave equations lectures given at the euro summer school what is integrability isaac newton institute cambridge uk 13 24 august integrability lecture notes in physics vol 767 ed a mikhailov berlin springer to test the asymptotic integrability properties of the discrete system and its distance from its continuous limit iii the use of the main output of the dp test to construct infinitely many approximate symmetries and constants of motion of the discrete system through novel and simple formulas

location scale cumulative odds models for ordinal data a generalized non linear model approach proportional odds regression models for multinomial probabilities based on ordered categories have been generalized in two somewhat different directions models having scale as well as location parameters for adjustment of boundaries on an unobservable underlying continuum between categories have been employed in the context of roc analysis partial proportional odds models having different regression adjustments for different multinomial categories have also been proposed this paper considers a synthesis and further generalization of these two families with use of a number of examples i discuss and illustrate properties of this extended family of models emphasis is on the computation of maximum likelihood estimates of parameters asymptotic standard deviations and goodness of fit statistics with use of non linear regression programs in standard statistical software such as sas

the 3 manifold recognition problem we introduce a natural relative simplicial approximation property for maps from a 2 cell to a generalized 3 manifold and prove that modulo the poincare conjecture 3 manifolds are precisely the generalized 3 manifolds satisfying this approximation property the central technical result establishes that every generalized 3 manifold with this relative simplicial approximation property is the cell like image of some generalized 3 manifold having just a 0 dimensional set of nonmanifold singularities

discrete third order spectral problems and a new toda type equation in this paper we construct the class of equations associated with a discrete spectral problem of third order among the equations of this class we find an integrable differential equation on the lattice with exponential nonlinearity by considering its associated darboux transformation we construct an explicit solution

multiple scale perturbation beyond the nonlinear schroedinger equation i abstract we consider the effect of weak nonlinearity on the propagation of one dimensional strongly dispersive waves in the standard quasi monochromatic approximation it is well known that the first order amplitude modulation satisfies the nonlinear schroedinger equation in slow variables with the assumption that this amplitude modulation has no discrete spectrum component i e no soliton we explore the higher order effects and provide a well defined procedure to compute all coefficients of the perturbative expansion as relatively bounded functions no secularity effects of slow variables the main effect of this procedure is that the leading amplitude modulation satisfies at higher orders the nonlinear schroedinger hierarchy of evolution equations in slow variables key ingredient is the integrability of the nonlinear schroedinger equation and its commuting symmetries

bivariate modelling of clustered continuous and ordered categorical outcomes simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution the approach is then extended to allow for clustering of the bivariate outcomes the model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome this factorization suggests convenient parameter estimation using estimating equations foetal weight and malformation data from a developmental toxicity experiment illustrate the results

exact inference for contingency tables with ordered categories abstract this article proposes an efficient numerical algorithm for small sample exact inferences in contingency tables having ordinal classifications the inferences which apply conditional on the observed marginal totals also provide an exact analysis for the log linear model of linear by linear association for cell probabilities an exact test of independence has a one sided p value equal to the null probability that model based maximum likelihood estimates of odds ratios are at least as large as the observed estimates the conditional nonnull distribution yields confidence intervals for odds ratios having a linear by linear structure the computations utilize an extension of the network algorithm proposed by mehta and patel 1983

universal c integrable nonlinear partial differential equation in n 1 dimensions a nonlinear partial differential equation of evolution in n 1 dimensions is exhibited which is c integrable namely integrable via an appropriate change of variables and which also possesses an element of universality as it is obtained by applying a limiting procedure to a class of nonlinear partial differential equations since this limiting procedure corresponds to physical conditions likely to prevail in some phenomenological circumstances it is expected that this equation shall have applicative relevance but this possibility is not pursued in this paper the method whereby this equation has been obtained as well as its integrable character qualify it as a n 1 dimensional analog of the eckhaus equation to which it does indeed reduce for n 1

the analysis of multivariate contingency tables by restricted canonical and restricted association models abstract restricted canonical models and restricted association models are proposed and applied to multiway contingency tables these models have been previously applied to two way contingency tables however multivariate generalization has been impeded in the past since canonical and association models both depend on singular value decompositions that apply only to two way arrays in this article this restriction to two way arrays is overcome by division of the cross classified variables into explanatory and response variables the explanatory variables are treated as a single polytomous variable and the response variables are treated as a second single polytomous variable in this fashion the multiway table is reduced to a two way array to which traditional canonical and association models may be applied use of linear restrictions on parameters in canonical and association models is especially important in multiway tables if useful models are to be constructed the class of models considered in th

inference for likelihood ratio ordering in the two sample problem abstract we obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered we extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators we also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense finally we examine a data set pertaining to average daily insulin dose from the boston collaborative drug surveillance program and compare our testing procedure to testing procedures for other stochastic orderings

quasisymmetric models for the analysis of square contingency tables summary a parametric model is presented for the analysis of square contingency tables where there is a one to one correspondence between the categories of the row variable and the categories of the column variable the model is applicable to cross classifications where the categories are unordered partially ordered or completely ordered but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered connections with the mover stayer model and the usual model of quasisymmetry are described two data sets are used to illustrate the utility of the model