measurement errors in caries diagnosis some further latent class models latent class models have been proposed for assessing relative errors in discrete measurements arising for example in caries diagnosis those models however that turned out to fit empirical data n 3 869 teeth 5 dentists to a sufficient degree needed the inclusion of interaction terms for pairs of raters at the latent levels in order to describe the observed interrelations of the judgments now it is shown that instead of giving up the concept of local stochastic independence increasing the number of classes while possibly restricting their parameters in the end has the same effect both the unrestricted three class model which can be interpreted to be the generalization of the carlos senning assumptions and a restricted four class model which resembles the latent distance model well known from psychometrics give good and excellent fit respectively to the caries data for the case of the four class model a second solution exists that exhibits exactly the same fit giving rise to warnings against the possibility of multiple solutions to the likelihood equations

latent structure analysis of a set of multidimensional contingency tables abstract statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables three basic classes of models are considered a models that assume complete homogeneity across tables b models that allow partial homogeneity across tables and c models that allow complete heterogeneity methods are presented for testing whether these models are congruent with the data in the tables and for assessing the significance of differences among the tables in the estimated parameters to illustrate the wide applicability of these models and methods we present analyses of two quite different sets of data

random effects modeling approaches for estimating roc curves from repeated ordinal tests without a gold standard estimating diagnostic accuracy without a gold standard is an important problem in medical testing although there is a fairly large literature on this problem for the case of repeated binary tests there is substantially less work for the case of ordinal tests a noted exception is the work by zhou castelluccio and zhou 2005 biometrics 61 600 609 which proposed a methodology for estimating receiver operating characteristic roc curves without a gold standard from multiple ordinal tests a key assumption in their work was that the test results are independent conditional on the true test result i propose random effects modeling approaches that incorporate dependence between the ordinal tests and i show through asymptotic results and simulations the importance of correctly accounting for the dependence between tests these modeling approaches along with the importance of accounting for the dependence between tests are illustrated by analyzing the uterine cancer pathology data analyzed by zhou et al 2005

a probit latent class model with general correlation structures for evaluating accuracy of diagnostic tests traditional latent class modeling has been widely applied to assess the accuracy of dichotomous diagnostic tests these models however assume that the tests are independent conditional on the true disease status which is rarely valid in practice alternative models using probit analysis have been proposed to incorporate dependence among tests but these models consider restricted correlation structures in this article we propose a probit latent class model that allows a general correlation structure when combined with some helpful diagnostics this model provides a more flexible framework from which to evaluate the correlation structure and model fit our model encompasses several other plc models but uses a parameter expanded monte carlo em algorithm to obtain the maximum likelihood estimates the parameter expanded em algorithm was designed to accelerate the convergence rate of the em algorithm by expanding the complete data model to include a larger set of parameters and it ensures a simple solution in fitting the plc model we demonstrate our estimation and model selection methods using a simulation study and two published medical studies

identifying the odds ratio estimated by a two stage instrumental variable analysis with a logistic regression model an adjustment for an uncorrelated covariate in a logistic regression changes the true value of an odds ratio for a unit increase in a risk factor even when there is no variation due to covariates the odds ratio for a unit increase in a risk factor also depends on the distribution of the risk factor we can use an instrumental variable to consistently estimate a causal effect in the presence of arbitrary confounding with a logistic outcome model we show that the simple ratio or two stage instrumental variable estimate is consistent for the odds ratio of an increase in the population distribution of the risk factor equal to the change due to a unit increase in the instrument divided by the average change in the risk factor due to the increase in the instrument this odds ratio is conditional within the strata of the instrumental variable but marginal across all other covariates and is averaged across the population distribution of the risk factor where the proportion of variance in the risk factor explained by the instrument is small this is similar to the odds ratio from a rct without adjustment for any covariates where the intervention corresponds to the effect of a change in the population distribution of the risk factor this implies that the ratio or two stage instrumental variable method is not biased as has been suggested but estimates a different quantity to the conditional odds ratio from an adjusted multiple regression a quantity that has arguably more relevance to an epidemiologist or a policy maker especially in the context of mendelian randomization

an ordering of dependence for contingency tables abstract a majorization ordering is defined on matrices with the same row and column sums this ordering is used as an ordering of dependence for contingency tables results are derived for maximal and minimal matrices with respect to the majorization ordering this theory can be used to maximize and minimize schur concave functions defined over matrices when there are row and column sum constraints in this paper it is applied to the algorithm of mehta and patel 1983 for finding the p value of fisher s exact test

dual synchronization based on two different chaotic systems lorenz systems and rossler systems in this paper we improve and extend the works of liu and davids dual synchronization of chaos phys rev e 61 2000 2176 2179 which only introduce the dual synchronization of 1 d discrete chaotic systems the dual synchronization of two different 3 d continuous chaotic systems lorenz systems and rossler systems is discussed and a sufficient condition of dual synchronization about the two different chaotic systems is obtained theories and numerical simulations show the possibility of dual synchronization and the effectiveness of the method

relative submajorization and its use in quantum resource theories we introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics bipartite entanglement and quantum coherence relative majorization is an ordering on pairs of vectors induced by stochastic transformations one pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair in the context of resource theories we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another also when assisted by additional standard resources such as useful work or maximally entangled states these characterizations have a geometric formulation as the ratios or differences respectively between the lorenz curves associated with the input and output resources making them efficient to compute we also find several interesting bounds on the reversibility of a given transformation in terms of the properties of the forward transformation the main technical tool used to establish these results is the linear programming duality which is used to show that any instance of relative submajorization can be dilated to an instance of strict relative majorization we introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics bipartite entanglement and quantum coherence relative majorization is an ordering on pairs of vectors induced by stochastic transformations one pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair in the context of resource theories we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another also when assisted by additional standard resources such as useful work or maximally entangled states these characterizations have a geometric formulation as the ratios or differences respectively

modeling conditional dependence among multiple diagnostic tests when multiple imperfect dichotomous diagnostic tests are applied to an individual it is possible that some or all of their results remain dependent even after conditioning on the true disease status the estimates could be biased if this conditional dependence is ignored when using the test results to infer about the prevalence of a disease or the accuracies of the diagnostic tests however statistical methods correcting for this bias by modelling higher order conditional dependence terms between multiple diagnostic tests are not well addressed in the literature this paper extends a bayesian fixed effects model for 2 diagnostic tests with pairwise correlation to cases with 3 or more diagnostic tests with higher order correlations simulation results show that the proposed fixed effects model works well both in the case when the tests are highly correlated and in the case when the tests are truly conditionally independent provided adequate external information is available in the form of fixed constraints or prior distributions a data set on the diagnosis of childhood pulmonary tuberculosis is used to illustrate the proposed model

majorization entropy and paired comparisons on obtient des resultats pour des matrices de probabilite maximales et minimales relativement a la relation d ordre de majoration on montre que les modeles de bradley terry et de thurstone mosteller sont des modeles a entropie maximale on obtient de nouveaux modeles a entropie maximale

majorization and divergence abstract a majorization ordering of the distance or divergence of a positive function from a fixed positive function q on a measure space is studied if a function p1 is smaller than a function p2 relative to the ordering then p1 is closer to q than p2 applications are given to measures of divergence markov chains and qualitative conditions for probability densities closest to q subject to first and second moment constraints in addition a generalization of the path result of r f muirhead 1903 proc edinburgh math soc 21 144 157 and g h hardy j e littlewood and g polya inequalities 2nd ed cambridge univ press london 1952 is given

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

the biplot as a diagnostic tool of local dependence in latent class models a medical application latent class models lcms can be used to assess diagnostic test performance when no reference test a gold standard is available considering two latent classes representing disease or non disease status one of the basic assumptions in such models is that of local or conditional independence all indicator variables tests are statistically independent within each latent class however in practice this assumption is often violated hence the two lcm fits the data poorly in this paper we propose the use of biplot methods to identify the conditional dependence between pairs of manifest variables within each latent class additionally we propose incorporating such dependence in the corresponding latent class using the log linear formulation of the model

iterative automated record linkage using mixture models the goal of record linkage is to link quickly and accurately records that correspond to the same person or entity whereas certain patterns of agreements and disagreements on variables are more likely among records pertaining to a single person than among records for different people the observed patterns for pairs of records can be viewed as arising from a mixture of matches and nonmatches mixture model estimates can be used to partition record pairs into two or more groups that can be labeled as probable matches links and probable nonmatches nonlinks a method is proposed and illustrated that uses marginal information in the database to select mixture models identifies sets of records for clerks to review based on the models and marginal information incorporates clerically reviewed data as they become available into estimates of model parameters and classifies pairs as links nonlinks or in need of further clerical review the procedure is illustrated with five datasets from the u s bureau

estimation of operating characteristics for dependent diagnostic tests based on latent markov models we describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test log linear models are adopted for the classification distributions conditional on the latent state where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests a marginal likelihood is constructed by marginalizing over a latent two state markov process specific latent processes we consider include a first order markov model a second order markov model and a time nonhomogeneous markov model although the method is described in full generality adaptations to handle missing data are described model diagnostics are considered based on the bootstrap distribution of conditional residuals the methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement

strong collapsibility of association measures in linear models a measure of association in linear models is strongly collapsible over a discrete background variable if it remains unchanged no matter how the background variable is partially pooled and if it also coincides with the corresponding marginal measure of association strong collapsibility implies that the measure of association can be studied no matter how the background variable is categorized and no matter whether or not it is recorded in this paper necessary and sufficient conditions are given for strong collapsibility of the measure of association in linear models

probability inequalities for multivariate distributions with dependence structures abstract let x 1 xn be a sequence of random variables with a given positive or negative dependence structure in this article we exploit the assumed dependence structure to construct a sequence of bounds for the p xi e ci i 1 n where ci are infinite intervals of the same type these bounds are superior to the well known product bounds that are based solely on the marginal probabilities moreover the new bounds can serve as respectable approximations for the p xi e ci i 1 n

analytic solutions to a class of nonlinear infinite delay differential equations abstract the infinite delay differential equations iddes are studied and the analytic solution of a class of nonlinear iddes is presented based on the characteristics of the reproducing kernel space w 2 0 besides the exact solution is represented in the form of series it is proved that the n term approximation u n x converges to the exact solution u x of the iddes moreover the approximate error of u n x is monotone decreasing the results of experiments showed that the proposed method in this paper is computationally efficient

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

local analytic solutions of a functional differential equation αz βx z x az bx z in this paper we are concerned with the existence of analytic solution of a functional differential equation email protected z x az bx z where a b a b are four complex numbers we first discuss the existence of analytic solutions for some special cases of the above equation then by reducing the equation with the schroder transformation to the another functional equation with proportional delay an existence theorem is established for analytic solutions of the original equation for the constant l given in the schroder transformation we discuss the case 0 l 1 and l on the unit circle s 1 i e l 1 we study l is at resonance i e at a root of the unity and l is near resonance under the brjuno condition

chaotic synchronization by the intermittent feedback method this paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient a sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a lyapunov function and differential inequalities numerical simulations for the chaotic chua oscillator are presented to illustrate the theoretical results

a model for evaluating sensitivity and specificity for correlated diagnostic tests in efficacy studies with an imperfect reference test abstract the purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests usually the diagnostic tests are correlated conditional on disease status and the reference test is subject to error in the chlamydia trachomatis study five screening tests for detecting chlamydia in endocervical specimens were compared the five tests are correlated and the reference test the cell culture test has less than 100 sensitivity the conventional method ignores both the correlations between the tests and the misclassification of the reference test and thus cannot provide a valid analysis we propose a model to evaluate and compare the sensitivities and specificities of correlated diagnostic tests when there is either an imperfect reference test or even no reference test the model also can estimate the effects of covariates it is a generalized linear mixed model with two unobserved variables one continuous and one dichotomous we use a hybrid

collapsibility of logistic regression coefficients summary in this paper we discuss collapsibility of logistic regression coefficients over a background variable and present necessary and sufficient conditions for collapsibility

bayesian approaches to modeling the conditional dependence between multiple diagnostic tests many analyses of results from multiple diagnostic tests assume the tests are statistically independent conditional on the true disease status of the subject this assumption may be violated in practice especially in situations where none of the tests is a perfectly accurate gold standard classical inference for models accounting for the conditional dependence between tests requires that results from at least four different tests be used in order to obtain an identifiable solution but it is not always feasible to have results from this many tests we use a bayesian approach to draw inferences about the disease prevalence and test properties while adjusting for the possibility of conditional dependence between tests particularly when we have only two tests we propose both fixed and random effects models since with fewer than four tests the problem is nonidentifiable the posterior distributions are strongly dependent on the prior information about the test properties and the disease prevalence even with large sample sizes if the degree of correlation between the tests is known a priori with high precision then our methods adjust for the dependence between the tests otherwise our methods provide adjusted inferences that incorporate all of the uncertainty inherent in the problem typically resulting in wider interval estimates we illustrate our methods using data from a study on the prevalence of strongyloides infection among cambodian refugees to canada

ergodicity of p majorizing nonlinear markov operators on the finite dimensional space abstract a nonlinear markov chain is a discrete time stochastic process whose transitions may depend on both the current state and the current distribution of the process the nonlinear markov chain over a finite state space can be identified by a continuous mapping the so called nonlinear markov operator defined on a set of all probability distributions which is a simplex of the finite state space and by a family of transition matrices depending on occupation probability distributions of states in this paper we introduce a notion of dobrushin s ergodicity coefficients for stochastic hypermatrices and provide a criterion for the contraction nonlinear markov operator by means of dobrushin s ergodicity coefficients we also introduce a notion of p majorizing nonlinear markov operators associated with stochastic hypermatrices and provide a criterion for strong ergodicity of such kind of operator we show that the p majorizing nonlinear markov operators associated with scrambling sarymsakov and wolfowitz stochastic hypermatrices are strongly ergodic these classes of p majorizing nonlinear markov operators assure an existence of a residual set of strongly ergodic nonlinear markov operators which are not contractions some supporting examples are also provided

collapsibility of relative risk in contingency tables with a response variable we consider the collapsibility of relative risks in contingency tables with a polytomous response variable simple collapsibility of relative risks means that they are consistent over all levels of a collapsed variable and also coincide with the corresponding marginal relative risk strong collapsibility of relative risks means that they retain simple collapsibility no matter how the variable is partially collapsed we present necessary and sufficient conditions for simple and strong collapsibilities of relative risks

using latent class models to characterize and assess relative error in discrete measurements whenever a definitive standard is not available to mark accuracy in a classification process discrete measurement error can be discussed only in relative terms if strong assumptions concerning the underlying discrete processes can be made latent class models allow one to characterize patterns of agreement disagreement among raters while simultaneously producing consensus estimates of prevalence a hypothetical definitive standard serves as the latent factor the discrete data are treated as incomplete and log linear models can be used to parameterize latent class models and extensions of latent class models data from the radiographic diagnosis of dental caries by five dentists were explored to estimate prevalence assess relative error and examine the validity of several traditional assumptions concerning diagnostic reliability latent class analysis allowed a more detailed description of diagnostic error than provided by commonly used summary statistics

a new perspective on priors for generalized linear models abstract this article deals with specifications of informative prior distributions for generalized linear models our emphasis is on specifying distributions for selected points on the regression surface the prior distribution on regression coefficients is induced from this specification we believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model dependent regression coefficients previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression we expand on the idea of conditional means priors and extend these to arbitrary generalized linear models we also consider data augmentation priors where the prior is of the same form as the likelihood we show that data augmentation priors are special cases of conditional means priors with current monte carlo methodology such as importance sampling and gibbs sampling our priors result in

when do latent class models overstate accuracy for diagnostic and other classifiers in the absence of a gold standard summary latent class models are increasingly used to assess the accuracy of medical diagnostic tests and other classifications when no gold standard is available and the true state is unknown when the latent class is treated as the true class the latent class models provide measures of components of accuracy including specificity and sensitivity and their complements type i and type ii error rates the error rates according to the latent class model differ from the true error rates however and empirical comparisons with a gold standard suggest the true error rates often are larger we investigate conditions under which the true type i and type ii error rates are larger than those provided by the latent class models results from uebersax 1988 psychological bulletin 104 405 416 are extended to accommodate random effects and covariates affecting the responses the results are important for interpreting the results of latent class analyses an error decomposition is presented that incorporates an error component from invalidity of the latent class model

majorization randomness and dependence for multivariate distributions the preorder relation of hardy littlewood and polya 1929 day 1973 and chong 1974 1976 is applied to multivariate probability densities this preorder which is called majorization here can be interpreted as an ordering of randomness when used to compare multivariate densities with the same marginal densities it can be interpreted as an ordering of dependence or conditional dependence results in hickey 1983 1984 and joe 1985 are generalized a relative entropy function is proposed as a measure of dependence or conditional dependence for multivariate densities with the same marginals

the functional differential equation x t x x t abstract a classification of the solutions of the functional differential equation x t x x t is given and it is proved that every solution either vanishes identically or is strictly monotonie for monotonically increasing solutions existence and uniqueness of the solution x are proved with the condition x t0 x0 where t0 x0 is any given pair of reals in some specified subset of r 2 every monotonically increasing solution is thus obtained it is analytic and depends analytically on t0 and x0 only for t0 x0 1 is the question of analyticity still open

model determination for categorical data with factor level merging we deal with contingency table data that are used to examine the relationships between a set of categorical variables or factors we assume that such relationships can be adequately described by the conditional independence structure that is imposed by an undirected graphical model if the contingency table is large a desirable simplified interpretation can be achieved by combining some categories or levels of the factors we introduce conditions under which such an operation does not alter the markov properties of the graph implementation of these conditions leads to bayesian model uncertainty procedures based on reversible jump markov chain monte carlo methods the methodology is illustrated on a 2 x 3 x 4 and up to a 4 x 5 x 5 x 2 x 2 contingency table

on the behaviour of wald statistics for the disjunction of two regular hypotheses occasionally hypotheses arise which although not themselves regular have the logical structure of the disjunction of two or in general several regular hypotheses an example of such a hypothesis is that of collapsibility in a three way contingency table as defined by whittemore when such a hypothesis is to be tested a wald test appears superficially to offer a convenient solution however closer inspection reveals that the irregularity intrinsic to such problems precludes the regularity conditions required for the valid construction of a wald test statistic the purpose of this paper is to describe explicitly the nature of the irregularity and its effect on the asymptotic behaviour of the wald test statistic

simultaneous confidence intervals and sample size determination for multinomial proportions abstract simultaneous confidence interval procedures for multinomial proportions are used in many areas of science in this article two new simultaneous confidence interval procedures are introduced numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature from the results presented in this article it is evident that the new procedures are more accurate than the established ones where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves in the sample size determination problem the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications because both procedures performed equally well the procedure that requires the least amount of computing time is recommended

the role of exchangeability in inference abstract this paper is concerned with basic problems of statistical inference the thesis is in three parts 1 that inference is a procedure whereby one passes from a population or sample to a new individual 2 that this connection can be established using de finetti s idea of exchangeability or fisher s concept of a subpopulation and 3 in making the connection use must be made of the appropriate probability these three principles are used in a variety of situations and the topics discussed include analysis of variance and covariance contingency tables and calibration some comments on randomization are also included author

analytic solutions of a second order iterative functional differential equation abstract this paper is concerned with a second order iterative functional differential equation x z x m z 2 its analytic solutions are discussed by locally reducing the equation to another functional differential equation with proportional delays 2 y z y z y z y z y z 3 y m z 2 and by constructing a convergent power series solutions for the latter equation

smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients using the fixed point theorems of banach and schauder in this paper we discuss the existence uniqueness and stability of smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients

collapsibility and response variables in contingency tables summary various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent necessary and sufficient conditions for collapsibility are found in terms of the generating class it is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables some key word8 collapsibility contingency table graphical model interaction graph log linear model response variable s sufficiency shown to be closely related some models have the property that relations between a set of the classifying factors may be studied by examination of the table of marginal totals formed by summing over the remaining factors such models are said to be collapsible onto the given set of factors collapsibility has important consequences for hypothesis testing and model selection and can be useful in data reduction we consider various definitions of collapsibility and show their equivalence furthermore necessary and sufficient conditions for collapsi bility are found in terms of the generating class many tables analysed in practice involve response variables simple examples one of which is given in 3 suffice to show the importance of distinguishing between response and explanatory variables first that inappropriate models may be avoided and second that natural and relevant models that are not log linear may be considered this paper characterizes appropriate and inappropriate log linear models for tables with response variables and some alternative approaches for the analysis of such tables are briefly considered we consider a multidimensional contingency table n based on a set of classifying factors f for a given subset a of f we are interested in the table of marginal totals na that is to say the table of cell counts summed over the remaining factors ac that is the complement of a in f we identify a hierarchical log linear model l that is the set of probabilities p e l with its generating class whose elements generators are given in square brackets thus for example the model ab bcd for a 4 way table corresponds

maximum likelihood estimation and model selection in contingency tables with missing data abstract in many studies the values of one or more variables are missing for subsets of the original sample this article focuses on the problem of obtaining maximum likelihood estimates mle for the parameters of log linear models under this type of incomplete data the appropriate systems of equations are presented and the expectation maximization em algorithm dempster laird and rubin 1977 is suggested as one of the possible methods for solving them the algorithm has certain advantages but other alternatives may be computationally more effective tests of fit for log linear models in the presence of incomplete data are considered the data from the protective services project for older persons blenkner bloom and nielsen 1971 blenkner bloom and weber 1974 are used to illustrate the procedures discussed in the article

estimating incidence and diagnostic error rates for bivariate progressive processes estimating the times until incidences of bivariate progressive processes that are categorical is a common problem in ophthalmology audiology pulmonary medicine and other fields of medical research we consider study designs in which diagnoses of subject s bivariate status are performed repeatedly across time and when diagnosis is subject to error in such situations error confounds the interpretation of the time until an event a composite model is proposed for parameterizing both the incidence and error distributions which allows for correlation between sites with respect to both incidence and diagnostic error an em algorithm is described for this model which allows categorical covariates for both incidence and error the methodology is applied to two examples the first represents a situation in which bivariate incidence and error can reasonably be assumed symmetric prospective data concerning the development of ocular lens opacities in a large pharmaceutical clinical trial the second example represents a situation in which bivariate incidence and error may not be symmetric clinical evaluations of sexual maturation status with respect to two different anatomical indices in the cooperative study of sickle cell disease the methodology described in this paper is used in each case to estimate incidence characterize error rates and assess bivariate correlations

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

analytic solutions of a second order nonautonomous iterative functional differential equation abstract in this paper a second order nonautonomous iterative functional differential equation is considered by reducing the equation with the schroder transformation to another functional differential equation without iteration of the unknown function we give existence of its local analytic solutions we first discuss the case that the constant given in the schroder transformation does not lie on the unit circle in c and the case that the constant lies on the circle but fulfills the diophantine condition then we further study the case that the constant is a unit root in c but the diophantine condition is offended finally we investigate analytic solutions of the form of power functions

analytic solutions of an iterative functional differential equation abstract this paper is concerned with an iterative functional differential equation x z x m z where x m z x x x z is the m th iterate of the function x z by constructing a convergent power series solution y z of a companion equation of the form y z y z y m z analytic solutions of the form y y 1 z for the original differential equation are obtained

a cautionary note on the robustness of latent class models for estimating diagnostic error without a gold standard modeling diagnostic error without a gold standard has been an active area of biostatistical research in a majority of the approaches model based estimates of sensitivity specificity and prevalence are derived from a latent class model in which the latent variable represents an individual s true unobserved disease status for simplicity initial approaches assumed that the diagnostic test results on the same subject were independent given the true disease status i e the conditional independence assumption more recently various authors have proposed approaches for modeling the dependence structure between test results given true disease status this note discusses a potential problem with these approaches namely we show that when the conditional dependence between tests is misspecified estimators of sensitivity specificity and prevalence can be biased importantly we demonstrate that with small numbers of tests likelihood comparisons and other model diagnostics may not be able to distinguish between models with different dependence structures we present asymptotic results that show the generality of the problem further data analysis and simulations demonstrate the practical implications of model misspecification finally we present some guidelines about the use of these models for practitioners

a representation for multinomial cumulative distribution functions a re expression of the usual representation of the multinomial distribution as the conditional distribution of independent poisson random variables given fixed sum provides a convenient new way to compute multinomial cumulative distribution functions

ergodicity of nonlinear markov operators on the finite dimensional space abstract a nonlinear markov chain is a discrete time stochastic process whose transition matrices may depend not only on the current state of the process but also on the current distribution of the process in this paper we study strong and uniform ergodicity of nonlinear markov operators defined by stochastic hypermatrices higher order matrix we introduce dobrushin s ergodicity coefficient for a stochastic hypermatrix which enables to study ergodicity of nonlinear markov operators by introducing a notion of scrambling stochastic hypermatrix we study the strong ergodicity of scrambling nonlinear markov operators

intermittent dynamical control abstract this paper describes the method of synchronizing slave to the master trajectory using intermittent coupling the information about master trajectory is limited only to the coordinates and timings of intersection points of that trajectory with the arbitrarily chosen poincare section making the coupling sporadic the application of the method is first exemplified on the two identically coupled rossler and lorenz oscillators and then is extended to the case when the two rossler oscillators exhibit initially different dynamical properties different values of the control parameters

on neutral functional differential equations with proportional delays abstract in this paper we develop a comprehensive theory on the well posedness of the initial value problem for the neutral functional differential equation y t ay t i 1 b i y q i t i 1 c i y p i t t 0 y 0 y 0 and the asymptotic behaviour of its solutions we prove that the existence and uniqueness of solutions depend mainly on the coefficientsci i 1 2 and on the smoothness of functions in the solution space as far as the asymptotic behaviour of analytic solutions is concerned thecihave little effect we prove that if re a 0 then the solutiony t either grows exponentially or is polynomial the most interesting result is that if re a 0 anda 0 then the asymptotic behaviour of the solution depends mainly on the characteristic equation a i 1 b i q i 0 these results can be generalized to systems of equations finally we present some examples to illustrate the change of asymptotic behaviour in response to the variation of some parameters the main idea used in this paper is to express the solution in either dirichlet or dirichlet taylor series form

testing collapsibility in contingency tables on etudie en particulier le cas important des tables 2 2 k d ou il decoule les extensions aux tables plus grandes

quick simultaneous confidence intervals for multinomial proportions abstract opinion polls often give an indication of sampling error based on the standard conservative confidence intervals for a single binomial proportion we give a lower bound for the simultaneous coverage probability when such intervals are applied to all of the proportions in a poll this bound is equal to 1 2 for small values of the same result is shown to apply to the standard confidence intervals for changes in proportions between surveys

criteria for confounders in epidemiological studies the paper addresses a formal definition of a confounder based on the qualitative definition that is commonly used in standard epidemiology text books to derive the criterion for a factor to be a confounder given by miettinen and cook and to clarify inconsistency between various criteria for a confounder we introduce the concepts of an irrelevant factor an occasional confounder and a uniformly irrelevant factor we discuss criteria for checking these and show that miettinen and cook s criterion can also be applied to occasional confounders moreover we consider situations with multiple potential confounders and we obtain two necessary conditions that are satisfied by each confounder set none of the definitions and results presented in this paper require the ignorability and sufficient control confounding assumptions which are commonly employed in observational and epidemiological studies

observer based periodically intermittent control for linear systems via piecewise lyapunov function method abstract this paper focuses on the observer based periodically intermittent control issue for linear systems by utilizing piecewise lyapunov function method based on the concept of intermittent control the description of an observer based periodically intermittent controller is initially proposed then stability of the corresponding periodically intermittent control system is analyzed by resorting to piecewise lyapunov function method here the so called piecewise lyapunov function means that lyapunov function on control time intervals differs from the one on free time intervals besides the existence of an observer based periodically intermittent controller is converted into the feasibility of linear matrix inequalities it is worth pointing out that in comparison with an observer based continuous controller the designed observer based periodically intermittent controller can still retain satisfactory performance with shorter control task execution time finally an illustrative simulation example is given to show the validity and superiority of the result

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed results