bias correction of two state latent markov process parameter estimates under misclassification a discretely observed two state process may misclassify the state of an unobservable continuous time two state markov process we examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities since maximum likelihood estimators are not available in closed form we provide two alternatives for bias adjusted estimation in the case of large samples the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities for finite samples we provide an approximation based on partial derivatives estimators that are bias adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small simulation studies reveal the effect of misclassification on estimation repeated diagnostic testing data illustrate the approaches

a general goodness of fit test for markov and hidden markov models markov models are a convenient and useful method of estimating transition rates between levels of a categorical response variable such as a disease stage which changes over time in medical applications the response variable is typically observed at irregular intervals a pearson type goodness of fit test for such models was proposed by aguirre hernandez and farewell statist med 2002 21 1899 1911 but this test is not applicable in the common situation where the process includes an absorbing state such as death for which the time of entry is known precisely nor when the data include censored state observations this paper presents a modification to the pearson type test to allow for these cases an extension of the method to allow for the class of hidden markov models where the response variable is subject to misclassification error is given the method is applied to data on cardiac allograft vasculopathy in post heart transplant patients

on some relations between chaney s generalizedsecond order directional derivative and that of ben tal andzowe for a locally lipschitz real valued function f on bbb r n and x u in bbb r n our main result implies that if x is in clarke s subdifferential partial f x coming from the direction u in chaney s sense such that x u equals the directional derivative f x u then chaney s second order directional derivative f x x u when it exists coincides with the value at x of the conjugate function of the ben tal zowe second order directional derivative provided that this value is finite

nonparametric estimation of a markov illness death process from interval censored observations with application to diabetes survival data summary the nonparametric estimation of the cumulative transition intensity functions in a threestate time nonhomogeneous markov process with irreversible transitions an illness death model is considered when times of the intermediate transition e g onset of a disease are interval censored the times of death are assumed to be known exactly or to be rightcensored in addition the observed process may be left truncated data of this type arise when the process is sampled periodically for example when the patients are monitored through periodic examinations the observations on times of change in their disease status will be interval censored under the sampling scheme considered here the nelson aalen estimator aalen 1978 for a cumulative transition intensity is not applicable in the proposed method the maximum likelihood estimators of some of the transition intensities are derived from the estimators of the corresponding subdistribution functions the maximum likelihood estimators are shown to have a self consistency property the self consistency algorithm is developed for the computation of the estimators this approach generalises the results from turnbull 1976 and frydman 1992 the methods are illustrated with diabetes survival data

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

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

marginal methods for correlated binary data with misclassified responses misclassification is a longstanding concern in medical research although there has been much research concerning error prone covariates relatively little work has been directed to problems with response variables subject to error in this paper we focus on misclassification in clustered or longitudinal outcomes we propose marginal analysis methods to handle binary responses which are subject to misclassification the proposed methods have several appealing features including simultaneous inference for both marginal mean and association parameters and they can handle misclassified responses for a number of practical scenarios such as the case with a validation subsample or replicates furthermore the proposed methods are robust to model misspecification in a sense that no full distributional assumptions are required numerical studies demonstrate satisfactory performance of the proposed methods under a variety of settings copyright 2011 oxford university press

global error bounds with fractional exponents using the partial order induced by a proper weakly lower semicontinuous function on a reflexive banach space x we give a sufficient condition for f to have error bounds with fractional exponents application is given to identify the set of such exponents for quadratic functions

on first and second order conditions linebreak for error bounds we establish first order and second order sufficient conditions ensuring that a proper lower semicontinuous function f on a banach space x has an error bound we also consider similar problems with constraint namely that f is replaced by its restriction to a subset of x these results are employed to identify exactly when a quadratic function on x has an error bound

a nonparametric test for panel count data summary panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points in this situation observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points we propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available the asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance the method is illustrated using data from a medical follow up study

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

estimation of parasitic infection dynamics when detectability is imperfect the simultaneous estimation of infection rate cure rate and detectability of parasitic infections is considered a new method for this estimation based on a simple statistical model assuming constant transition rates between parasite states is proposed repeated observations on the infection status of the same individuals is required for this method a maximum likelihood approach is used for parameter estimation and the calculation of standard errors of the estimates the method is illustrated by a longitudinal study of the presence of giardia lamblia infection in kenyan children

the gamma frailty poisson model for the nonparametric estimation of panel count data summary in this article we study nonparametric estimation of the mean function of a counting process with panel observations we introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo likelihood estimate with the frailty variable three simulated examples are given to show that this estimation procedure while preserving the robustness and simplicity of the computation improves the efficiency of the nonparametric maximum pseudo likelihood estimate studied in wellner and zhang 2000 annals of statistics28 779 814 a real example from a bladder tumor study is used to illustrate the method

real double coset spaces and their invariants abstract let g be a real form of a complex reductive group suppose that we are given involutions and of g let h g denote the fixed group of and let k g denote the fixed group of we are interested in calculating the double coset space h g k we use moment map and invariant theoretic techniques to calculate the double cosets especially the ones that are closed one salient point of our results is a stratification of a quotient of a compact torus over which the closed double cosets fiber as a collection of trivial bundles

nonparametric k sample tests with panel count data we study the nonparametric k sample test problem with panel count data the asymptotic normality of a smooth functional of the nonparametric maximum pseudolikelihood estimator wellner zhang 2000 is established under some mild conditions we construct a class of easy to implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality we conduct various simulations to validate and compare the tests the simulations show that the tests perform quite well and generally have good power to detect differences among the mean functions the method is illustrated with a real life example

convexity properties of gradient maps abstract we consider the action of a real reductive group g on a kahler manifold z which is the restriction of a holomorphic action of a complex reductive group h we assume that the action of a maximal compact subgroup u of h is hamiltonian and that g is compatible with a cartan decomposition of h we have an associated gradient map p z p where g k p is the cartan decomposition of g for a g stable subset y of z we consider convexity properties of the intersection of p y with a closed weyl chamber in a maximal abelian subspace a of p our main result is a convexity theorem for real semi algebraic subsets y of z p v where v is a unitary representation of u

semi markov models with phase type sojourn distributions continuous time multistate models are widely used for categorical response data particularly in the modeling of chronic diseases however inference is difficult when the process is only observed at discrete time points with no information about the times or types of events between observation times unless a markov assumption is made this assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state such a formulation results in a semi markov model we show that the computational problems associated with fitting semi markov models to panel observed data can be alleviated by considering a class of semi markov models with phase type sojourn distributions this allows methods for hidden markov models to be applied in addition extensions to models where observed states are subject to classification error are given the methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post lung transplantation patients

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

on minimizing and critical sequences in nonsmooth optimization let f be a bounded below lower semicontinuous function from a banach space into r cup infty we study the relationships between minimizing and critical sequences of f where the criticality condition is given in terms of some subdifferential partial here the objective function f is not supposed to be convex or smooth our work extends that of auslender and crouzeix and that of chou ng and pang

on generalized second order derivatives and taylor expansions in nonsmooth optimization a representation of cominetti and correa s generalized second order directional derivative siam j control optim 28 1990 pp 789 809 is given and then applied to obtain a taylor theorem type result a conjecture in siam j control optim 28 1990 pp 789 809 concerning functions of the form max 1 leq i leq n g i x is proved under a strengthened assumption but not true otherwise

a generalized second order derivative in nonsmooth optimization in this work a new notion of generalized second order directional derivative and generalized hessian for nonsmooth real valued functions is studied the general properties of these mathematical objects are investigated together with some calculus rules that may facilitate their practical computation two applications of these derivatives in optimization theory are considered first to obtaining necessary and sufficient second order optimality conditions for problems with or without constraints and second to extending the newton method for the minimization of a mathcal c 1 1 function

cartan decomposition of the moment map we investigate a class of actions of real lie groups on complex spaces using moment map techniques we establish the existence of a quotient and a version of luna s slice theorem as well as a version of the hilbert mumford criterion a global slice theorem is proved for proper actions we give new proofs of results of mostow on decompositions of groups and homogeneous spaces

semistable points with respect to real forms we consider actions of real lie subgroups g of complex reductive lie groups on kahlerian spaces our main result is the openness of the set of semistable points with respect to a momentum map and the action of g

nonparametric estimation of stage occupation probabilities in a multistage model with current status data multistage models are used to describe individuals or experimental units moving through a succession of stages corresponding to distinct states e g healthy diseased diseased with complications dead the resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied traditional survival analysis is the simplest example of a multistage model where individuals begin in an initial stage say alive and move irreversibly to a second stage death in this article we consider general multistage models with a directed tree structure progressive models in which individuals traverse through stages in a possibly non markovian manner we construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards empirical calculations of these quantities are not possible due to the lack of complete data we consider current status information which represents a more severe form of censoring than the commonly used right censoring asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators finite sample behavior of our estimators is studied by simulation in which we show that our estimators based on these limited data compare well with those based on complete data we also apply our method to a real life data set arising from a cardiovascular diseases study in taiwan

correcting for misclassification for a monotone disease process with an application in dental research motivated by a longitudinal oral health study we evaluate the performance of binary markov models in which the response variable is subject to an unconstrained misclassification process and follows a monotone or progressive behavior theoretical and empirical arguments show that the simple version of the model can be used to estimate the prevalence incidences and misclassification parameters without the need of external information and that the incidence estimators associated with the model outperformed approaches previously proposed in the literature we propose an extension of the simple version of the binary markov model to describe the relationship between the covariates and the prevalence and incidence allowing for different classifiers we implemented a bayesian version of the extended model and show that under the settings of our motivating example the parameters can be estimated without any external information finally the analyses of the motivating problem are presented

on distinguished orbits of reductive representations abstract let g be a real reductive lie group and let g gl v be a real reductive representation of g with restricted moment map m g v 0 g in this work we introduce the notion of nice space of a real reductive representation to study the problem of how to determine if a g orbit is distinguished i e it contains a critical point of the norm squared of m g we give an elementary proof of the well known convexity theorem of atiyah guillemin sternberg in our particular case and we use it to give an easy to check sufficient condition for a g orbit of an element in a nice space to be distinguished in the case where g is algebraic and is a rational representation the above condition is also necessary making heavy use of recent results of michael jablonski obtaining a generalization of nikolayevsky s nice basis criterion we also provide useful characterizations of nice spaces in terms of the weights of finally some applications to ternary forms are presented

comparison of variance estimation approaches in a two state markov model for longitudinal data with misclassification we examine the behaviour of the variance covariance parameter estimates in an alternating binary markov model with misclassification transition probabilities specify the state transitions for a process that is not directly observable the state of an observable process which may not correctly classify the state of the unobservable process is obtained at discrete time points misclassification probabilities capture the two types of classification errors variance components of the estimated transition parameters are calculated with three estimation procedures observed information jackknife and bootstrap techniques simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation the three approaches generally provide similar variance estimates for large samples and moderate misclassification in these situations the resampling methods are reasonable alternatives when programming partial derivatives is not appealing with smaller chains or higher misclassification probabilities the bootstrap method appears to be the best choice

modeling repeated measures with monotonic ordinal responses and misclassification with applications to studying maturation abstract many longitudinal studies of children are concerned with the modeling of monotonic responses such as growth and sexual maturation the national heart lung and blood institute growth and health study nghs is a longitudinal study designed to examine the effect of growth and maturation on the development of obesity and related cardiovascular risk factors among black and white adolescent girls sexual maturation is measured with an ordinal outcome and is known to be measured with sizable diagnostic error of interest is examining the effects of race and age on the sexual maturation process here we propose a class of models for analyzing repeated monotonic ordinal responses with diagnostic misclassification in which we separately model the underlying monotonic response and misclassification processes we develop an em algorithm for maximum likelihood estimation that incorporates covariates and randomly missing data we use the method to analyze the nghs sexual maturation data

second order sufficient conditions for error bounds in banach spaces recently huang and ng presented second order sufficient conditions for error bounds of continuous and ga teaux differentiable functions in banach spaces wu and ye dropped the assumption of huang and ng on ga teaux differentiability but required the space to be a hilbert space we carry on this research in two directions first we extend wu and ye s result to some non hilbert spaces second same as huang and ng we work on banach spaces but provide different second order sufficient conditions that may allow the function to be non ga teaux differentiable

error bounds for lower semicontinuous functions in normed spaces without the convexity or analyticity assumption we study error bounds for an inequality system defined by a general lower semicontinuous function and establish sufficient necessary conditions on the existence of error bounds in infinite dimensional normed spaces some characterizations for a convex inequality system to possess an error bound in a reflexive banach space are also given as applications in dealing with the hoffman error bound result in normed spaces we give a computable lipschitz bound constant which is better than previous lipschitz bound constants in some examples we also consider error bounds for quadratic functions on rn

a pearson type goodness of fit test for stationary and time continuous markov regression models markov regression models describe the way in which a categorical response variable changes over time for subjects with different explanatory variables frequently it is difficult to measure the response variable on equally spaced discrete time intervals here we propose a pearson type goodness of fit test for stationary markov regression models fitted to panel data a parametric bootstrap algorithm is used to study the distribution of the test statistic the proposed technique is applied to examine the fit of a markov regression model used to identify markers for disease progression in psoriatic arthritis

modeling of multivariate monotone disease processes in the presence of misclassification motivated by a longitudinal oral health study the signal tandmobiel study we propose a multivariate binary inhomogeneous markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior the multivariate baseline distributions and markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions distinct misclassification models are discussed in all cases the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account a full bayesian implementation of the model is described and its performance is evaluated using simulated data we provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters finally the analyses of the motivating study are presented a

kahlerian potentials and convexity properties of the moment map since kostant proved his convexity theorems for torus actions on ag varieties ko there have been numerous contributions to this subject in the more general symplectic and k ahlerian setting for example let k be a compact lie group acting in a hamiltonian fashion on a connected compact symplectic manifold x then the intersection x of the image of the moment map x liek with a positive weyl chamber t is convex thus x k x where x is a natural convex section this was proved by atiyah and guillemin sternberg a g s in the abelian case i e where k t is a compact torus by mumford m for x projective algebraic with an integral k ahlerian structure and k not necessarily abelian and in its nal form in the compact symplectic case by kirwan k a precise description of x x t in the compact k ahlerian framework can be given in terms of the image of the components of the set of t xed points in x in the projective case where the k ahlerian structure comes from a projective embedding there are explicit connections to the representations theory of g kc which are due to brion and to mumford ness b n the purpose of the present paper is to prove convexity properties of in the setting of non compact k ahlerian spaces note that by removing an appropriate k invariant subset from x one can easily construct non convex images from convex ones on the other hand hilgert neeb plank proved h n p that convexity holds for a proper moment map x liek another convexity result has been obtained by sjamaar for x a ne and the restriction of the moment map of a representation s2 here the representation theoretical approach of brion is used now let x be an irreducible complex space endowed with a holomorphic action of a complex reductive group g assume that a maximal

the analysis of asthma control under a markov assumption with use of covariates in studies of disease states and their relation to evolution data on the state are usually obtained at in frequent time points during follow up moreover in many applications there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution we developed a continuous time markov model with use of time dependent covariates and a markov model with piecewise constant intensities to model asthma evolution methods to estimate the effect of covariates on transition intensities to test the assumption of time homogeneity and to assess goodness of fit are proposed we apply these methods to asthma control we consider a three state model and we discuss in detail the analysis of asthma control evolution copyright 2003 john wiley sons ltd

bias and efficiency loss due to misclassified responses in binary regression summary methods that ignore errors in binary responses yield biased estimators of the associations of covariates with response this paper derives general expressions for the magnitude of the bias due to errors in the response and shows that unless both the sensitivity and specificity are very high ignoring errors in the responses will yield highly biased covariate effect estimators when the true error free response follows a generalised linear model and misclassification probabilities are known and independent of covariate values responses observed with error also follow such a model with a modified link function we describe a simple method to obtain consistent estimators of covariate effects and associated errors in this case and derive an expression for the asymptotic relative efficiency of covariate effect estimators from the correct likelihood for the responses with errors with respect to estimates based on the true error free responses this expression shows that errors in the response can lead to substantial losses of information about covariate effects data from a study on infection with human papilloma virus among women and simulation studies motivate this work and illustrate the findings

merit functions in vector optimization we study the weak domination property and weakly efficient solutions in vector optimization problems in particular scalarization of these problems is obtained by virtue of some suitable merit functions some natural conditions to ensure the existence of error bounds for merit functions are also given

perturbation of error bounds our aim in the current article is to extend the developments in kruger et al siam j optim 20 6 3280 3296 2010 doi 10 1137 100782206 and more precisely to characterize in the banach space setting the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations we propose new concepts of arbitrary convex and linear perturbations of the given function defining the system under consideration which turn out to be a useful tool in our analysis the characterizations of error bounds for families of perturbations can be interpreted as estimates of the radius of error bounds the definitions and characterizations are illustrated by examples