cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

regression analysis for recurrent events data under dependent censoring summary recurrent events data are commonly seen in longitudinal follow up studies dependent censoring often occurs due to death or exclusion from the study related to the disease process in this article we assume flexible marginal regression models on the recurrence process and the dependent censoring time without specifying their dependence structure the proposed model generalizes the approach by ghosh and lin 2003 biometrics 59 877 885 the technique of artificial censoring provides a way to maintain the homogeneity of the hypothetical error variables under dependent censoring here we propose to apply this technique to two gehan type statistics one considers only order information for pairs whereas the other utilizes additional information of observed censoring times available for recurrence data a model checking procedure is also proposed to assess the adequacy of the fitted model the proposed estimators have good asymptotic properties their finite sample performances are examined via simulations finally the proposed methods are applied to analyze the aids linked to the intravenous experiences cohort data

a class of semiparametric mixture cure survival models with dependent censoring modern cancer treatments have substantially improved cure rates and have generated a great interest in and need for proper statistical tools to analyze survival data with nonnegligible cure fractions data with cure fractions often are complicated by dependent censoring and the analysis of this type of data typically involves untestable parametric assumptions on the dependence of the censoring mechanism and the true survival times motivated by the analysis of prostate cancer survival trends we propose a class of semiparametric transformation cure models that allows for dependent censoring without making parametric assumptions on the dependence relationship the proposed class of models encompasses a number of common models for the latency survival function including the proportional hazards model and the proportional odds model and also allows for time dependent covariates an inverse censoring probability reweighting scheme is used to derive unbiased estimating equations small sample properties wit

on a new non isospectral variant of the boussinesq hierarchy we give a new non isospectral extension to 2 1 dimensions of the boussinesq hierarchy such a non isospectral extension of the third order scattering problem xxx u x v 0 has not been considered previously this extends our previous results on one component hierarchies in 2 1 dimensions associated to third order non isospectral scattering problems we characterize our entire 2 1 dimensional hierarchy and its linear problem using a single partial differential equation and its corresponding non isospectral scattering problem this then allows an alternative approach to the construction of linear problems for the entire 2 1 dimensional hierarchy reductions of this hierarchy yield new integrable hierarchies of systems of ordinary differential equations together with their underlying linear problems in particular we obtain a fourth painleve hierarchy i e a hierarchy of ordinary differential equations having the fourth painleveequation as its first member we also obtain a hierarchy having as its first member a generalization of an equation defining a new transcendent due to cosgrove

the painleve property lax pair auto backlund transformation and recursion operator of a perturbed korteweg de vries equation using painlevt property analysis we obtained the lax pair auto backlund transformation and recursion operator of a perturbed korteweg de vries equation u 6uu u f f u 0 the exact form off f for which the system is completely integrable is reported in this letter

factorization of operators ii we extend the methods of a previous paper j math phys 21 2508 1980 factorizing the general scalar third order differential operator and obtain a miura transformation for the boussinesq equation we give a general factorized eigenvalue problem we also give a hamiltonian structure associated with the factorized eigenvalue problem we derive several isospectral flows some of klein gordon type

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

regression splines in the time dependent coefficient rates model for recurrent event data many epidemiologic studies involve the occurrence of recurrent events and much attention has been given for the development of modeling techniques that take into account the dependence structure of multiple event data this paper presents a time dependent coefficient rates model that incorporates regression splines in its estimation procedure such methods would be appropriate in situations where the effect of an exposure or covariates changes over time in recurrent event data settings the finite sample properties of the estimators are studied via simulation using data from a randomized community trial that was designed to evaluate the effect of vitamin a supplementation on recurrent diarrheal episodes in small children we model the functional form of the treatment effect on the time to the occurrence of diarrhea the results describe how this effect varies over time in summary we observed a major impact of the vitamin a supplementation on diarrhea after 2 months of the dosage with the effect diminishing after the third dosage the proposed method can be viewed as a flexible alternative to the marginal rates model with constant effect in situations where the effect of interest may vary over time

a copula based mixed poisson model for bivariate recurrent events under event dependent censoring in many chronic disease processes subjects are at risk of two or more types of events we describe a bivariate mixed poisson model in which a copula function is used to model the association between two gamma distributed random effects the resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process methods for parameter estimation are described for parametric and semiparametric models based on an em algorithm we also consider the issue of event dependent censoring based on one type of event which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study the asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed as well as associated treatment effects because the joint model is fit based on a likelihood consistent estimates are obtained simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach

a semiparametric additive rate model for recurrent events with an informative terminal event we propose a semiparametric additive rate model for modelling recurrent events in the presence of a terminal event the dependence between recurrent events and terminal event is nonparametric a general transformation model is used to model the terminal event we construct an estimating equation for parameter estimation and derive the asymptotic distributions of the proposed estimators simulation studies demonstrate that the proposed inference procedure performs well in realistic settings application to a medical study is presented

a groupoid approach to discrete inverse semigroup algebras abstract let k be a commutative ring with unit and s an inverse semigroup we show that the semigroup algebra ks can be described as a convolution algebra of functions on the universal etale groupoid associated to s by paterson this result is a simultaneous generalization of the author s earlier work on finite inverse semigroups and paterson s theorem for the universal c algebra it provides a convenient topological framework for understanding the structure of ks including the center and when it has a unit in this theory the role of gelfand duality is replaced by stone duality using this approach we construct the finite dimensional irreducible representations of an inverse semigroup over an arbitrary field as induced representations from associated groups generalizing the case of an inverse semigroup with finitely many idempotents more generally we describe the irreducible representations of an inverse semigroup s that can be induced from associated groups as precisely those satisfying a certain finiteness condition this finiteness condition is satisfied for instance by all representations of an inverse semigroup whose image contains a primitive idempotent

a completely integrable system and parametric representation of solutions of the wadati konno ichikawa hierarchy a finite dimensional involutive system is presented and the wadati konno ichikawa wki hierarchy of nonlinear evolution equations and their commutator representations are discussed in this article by this finite dimensional involutive system it is proven that under the so called bargmann constraint between the potentials and the eigenfunctions the eigenvalue problem called the wki eigenvalue problem studied by wadati konno and ichikawa j phys soc jpn 47 1698 1979 is nonlinearized as a completely integrable hamiltonian system in the liouville sense moreover the parametric representation of the solution of each equation in the wki hierarchy is obtained by making use of the solution of two compatible systems

new hierarchies of isospectral and non isospectral integrable nlees derived from the harry dym spectral problem abstract by making use of our previous framework we display the hierarchies of generalized nonlinear evolution equations gnlees associated with the harry dym spectral problem and construct the corresponding generalized lax representations glr in this paper it will be clearly seen that the generalized hierarchies can include not only the well known harry dym hierarchy of isospectral nlees but also other new integrable hierarchies of isospectral and non isospectral nlees through choosing the so called seed function these new hierarchies of nlees give some new integrable evolution equations which are very likely to have potential applications in theoretical and experimental physics all of these hierarchies of nlees possess the glr

the generalized neumann hierarchy associated with the energy dependent schro dinger equation abstract a generalized neumann hierarchy is obtained by restricting the hierarchy of integrable evolution equations associated with the energy dependent schrodinger equation to the invariant subspace of its recursion operator the integrals of motion and hamiltonian functions for this hierarchy are constructed by using a recursion formula related to the eigenvalue problem the generalized neumann systems are shown to be completely integrable and to commute with each other this provides a way to solve the evolution equation

on the n 2 supersymmetric camassa holm and hunter saxton equations we consider n 2 supersymmetric extensions of the camassa holm and hunter saxton equations we show that they admit geometric interpretations as euler equations on the superconformal algebra of contact vector fields on the 1 2 dimensional supercircle we use the bi hamiltonian formulation to derive lax pairs moreover we present some simple examples of explicit solutions as a by product of our analysis we obtain a description of the bounded traveling wave solutions for the two component hunter saxton equation

hamiltonian structure of the general integrable equations under reductions the general form of the nonlinear evolution equations integrable by the linear matrix spectral problem and their hamiltonian structures are presented for potentials with nonzero constant asymptotic values the reduction problem is discussed within the framework of the akns method a method is proposed for the calculation of the hamiltonian structures for the integrable equations under reductions matrix zn and n reductions and some other reductions are considered as examples general forms of the corresponding reduced equations and their hamiltonian structures are found

coarsening at random in general sample spaces and random censoring in continuous time heitjan and rubin proposed a concept coarsening at random generalizing rubin s theory of missing at random their analysis was done in discrete sample spaces we propose a generalization to general sample spaces among heitjan and rubin s applications was right censoring in survival analysis we discuss the application of the generalized theory to various censoring patterns in continuous time and connect to the modern theory of random censoring

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

trace functions on the algebras of certain e unitary inverse semigroups a construction is given for a trace function on the semigroup algebra of a certain type of e unitary inverse semigroup over any subfield of the complex field that is closed under complex conjugation in particular the method applies to the semigroup algebras of free inverse semigroups of arbitrary rank

the action angle transformation for soliton equations abstract for third order completely integrable equations in 1 1 dimensions canonical transformations which map in the multi soliton case gradients of action variables to gradients of angle variables are constructed furthermore this action angle map is shown always to be an infinitesimal symmetry group generator of the interacting soliton equation

semiparametric transformation models with random effects for recurrent events in this article we study a class of semiparametric transformation models with random effects for the intensity function of the counting process these models provide considerable flexibility in formulating the effects of possibly time dependent covariates on the developments of recurrent events while accounting for the dependence of the recurrent event times within the same subject we show that the nonparametric maximum likelihood estimators npmles for the parameters of these models are consistent and asymptotically normal the limiting covariance matrices for the estimators of the regression parameters achieve the semiparametric efficiency bounds and can be consistently estimated the limiting covariance function for the estimator of any smooth functional of the cumulative intensity function also can be consistently estimated we develop a simple and stable em algorithm to compute the npmles as well as the variance and covariance estimators simulation studies demonstrate that the proposed methods per

understanding cox s regression model a martingale approach abstract an informal discussion is given of how martingale techniques can be used to extend cox s regression model and to derive its large sample properties

lax pairs spectral problems and recursion operators we present various examples for the connection between lax pairs and recursion operators from this connection a new method for constructing recursion operators is derived as an application we find recursion operators to some integrable equations newly found by wadati et al j phys soc jpn lett 46 1965 1979 j phys soc jpn 47 1698 1979

the bi hamiltonian formulation of the landau lifshiftz equation the landau lifshitz ll equation is a universal model for integrable magnetic systems it contains the sine gordon sg nonlinear schrodinger nls and the heisenberg model hm equations as particular or limiting cases it is well known that the nls sg and hm equations possess recursion operators a recursion operator of an equation in hamiltonian form generates a a hierarchy of integrable equations and b a second hamiltonian operator and more generally a hierarchy of poisson structures here the recursion operator of the ll equation is obtained algorithmically and hence its bi hamiltonian formulation is established

a direct approach to studying soliton perturbations starting with an integrable nonlinear evolution equation the author investigates perturbations about a one soliton solution through the inversion of a linear equation for the first order correction to the soliton solution this inversion differs from past methods as the proposed method takes place in coordinate space not spectral space while it employs some of the tools of inverse scattering theory the method is applied to the korteweg de vries nonlinear schrodinger and sine gordon equations the first order corrections are then obtained

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

reduction technique for matrix nonlinear evolution equations solvable by the spectral transform the main purpose of this paper is to describe a technique of reduction whereby from the class of evolution equations for matrices of order n solvable via the spectral transform associated to the matrix linear schrodinger eigenvalue problem one derives subclasses of nonlinear evolution equations involving less than n2 fields to illustrate the method from the equations for matrices of order 2 two subclasses of equations for 2 fields rather than 4 are obtained the first class coincides or rather includes that solvable via the spectral transform associated to the generalized zakharov shabat spectral problem further reduction to nonlinear evolution equations for a single field reproduces a number of well known equations but also yields a novel one highly nonlinear the second class also yields highly nonlinear equations some examples are given including another novel evolution equation for a single field

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

a formula for obtaining new hereditary symmetries and new integrable equations in this paper we give a simple formula to obtain hereditary symmetries related to the isospectral eigenvalue problem of integrable equations using this formula i we prove that eigenfunctions of hereditary strong symmetry are symmetries for the whole hierarchy which improves the result of fokas and anderson j math phys 23 1066 1982 ii we find new integrable equations and iii we give strong symmetries of these new integrable equations and various equations for eigenfunctions of the isospectral eigenvalue problems

on a new hierarchy of hamiltonian soliton equations a method is suggested for studying the hamiltonian structure of the nonlinear partial differential equations that can be solved by the use of the spectral transform soliton equations the method is applied to a new hierarchy of n 1 coupled partial differential equations related to a schrodinger like spectral problem it is shown that these soliton equations are integrable hamiltonian equations with commuting flows for n 1 and n 2 a miura like transformation is computed and the corresponding modified equations are explicitly given

recurrent events analysis in the presence of time dependent covariates and dependent censoring summary recurrent events models have had considerable attention recently the majority of approaches show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates that are included in the model we provide an overview of available recurrent events analysis methods and present an inverse probability of censoring weighted estimator for the regression parameters in the andersen gill model that is commonly used for recurrent event analysis this estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently and it generally improves on the naive estimator for the andersen gill model in the case of independent censoring we illustrate the bias of ad hoc estimators in the presence of informative censoring with a simulation study and provide a data analysis of recurrent lung exacerbations in cystic fibrosis patients when some patients are lost to follow up

on the use of isospectral eigenvalue problems for obtaining hereditary symmetries for hamiltonian systems we present an algorithmic method for obtaining an hereditary symmetry the generalized squared eigenfunction operator from a given isospectral eigenvalue problem this method is applied to the n n eigenvalue problem considered by ablowitz and haberman and to the eigenvalue problem considered by alonso the relevant hamiltonian formulations are also determined finally an alternative method is presented in the case two evolution equations are related by a miura type transformation and their hamiltonian formulations are known

on contracted semigroup rings sufficient conditions are given for a contracted semigroup ring in which the two sided ideals have a certain property to be a semiprime b semiprimitive c prime d primitive the results are applied to the contracted semigroup rings of inverse semigroups where they provide new proofs of theorems of domanov

category of nonlinear evolution equations algebraic structure and r matrix in this paper we deal with the category of nonlinear evolution equations nlees associated with the spectral problem and provide an approach for constructing their algebraic structure and r matrix first we introduce the category of nlees which is composed of various positive order and negative order hierarchies of nlees both integrable and nonintegrable the whole category of nlees possesses a generalized lax representation next we present two different lie algebraic structures of the lax operator one of them is universal in the category i e independent of the hierarchy while the other one is nonuniversal in the hierarchy i e dependent on the underlying hierarchy moreover we find that two kinds of adjoint maps are r matrices under the algebraic structures in particular the virasoro algebraic structures without a central extension of isospectral and nonisospectral lax operators can be viewed as reductions of our algebraic structure finally we give several concrete examples to illustrate

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided