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

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed

bifurcations stability and monotonicity properties of a delayed neural network model abstract a delay differential equation modelling an artificial neural network with two neurons is investigated a linear stability analysis provides parameter values yielding asymptotic stability of the stationary solutions these can lose stability through either a pitchfork or a hopf bifurcation which is shown to be supercritical at appropriate parameter values an interaction takes place between the pitchfork and hopf bifurcations conditions are also given for the set of initial conditions that converge to a stable stationary solution to be open and dense in the functional phase space analytic results are illustrated with numerical simulations

1 norm based regularization scheme for system identification of structures with discontinuous system parameters this paper presents a new class of regularization functions and the associated regularization scheme for structural system identification in particular 1 norm regularization functions are investigated to overcome the smearing effect of 2 norm regularization functions for the identification of discontinuous system parameters of structures the truncated singular value decomposition is employed to filter out noise polluted solution components and to impose the 1 norm regularization function on si the bilinear fitting method is proposed for selecting an optimal truncation number of the truncated singular value decomposition the validity of the proposed method is demonstrated through the identification of an inclusion in a square plate and damaged members in a two span truss copyright 2006 john wiley sons ltd

determination of an optimal regularization factor in system identification with tikhonov regularization for linear elastic continua this paper presents a geometric mean scheme gms to determine an optimal regularization factor for tikhonov regularization technique in the system identification problems of linear elastic continua the characteristics of non linear inverse problems and the role of the regularization are investigated by the singular value decomposition of a sensitivity matrix of responses it is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution based on this observation the optimal regularization factor is defined as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses the validity of the gms is demonstrated through two numerical examples with measurement errors and modelling errors copyright 2001 john wiley sons ltd

generalizing quantile regression for counting processes with applications to recurrent events in survival analysis quantile regression has become a useful approach to account for covariate effects on the distribution of an event time of interest in this article we discuss how quantile regression can be extended to model counting processes and thus lead to a broader regression framework for survival data we specifically investigate the proposed modeling of counting processes for recurrent events data we show that the new recurrent events model retains the desirable features of quantile regression such as easy interpretation and good model flexibility while accommodating various observation schemes encountered in observational studies we develop a general theoretical and inferential framework for the new counting process model which unifies with an existing method for censored quantile regression as another useful contribution of this work we propose a sample based covariance estimation procedure which provides a useful complement to the prevailing bootstrapping approach we demonstrate t

conditional regression analysis for recurrence time data abstract recurrence time data can be regarded as a specific type of correlated survival data in which recurrent event times of a subject are stochastically ordered given the ordinal nature of recurrence times this article focuses on conditional regression analysis a semiparametric hazards model including the structural and episode specific parameters is proposed for recurrence time data in this model the order of episodes serves as the stratification variable estimation of the structural parameter can be constructed on the basis of all of the observed recurrence times the structural parameter is estimated by the profile likelihood approach although the structural parameter estimator is asymptotically normal the episode specific parameters may or may not be estimated consistently due to the sparseness of data for specific events examples are presented to illustrate the performance of the estimators of the structural and episode specific parameters an extension of the univariate recurrent events

statistical analysis of repeated events forming renewal processes for each of several individuals a sequence of repeated events forming a renewal process is observed up to some censoring time the object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals medical motivation comes from gastroenterology and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state two statistical models are considered one is the standard variance component model adapted to censored data and the other is a recent intensity based model with a random proportionality factor representing interindividual variation these models are applied to the motility data and their advantages are discussed the intensity based model allows simple empirical bayes estimation of the expected interevent times for an individual in the presence of censoring

delay induced periodicity in a neural netlet of excitation and inhibition abstract the dynamical behaviour of a two neuron netlet of excitation and inhibition with a transmission delay is investigated it is shown that in the absence of delay the netlet relaxes to the trivial resting state if the delay is of sufficient magnitude the network is excited to a temporally periodic cyclic behaviour the analytical mechanism for the onset of cyclic behaviour is through a hopf type bifurcation approximate solusions to the periodic output of the netlet is calculated stability of the temporally periodic cycle is investigated it is shown that the bifurcation is supercritical a related discrete version of the continuous time system is formulated it is found that the discrete system also displays a cyclic behaviour results of a number of computer simulations are displayed graphically the article concludes with a brief neurobiological discussion

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

bifurcation analysis on a discrete time tabu learning model in this paper we consider a discrete time tabu learning single neuron model after investigating the stability of the given system we demonstrate that pichfork bifurcation flip bifurcation and neimark sacker bifurcation will occur when the bifurcation parameter exceed a critical value respectively a formula is given for determining the direction and stability of neimark sacker bifurcation by applying the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical results are also provided

convergence and periodicity in a discrete time network of two neurons with self connections abstract in this paper we study a class of difference systems modelling a two neuron network with feedback and mcculloch pitts type activation which includes the discrete version of the two neuron model with piecewise constant argument as its special case we obtain some interesting sufficient conditions insuring the convergence of solutions as well as the existence of periodic solutions

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

a new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body this paper presents a system identification scheme to determine the geometric shape of an inclusion in a finite body the proposed algorithm is based on the minimization of the least squared errors between the measured displacement field and calculated displacement field by the finite element model the domain parameterization technique is adopted to manipulate the shape variation of an inclusion to stabilize the optimization process a new regularization function defined by the length of the boundary curve of an inclusion is added to the error function a variable regularization factor scheme is proposed for a consistent regularization effect the modified newton method with the active set method is adopted for optimization copyright 1999 john wiley sons ltd

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

semiparametric transformation models with time varying coefficients for recurrent and terminal events in this article we propose a family of semiparametric transformation models with time varying coefficients for recurrent event data in the presence of a terminal event such as death the new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time for the inference on the proposed models a class of estimating equations is developed and asymptotic properties of the resulting estimators are established in addition a lack of fit test is provided for assessing the adequacy of the model and some tests are presented for investigating whether or not covariate effects vary with time the finite sample behavior of the proposed methods is examined through monte carlo simulation studies and an application to a bladder cancer study is also illustrated

pseudomartingale estimating equations for modulated renewal process models summary we adapt martingale estimating equations based on gap time information to a gen eral intensity model for a single realization of a modulated renewal process the consistency and asymptotic normality of the estimators is proved under ergodicity conditions previous work has considered either parametric likelihood analysis or semiparametric multiplicative models using partial likelihood the framework is generally applicable to semiparametric and paramet ric models including additive and multiplicative specifications and periodic models it facilitates a semiparametric extension of a popular parametric earthquake model simulations and empir ical analyses of taiwanese earthquake sequences illustrate the methodology s practical utility

nonparametric and semiparametric trend analysis for stratified recurrence times summary recurrent event data are frequently encountered in longitudinal follow up studies when the occurrences of multiple events are considered as the major outcomes suppose that the recurrent events are of the same type and the variable of interest is the recurrence time between successive events in many applications the distributional pattern of recurrence times can be used as an index for the progression of a disease such a distributional pattern is important for understanding the natural history of a disease or for confirming long term treatment effect in this article we discuss and define the comparability of recurrence times nonparametric and semiparametric methods are developed for testing trend of recurrence time distributions and estimating trend parameters in regression models the construction of the methods is based on comparable recurrence times from stratified data a real data example is presented to illustrate the use of methodology

information and asymptotic efficiency in some generalized proportional hazards models for counting processes proportional hazards models with stochastic baseline hazards and estimators of the relative risk coefficient in these models were proposed by prentice williams and peterson and by chang and hsiung in medical and industrial contexts the form of the estimating functions recommended varies according to the form of the unknown stochastic baseline hazards this paper examines the same estimation problem in the context of largesample theory it is shown that the proposed estimators are regular asymptotically normal and asymptotically efficient asymptotic information and representation theorems in the sensze of begun hall huang and wellner are also provided for these models

analysis of episodic data with application to recurrent pulmonary exacerbations in cystic fibrosis patients we consider a special type of recurrent event data termed recurrent episode data arising in episodic illness studies when an event occurs it lasts for a random length of time a naive recurrent event analysis disregards the length of the episodes which may contain important information about the severity of the disease the associated medical costs and quality of life bivariate gap time models have been suggested in which length of episodes and time between episodes are modeled jointly these models are useful but may obscure the overall effects of treatment and other prognostic factors the analysis can be further complicated if covariate effects change over time as may occur when the effects vary across episodes this article reviews the existing methods applied to recurrent episode data and approaches the problem using the recently developed temporal process regression novel endpoints are constructed that summarize both episode frequency and the length of episodes and time between episodes

estimating equations for hazard ratio parameters based on correlated failure time data summary weighted partial likelihood estimating equations are proposed for the estimation of marginal hazard ratio parameters based on correlated failure time data asymptotic distribution theory is derived for the solution to such equations using martingale convergence results and inverse function theory simulation studies and theoretical efficiency calculations indicate that the inclusion of weights in the estimating equation produces important efficiency gains only if the dependencies among the failure times are strong

the accelerated gap times model summary this paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process the model is a transparent extension of the accelerated failure time model for univariate survival data estimation of the regression parameter is motivated by semiparametric efficiency considerations extending the class of weighted log rank estimating functions originally proposed in prentice 1978 and subsequently studied in detail by tsiatis 1990 and ritov 1990 a novel rank based one step estimator for the regression parameter is proposed an aalen type estimator for the baseline intensity function is obtained asymptotics are handled with empirical process methods and finite sample properties are studied via simulation finally the new model is applied to the bladder tumour data of byar 1980

semiparametric transformation models for point processes in this article we propose a family of semiparametric transformation models for point processes with positive jumps of arbitrary sizes these models offer great flexibilities in formulating the effects of covariates on the mean function of the point process while leaving the stochastic structure completely unspecified we develop a class of estimating equations for the baseline mean function and the vector valued regression parameter based on censored point processes and covariate data these equations can be solved easily by the standard newton raphson algorithm the resultant estimator of the regression parameter is consistent and asymptotically normal with a covariance matrix that can be estimated consistently furthermore the estimator of the baseline mean function is uniformly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function we demonstrate through extensive simulation studies that the proposed inference procedu

stability bifurcation and multistability in a system of two coupled neurons with multiple time delays a system of delay differential equations representing a model for a pair of neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself is studied conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements it is shown that the trivial fixed point may lose stability via a pitchfork bifurcation a hopf bifurcation or one of three types of codimension two bifurcations multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations

tabu search for fuzzy optimization and applications in this paper we present a tabu search technique to approximately solve fuzzy optimization problems we demonstrate the performance of the proposed method by applying it to an elementary fuzzy optimization problem other applications of the method to fuzzy linear programming fuzzy regression and the training of fuzzy neural networks are also presented

reconstruction of dynamic displacement and velocity from measured accelerations using the variational statement of an inverse problem this paper presents two types of finite impulse response fir filters to reconstruct dynamic displacement induced by structural vibration from measured acceleration the governing equation for the reconstruction is derived by taking the variation of a minimization problem which defines an inverse problem on displacement a regularization function for overcoming the ill posedness of the inverse problem is included in the minimization problem the governing equation of the inverse problem becomes the same type of differential equation as that of a beam on an elastic foundation the conventional fir cfir filter directly approximates the transfer function of the governing equation while the fem based fir ffir filter is formulated by the discretization of the minimization problem with the finite element method for the finite element discretization the hermitian shape function is utilized the proposed ffir filter is capable of reconstructing displacement and velocity simultaneously the fundamental characteristics of the proposed filters are investigated in the frequency domain using the transfer and accuracy functions it is shown that the proposed fir filters suppress low frequency noise components in measured accelerations effectively and reconstruct physically meaningful displacement accurately the validity of the proposed filters is demonstrated through a numerical simulation study a field experiment and an evaluation of flutter derivatives using measurements taken from a wind tunnel test

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

structural system identification in time domain using measured acceleration this paper presents a system identification scheme in time domain to estimate stiffness and damping parameters of a structure using measured acceleration an error function is defined as the time integral of the least squared errors between measured accelerations and calculated accelerations by a numerical model of a structure to alleviate the ill posedness of si problems a regularization technique is employed and a new regularization function for the time domain si is proposed the regularization factor is determined by the geometric mean scheme the validity of the proposed method is demonstrated by a numerical simulation study on a two span truss bridge and by an experimental laboratory study on a three story shear building model

censored regression with the multistate accelerated sojourn times model many disease processes are characterized by two or more successive health states and it is often of interest and importance to assess state specific covariate effects however with incomplete follow up data such inference has not been satisfactorily addressed in the literature we model the logarithm transformed sojourn time in each state as linearly related to the covariates however neither the distributional form of the error term nor the dependence structure of the states needs to be specified we propose a regression procedure to accommodate incomplete follow up data asymptotic theory is presented along with some tools for goodness of fit diagnostics simulation studies show that the proposal is reliable for practical use we illustrate it by application to a cancer clinical trial

on the design of linear phase fir integrators for midband frequencies the ideal frequency responses 1 j spl omega an integrator and 1 spl omega an integrating hilbert transformer are usually approximated by iir structures this paper suggests their fir approximations maximal flatness at spl omega spl pi 2 yields exact mathematical formulas for computing the weights the proposed designs are particularly suitable for the frequency range 0 1 spl pi spl les spl omega spl les 0 90 spl pi

calibration regression of censored lifetime medical cost analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow up particularly the latter with limited study duration as is typical in medical research this article proposes the so called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time in a semiparametric fashion it is postulated that both outcomes on possibly transformed scales linearly relate to the covariates however the bivariate model error distribution is completely unspecified whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model this article proposes an inference procedure by extending the weighted log rank estimating function to the marked point process framework the resulting estimators are consistent and asymptotically normal in addition robustness and efficiency issues are discussed furthermore a novel sample based variance estimation procedure is proposed for es

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

nonparametric estimation of a recurrent survival function abstract recurrent event data are frequently encountered in studies with longitudinal designs let the recurrence time be the time between two successive recurrent events recurrence times can be treated as a type of correlated survival data in statistical analysis in general because of the ordinal nature of recurrence times statistical methods that are appropriate for standard correlated survival data in marginal models may not be applicable to recurrence time data specifically for estimating the marginal survival function the kaplan meier estimator derived from the pooled recurrence times serves as a consistent estimator for standard correlated survival data but not for recurrence time data in this article we consider the problem of how to estimate the marginal survival function in nonparametric models a class of nonparametric estimators is introduced the appropriateness of the estimators is confirmed by statistical theory and simulations simulation and analysis from schizophrenia data are pre

accelerated failure time models for counting processes summary we present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events a class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model in addition a nelson aalen type estimator for the mean function of the counting process is constructed which is consistent and properly normalised converges weakly to a zeromean gaussian process we assess the finite sample properties of the proposed estimators and the associated inference procedures through monte carlo simulation and provide an application to a well known bladder cancer study

smoothing spline anova frailty model for recurrent event data summary gap time hazard estimation is of particular interest in recurrent event data this article proposes a fully nonparametric approach for estimating the gap time hazard smoothing spline analysis of variance anova decompositions are used to model the log gap time hazard as a joint function of gap time and covariates and general frailty is introduced to account for between subject heterogeneity and within subject correlation we estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the newton raphson procedure the stochastic approximation algorithm saa and the markov chain monte carlo mcmc method the convergence of the algorithm is guaranteed by decreasing the step size of parameter update and or increasing the mcmc sample size along iterations model selection procedure is also developed to identify negligible components in a functional anova decomposition of the log gap time hazard we evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data

design of an fir filter for the displacement reconstruction using measured acceleration in low frequency dominant structures this paper presents a new class of displacement reconstruction scheme using only acceleration measured from a structure for a given set of acceleration data the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second order central finite difference of displacement the displacement is reconstructed by minimizing the least squared errors between measured and approximated acceleration within a finite time interval an overlapping time window is introduced to improve the accuracy of the reconstructed displacement the displacement reconstruction problem becomes ill posed because the boundary conditions at both ends of each time window are not known a priori furthermore random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement a tikhonov regularization scheme is adopted to alleviate the ill posedness it is shown that the proposed method is equivalent to an fir filter designed in the time domain the fundamental characteristics of the proposed method are presented in the frequency domain using the transfer function and the accuracy function the validity of the proposed method is demonstrated by a numerical example a laboratory experiment and a field test copyright 2009 john wiley sons ltd

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

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided