time varying coefficients models for recurrent event data when different varying coefficients admit different degrees of smoothness application to heart disease modeling we consider a class of semiparametric marginal rate models for analyzing recurrent event data in these models both time varying and time free effects are present and the estimation of time varying effects may result in non smooth regression functions a typical approach for avoiding this problem and producing smooth functions is based on kernel methods the traditional kernel based approach however assumes a common degree of smoothness for all time varying regression functions which may result in suboptimal estimators if the functions have different levels of smoothness in this paper we extend the traditional approach by introducing different bandwidths for different regression functions first we establish the asymptotic properties of the suggested estimators next we demonstrate the superiority of our proposed method using two finite sample simulation studies finally we illustrate our methodology by analyzing a real world heart disease dataset copyright 2016 john wiley sons ltd

robust tests for treatment effects based on censored recurrent event data observed over multiple periods summary we derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods these methods are based on estimating functions motivated by a working mixed poisson assumption under which conditioning can eliminate subject specific random effects robust pseudoscore test statistics are obtained via sandwich variance estimation the relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time homogeneous poisson model the robustness and empirical power of the semiparametric approach are assessed through simulation adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two period crossover trial of patients with bronchial asthma

formulations and benders decomposition algorithms for multidepot salesmen problems with load balancing this paper describes new models and exact solution algorithms for the fixed destination multidepot salesmen problem defined on a graph with n nodes where the number of nodes each salesman is to visit is restricted to be in a predefined range such problems arise when the time to visit a node takes considerably longer as compared to the time of travel between nodes in which case the number of nodes visited in a salesman s tour is the determinant of their load the new models are novel multicommodity flow formulations with o n 2 binary variables which is contrary to the existing formulations for the same and similar problems that typically include o n 3 binary variables the paper also describes benders decomposition algorithms based on the new formulations for solving the problem exactly results of the computational experiments on instances derived from tsplib show that some of the proposed algorithms perform remarkably well in cases where formulations solved by a state of the art optimization code fail to yield optimal solutions within reasonable computation time

combinatorial benders cuts for assembly line balancing problems with setups abstract the classical assembly line balancing problem consists of assigning assembly work to workstations in the presence of setup times that depend on the sequence of tasks assigned to each workstation the problem becomes more complicated given that two interdependent problems namely assignment and sequencing must be solved simultaneously the hierarchical nature of these two problems also suggest a natural decomposition of the problem this paper adopts such an approach and describes an exact algorithm based on benders decomposition to solve both simple and mixed model assembly line balancing problems with setups the algorithm is tested on a set of benchmark instances and numerically compared against a mixed integer linear programming formulation of the problem solved using a commercial optimizer

confidence interval procedures for the weibull process with applications to reliability growth the weibull process a nonhomogeneous poisson process with intensity r t t 1 is considered as a stochastic model for the duane 1964 reliability growth postulate under this model the mean time between failure mtbf for the system at time t is given by m t r t 1 small sample and asymptotic confidence intervals on m t are discussed for failure and time truncated testing tabled values to compute the confidence intervals and numercial examples illustrating these procedures are presented

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

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

inference on the rate ratio of recurrent events for the matched pairs design as statistical methods for testing the null hypothesis of no difference between two groups for the matched pairs design the paired t test wilcoxon signed rank sum test and mcnemar test are well known however there is no simple test for the comparison of incidence rate of recurrent events this paper proposes a simple statistical method and a sample size formula for the comparison of counts of recurrent events over a specified period of observation under the matched pairs design where the subject specific incidence of recurrent events is assumed to follow a time homogeneous poisson process as a special case the proposed method is found to be virtually equivalent in form to mantel haenszel method for a common rate ratio among the set of stratified tables based on person time data the proposed methods are illustrated with the within arm comparison of data from a clinical trial of 59 epileptics with baseline count data

semiparametric regression models for repeated events with random effects and measurement error abstract statistical methodology is presented for the regression analysis of multiple events in the presence of random effects and measurement error omitted covariates are modeled as random effects our approach to parameter estimation and significance testing is to start with a naive model of semiparametric poisson process regression and then to adjust for random effects and any possible covariate measurement error we illustrate the techniques with data from a randomized clinical trial for the prevention of recurrent skin tumors

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

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 and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

estimation of rate and mean functions from truncated recurrent event data abstract this article investigates data on recurrent events that arise from sources such as warranty claims where the observation period for a unit is unknown until it experiences at least one event this creates a type of truncation in the data we consider nonparametric estimation of means and rates of the event occurrences with such zero truncated data and examine the case where the population size and the distribution of observation times across units are at least approximately known we study the behaviors of the proposed estimators by simulation we examine some car warranty data by applying the methodology developed here and considering the underlying assumptions

the general arcangeli s method for solving ill posed problems the study of many mathematical physics problems leads to solving an operator of the first kind there are many examples e g determination of the initial temperature distribution given the temperature distribution at a later time location of tumors by tomography determination of atmospheric temperature profiles from telemetry data seismic prospecting system identification etc in any practical situation there are small errors in measuring therefore given quantities in the equation are not known precisely this type of problem is ill posed in particular if the solution exists it generally depends discontinuously upon the data many authors have studied methods of solving ill posed problems we mentioned the famous picard theorem and smidt theorem l tikhonov and arsenin 2 lavrent ev et al 3 morozov 4 groetsch s have also studied the problem of finding stabilizing approximate solutions and discussing the convergence of approximate solutions a particularly useful method is the method of tikhonov regularization this method determines the regularization operator and regularization parameter the stabilizing approximate solution obtained by this method is called the tikhonov regular solution in this paper the method of tikhonov regularization is used to solve an operator equation of the first kind with approximate operator and the right hand side we choose the regularization parameter by using the general arcangeli s criterion to give the convergence of the tikhonov regular solution and give the uniform convergence of the regular solution of an operator equation with a fredholm operator let x and y be real hilbert spaces t x y be a compact linear operator and consider the operator equation of the first kind tx y 1 l

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

a semiparametric model for the analysis of recurrent event panel data summary in many longitudinal studies interest focuses on the occurrence rate of some phenomenon for the subjects in the study when the phenomenon is nonterminating and possibly recurring the result is a recurrent event data set examples include epileptic seizures and recurrent cancers when the recurring event is detectable only by an expensive or invasive examination only the number of events occurring between follow up times may be available this article presents a semiparametric model for such data based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function a random subject specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data estimators are determined from quasi likelihood estimating functions because only first and second moment assumptions are required for quasi likelihood the method is more robust than those based on the specification of a full parametric likelihood consistency of the estimators depends only on the assumption of the proportional intensity model the semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators as with semiparametric methods in survival analysis the method provides useful diagnostics for specific parametric models including a quasi score statistic for testing specific baseline intensity functions the techniques are used to analyze cancer recurrences and a pheromone based mating disruption experiment in moths a simulation study confirms that for many practical situations the estimators possess appropriate small sample characteristics

confidence limits for recurrence data applied to cost or number of product repairs this article presents a plot and new confidence limits for censored recurrence data they are applied here to data on product repairs they also apply to sociological demographic production business disease and other recurrence data for concreteness reliability terminology is used

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

choice of stratification in poisson process analysis of recurrent event data with environmental covariates the poisson process approach for studying the association between environmental covariates and recurrent events depends on the stratification of study period into intervals within which the baseline intensities are assumed constant in this work we investigate the problem of bias and variance due to misspecification of this stratification we suggest a cross validation approach to choosing a stratification model to balance the trade off between bias and variance we also establish a connection between the poisson process approach and case cross over studies

joint scale change models for recurrent events and failure time recurrent event data arise frequently in various fields such as biomedical sciences public health engineering and social sciences in many instances the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event such as treatment failure and death in this article we propose a joint scale change model for the recurrent event process and the failure time where a shared frailty variable is used to model the association between the two types of outcomes in contrast to the popular cox type joint modeling approaches the regression parameters in the proposed joint scale change model have marginal interpretations the proposed approach is robust in the sense that no parametric assumption is imposed on the distribution of the unobserved frailty and that we do not need the strong poisson type assumption for the recurrent event process we establish consistency and asymptotic normality of the proposed semiparametric estimators under suitable regularity conditions to estimate the corresponding variances of the estimators we develop a computationally efficient resampling based procedure simulation studies and an analysis of hospitalization data from the danish psychiatric central register illustrate the performance of the proposed method

distinguishing heterogeneity from decreasing hazard rates different copies of a repairable machine or units often exhibit different failure rates if this heterogeneity is ignored a statistical model of the time until failure may estimate a spurious decreasing hazard rate resulting in incorrect inferences concerning the risk following repair this article develops a renewal proces model that accommodates both heterogeneity across units and decreasing hazard rates failure times for each unit are assumed weibull and the weibull scale parameter is assumed to vary across units according to a gamma distribution the model is illustrated using both proschan s air conditioner data and data on a u s navy radar

analysis of window observation recurrence data many systems experience recurrent events recurrence data are collected to analyze quantities of interest such as the mean cumulative number of events methods of analysis are available for recurrence data with left and or right censoring due to practical constraints however recurrence data are sometimes recorded only in windows between the windows are gaps over which the process cannot be observed this article extends existing statistical methods both nonparametric and parametric to window observation recurrence data the nonparametric estimator requires minimum assumptions but will be inconsistent if the size of the risk set is not positive over the entire period of interest no such difficulty arises when using a parametric model for the recurrence data for cases in which the size of the risk set is zero for some period of time we propose and compare two alternative hybrid estimators we illustrate the methods with two example applications

semiparametric modelling and estimation of covariate adjusted dependence between bivariate recurrent events a time dependent measure termed the rate ratio was proposed to assess the local dependence between two types of recurrent event processes in one sample settings however the one sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received the focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events we propose the covariate adjusted rate ratio a measure of covariate adjusted dependence we propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure we develop a pseudo partial likelihood to estimate the parameters in the proportional rate ratio model we establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies we illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence

marginal analysis of panel counts through estimating functions we develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations using two types of self consistent estimating equations the first is derived from the likelihood studied in wellner zhang 2000 assuming a poisson counting process and gives a nondecreasing estimator which is the same as the nonparametric maximum likelihood estimator of wellner zhang and thus is consistent without the poisson assumption motivated by the construction of parametric generalized estimating equations the second type is a set of data adaptive quasi score functions which are likelihood estimating functions under a mixed poisson assumption we evaluate the procedures via simulation and illustrate them with the data from a bladder cancer study

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

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

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

marginal regression analysis of recurrent events with coarsened censoring times motivated by an ongoing pediatric mental health care pmhc study this article presents weakly structured methods for analyzing doubly censored recurrent event data where only coarsened information on censoring is available the study extracted administrative records of emergency department visits from provincial health administrative databases the available information of each individual subject is limited to a subject specific time window determined up to concealed data to evaluate time dependent effect of exposures we adapt the local linear estimation with right censored survival times under the cox regression model with time varying coefficients cf cai and sun scandinavian journal of statistics 2003 30 93 111 we establish the pointwise consistency and asymptotic normality of the regression parameter estimator and examine its performance by simulation the pmhc study illustrates the proposed approach throughout the article

combinatorial benders cuts for mixed integer linear programming mixed integer programs mips involving logical implications modeled through big m coefficients are notoriously among the hardest to solve in this paper we propose and analyze computationally an automatic problem reformulation of quite general applicability aimed at removing the model dependency on the big m coefficients our solution scheme defines a master integer linear problem ilp with no continuous variables which contains combinatorial information on the feasible integer variable combinations that can be distilled from the original mip model the master solutions are sent to a slave linear program lp which validates them and possibly returns combinatorial inequalities to be added to the current master ilp the inequalities are associated to minimal or irreducible infeasible subsystems of a certain linear system and can be separated efficiently in case the master solution is integer the overall solution mechanism closely resembles the benders one but the cuts we produce are purely co

the partly aalen s model for recurrent event data with a dependent terminal event recurrent event data are commonly observed in biomedical longitudinal studies in many instances there exists a terminal event which precludes the occurrence of additional repeated events and usually there is also a nonignorable correlation between the terminal event and recurrent events in this article we propose a partly aalen s additive model with a multiplicative frailty for the rate function of recurrent event process and assume a cox frailty model for terminal event time a shared gamma frailty is used to describe the correlation between the two types of events consequently this joint model can provide the information of temporal influence of absolute covariate effects on the rate of recurrent event process which is usually helpful in the decision making process for physicians an estimating equation approach is developed to estimate marginal and association parameters in the joint model the consistency of the proposed estimator is established simulation studies demonstrate that the proposed approach is appropriate for practical use we apply the proposed method to a peritonitis cohort data set for illustration

regression models for nonstationary categorical time series asymptotic estimation theory for the analysis of nonstationary categorical time series a parsimonious and flexible class of models is proposed these models are generalizations of regression models for stochastically independent categorical observations consistency asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements some models for binary time series are discussed in detail to demonstrate asymptotic properties a theorem is given addressing maximum likelihood estimation for general stochastic processes then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series for this proof some lemmas are used which may be of interest in similar cases

two likelihood based semiparametric estimation methods for panel count data with covariates we consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data the basic model assumption is that the conditional mean function of the counting process is of the form efn t jzg exp fl t z 0 t where z is a vector of covariates and 0 is the baseline mean function the panel count observation scheme involves observation of the counting processn for an individual at a random number k of random time points both the number and the locations of these time points may difier across individuals we study semiparametric maximum pseudo likelihood and maximum likelihood estimators of the unknown parameters fl0 0 derived on the basis of a nonhomogeneous poisson process assumption the pseudo likelihood estimator is fairly easy to compute while the maximum likelihood estimator poses more challenges from the computational perspective we study asymptotic properties of both estimators assuming that the proportional mean model holds but dropping the poisson process assumption used to derive the estimators in particular we establish asymptotic normality for the estimators of the regression parameter fl0 under appropriate hypotheses the results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process

analysis of overdispersed count data by mixtures of poisson variables and poisson processes count data often show overdispersion compared to the poisson distribution overdispersion is typically modeled by a random effect for the mean based on the gamma distribution leading to the negative binomial distribution for the count this paper considers a larger family of mixture distributions including the inverse gaussian mixture distribution it is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures the same approach can be used to generate counting processes from poisson processes where the rate or the time is random a random rate corresponds to variation between patients whereas a random time corresponds to variation within patients

comparison of methods for the analysis of longitudinal interval count data longitudinal studies are often concerned with estimating the recurrence rate of a non fatal event in many cases only the total number of events occurring during successive time intervals is known we compared a mixed poisson gamma regression method proposed by thall and a quasi likelihood method proposed by zeger and liang for the analysis of such data in the case where the mean was correctly specified using simulation techniques with large samples both methods produced similar standard errors in most situations except in the case of time dependent covariates with non poisson gamma data where they were seriously underestimated by the thall method a simple method for discriminating between the variance forms of the two methods is described the findings are applied to the analyses of clinical trials of non melanoma skin cancer and familial polyposis this study extends the findings of breslow concerning variance misspecification in overdispersed poisson and quasi likelihood models to the longitudinal setting

combinatorial benders cuts for the strip packing problem we study the strip packing problem in which a set of two dimensional rectangular items has to be packed in a rectangular strip of fixed width and infinite height with the aim of minimizing the height used the problem is important because it models a large number of real world applications including cutting operations where stocks of materials such as paper or wood come in large rolls and have to be cut with minimum waste scheduling problems in which tasks require a contiguous subset of identical resources and container loading problems arising in the transportation of items that cannot be stacked one over the other the strip packing problem has been attacked in the literature with several heuristic and exact algorithms nevertheless benchmark instances of small size remain unsolved to proven optimality in this paper we propose a new exact method that solves a large number of the open benchmark instances within a limited computational effort our method is based on a benders decomposition in whi

regression analysis of panel count data with covariate dependent observation and censoring times panel count data often occur in a long term study where the primary end point is the time to a specific event and each subject may experience multiple recurrences of this event furthermore suppose that it is not feasible to keep subjects under observation continuously and the numbers of recurrences for each subject are only recorded at several distinct time points over the study period moreover the set of observation times may vary from subject to subject in this paper regression methods which are derived under simple semiparametric models are proposed for the analysis of such longitudinal count data especially we consider the situation when both observation and censoring times may depend on covariates the new procedures are illustrated with data from a well known cancer study

methods for the analysis and prediction of warranty claims this article discusses methods whereby reports of warranty claims can be used to estimate the expected number of warranty claims per unit in service as a function of the time in service these methods provide estimates that are adjusted for delays or lags corresponding to the time from the claim until it is entered into the data base used for analysis forecasts of the number and cost of claims on the population of all units in service are also developed along with standard errors for these forecasts the methods are based on a log linear poisson model for numbers of warranty claims both the case of a known distribution of reporting lag and simultaneous estimation of that distribution are considered the use of residuals for model checking extensions to allow for extra poisson variation and the estimation of warranty costs are also considered

nonparametric analysis of recurrent events and death this article is concerned with the analysis of recurrent events in the presence of a terminal event such as death we consider the mean frequency function defined as the marginal mean of the cumulative number of recurrent events over time a simple nonparametric estimator for this quantity is presented it is shown that the estimator properly normalized converges weakly to a zero mean gaussian process with an easily estimable covariance function nonparametric statistics for comparing two mean frequency functions and for combining data on recurrent events and death are also developed the asymptotic null distributions of these statistics together with consistent variance estimators are derived the small sample properties of the proposed estimators and test statistics are examined through simulation studies an application to a cancer clinical trial is provided

testing for monotone trend in recurrent event processes tests for the presence of monotone trends in recurrent event processes have been proposed and studied by many authors however a general concept of trend is elusive and the dependence of the behavior of tests on the assumed definitions of no trend and trend and on the observation periods for the processes has been largely ignored we discuss these issues and study them through analytical results and simulation studies the article also presents robust tests for trend across multiple processes extends them to deal with interval censored event times and compares them and other well known trend tests with respect to the issues mentioned

induced smoothing for rank based regression with recurrent gap time data various semiparametric regression models have recently been proposed for the analysis of gap times between consecutive recurrent events among them the semiparametric accelerated failure time aft model is especially appealing owing to its direct interpretation of covariate effects on the gap times in general estimation of the semiparametric aft model is challenging because the rank based estimating function is a nonsmooth step function as a result solutions to the estimating equations do not necessarily exist moreover the popular resampling based variance estimation for the aft model requires solving rank based estimating equations repeatedly and hence can be computationally cumbersome and unstable in this paper we extend the induced smoothing approach to the aft model for recurrent gap time data our proposed smooth estimating function permits the application of standard numerical methods for both the regression coefficients estimation and the standard error estimation large sample properties and an asymptotic variance estimator are provided for the proposed method simulation studies show that the proposed method outperforms the existing nonsmooth rank based estimating function methods in both point estimation and variance estimation the proposed method is applied to the data analysis of repeated hospitalizations for patients in the danish psychiatric center register

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

on estimands arising from misspecified semiparametric rate based analysis of recurrent episodic conditions marginal rate based analyses are widely used for the analysis of recurrent events in clinical trials in many areas of application the events are not instantaneous but rather signal the onset of a symptomatic episode representing a recurrent infection respiratory exacerbation or bout of acute depression in rate based analyses it is unclear how to best handle the time during which individuals are experiencing symptoms and hence are not at risk we derive the limiting value of the nelson aalen estimator and estimators of the regression coefficients under a semiparametric rate based model in terms of an underlying two state process we investigate the impact of the distribution of the episode durations heterogeneity and dependence on the asymptotic and finite sample properties of standard estimators we also consider the impact of these features on power in trials designed to test intervention effects on rate functions an application to a trial of individuals with herpes simplex virus is given for illustration

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

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

estimating the expected total number of events in a process we consider estimation of the cumulative mean function of a process recurring in time such as the numbers of arrests or migrations accrued by an individual as a function of their age we call this theage profile of a series of events in some situations we can expect a finite value for the total number of events experienced by an individual for example when the distribution of the interevent times is improper so that the process may cease at a finite time with positive probability we propose and analyze a new estimator constructed from kaplan meier km estimators of the interevent time distributions for such an age profile and compare it with the nelson aalen na estimator of the cumulative mean function of a process the km estimator is proved to be uniformly consistent for the age profile if and only if follow up in the sample is sufficient in a sense that is manifested in practice by the leveling off of the profiles at their right side ends and is asymptotically normally distributed around