efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

volume and surface integral equations for electromagnetic scattering by a dielectric body we derive and analyze two equivalent integral formulations for the time harmonic electromagnetic scattering by a dielectric object one is a volume integral equation vie with a strongly singular kernel and the other one is a coupled surface volume system of integral equations with weakly singular kernels the analysis of the coupled system is based on standard fredholm integral equations and it is used to derive properties of the volume integral equation

estimation of the mean function with panel count data using monotone polynomial splines we study nonparametric likelihood based estimators of the mean function of counting processes with panel count data using monotone polynomial splines the generalized rosen algorithm proposed by zhang jamshidian 2004 is used to compute the estimators we show that the proposed spline likelihood based estimators are consistent and that their rate of convergence can be faster than n 1 3 simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by wellner zhang 2000 a real example from a bladder tumour clinical trial is used to illustrate this method

semiparametric estimation methods for panel count data using monotone b splines we study semiparametric likelihood based methods for panel count data with proportional mean model e t z 0 t exp 0tz where z is a vector of covariates and 0 t is the baseline mean function we propose to estimate 0 t and 0 jointly with 0 t approximated by monotone b splines and to compute the estimators using generalized rosen algorithm proposed by jamshidian 2004 we show that the proposed spline based likelihood estimators of 0 t are consistent with a possibly better than n1 3 convergence rate if 0 t is sufficiently smooth the normality of the estimators of 0 is also established comparisons between the proposed estimators and their alternatives studied in wellner and zhang 2007 are made through simulations studies regarding their finite sample performance and computational complexity a real example from a bladder tumor clinical trial is used to illustrate the methods

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

a semiparametric pseudolikelihood estimation method for panel count data in this paper we study panel count data with covariates a semiparametric pseudolikelihood estimation method is proposed based on the assumption that given a covariate vector z the underlying counting process is a nonhomogeneous poisson process with the conditional mean function given by e n t z 0 t exp 0 z the proposed estimation method is shown to be robust in the sense that the estimator converges to its true value regardless of whether or not n t is a conditional poisson process given z an iterative numerical algorithm is devised to compute the semiparametric maximum pseudolikelihood estimator of 0 0 the algorithm appears to be attractive especially when 0 is a high dimensional regression parameter some simulation studies are conducted to validate the method finally the method is applied to a real dataset from a bladder tumour study

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

regression analysis of longitudinal data in the presence of informative observation and censoring times longitudinal data frequently occur in many studies such as longitudinal follow up studies to develop statistical methods and theory for the analysis of these data independent or noninformative observation and censoring times are typically assumed which naturally leads to inference procedures conditional on observation and censoring times but in many situations this may not be true or realistic that is longitudinal responses may be correlated with observation times as well as censoring times this article considers the analysis of longitudinal data where these correlations may exist and proposes a joint modeling approach that uses some latent variables to characterize the correlations for inference about regression parameters estimating equation approaches are developed and both large sample and final sample properties of the proposed estimators are established in addition some graphical and numerical procedures are presented for model checking the methodology is applied to a bladder cancer stu

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

two estimators of the mean of a counting process with panel count data we study two estimators of the mean function of a countingprocess based on panel count data the setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly different times duringa study following a model proposed by schick and yu we allow the number of observation times and the observation times themselves to be random variables our goal is to estimate the mean function of the counting process we show that the estimator of the mean function proposed by sun and kalbfleisch can be viewed as a pseudo maximum likelihood estimator when a non homogeneous poisson process model is assumed for the counting process we establish consistency of both the nonparametric pseudo maximum likelihood estimator of sun and kalbfleisch and the full maximum likeli hood estimator even if the underlying counting process is not a poisson process we also derive the asymptotic distribution of both estimators at a fixed time t and compare the resulting theoretical relative efficiency with finite sample relative efficiency by way of a limited monte carlo study

topological entropy for appropriately approximated c algebrasa classical topological entropy is one of the main numerical invariants in topological dynamics on compact spaces here the author s recent development of a noncommutative generalization of topological entropy in the natural setting of general c algebras as the noncommutative counterpart of continuous function algebras on compact spaces is presented in a slightly modified and improved form this includes both a survey of earlier results with some important corrections and also new general results in response to and inspired by a more recent counterproposal for a noncommutative topological entropy by thomsen finally some partially new examples for the calculation of the defined topological entropy are shown the rather self evident physical interpretation in the framework of operator algebraic quantum statistical mechanics and of chaotic quantum dynamical systems is briefly touched upon

meta analysis of studies with bivariate binary outcomes a marginal beta binomial model approach when conducting a meta analysis of studies with bivariate binary outcomes challenges arise when the within study correlation and between study heterogeneity should be taken into account in this paper we propose a marginal beta binomial model for the meta analysis of studies with binary outcomes this model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model chu and cole 2006 and sarmanov beta binomial model chen et al 2012 the advantages of the proposed marginal model include modeling the probabilities in the original scale not requiring any transformation of probabilities or any link function having closed form expression of likelihood function and no constraints on the correlation parameter more importantly because the marginal beta binomial model is only based on the marginal distributions it does not suffer from potential misspecification of the joint distribution of bivariate study specific probabilities such misspecification is difficult to detect and can lead to biased inference using currents methods we compare the performance of the marginal beta binomial model with the bivariate generalized linear mixed model and the sarmanov beta binomial model by simulation studies interestingly the results show that the marginal beta binomial model performs better than the sarmanov beta binomial model whether or not the true model is sarmanov beta binomial and the marginal beta binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications two meta analyses of diagnostic accuracy studies and a meta analysis of case control studies are conducted for illustration

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

maximum likelihood estimation for semiparametric transformation models with interval censored data interval censoring arises frequently in clinical epidemiological financial and sociological studies where the event or failure of interest is known only to occur within an interval induced by periodic monitoring we formulate the effects of potentially time dependent covariates on the interval censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models we consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject we devise an em type algorithm that converges stably even in the presence of time dependent covariates and show that the estimators for the regression parameters are consistent asymptotically normal and asymptotically efficient with an easily estimated covariance matrix finally we demonstrate the performance of our procedures through simulation studies and application to an hiv aids study conducted in thailand

semiparametric regression analysis of longitudinal data with informative observation times statistical analysis of longitudinal data has been discussed by many authors and a number of methods have been proposed most of the research have focused on situations where observation times are independent of or carry no information about the response variable and therefore rely on conditional inference procedures given the observation times this article considers a different situation where the independence assumption may not hold that is the observation times may carry information about the response variable for inference estimating equation approaches are proposed and both large sample and final sample properties of the proposed methods are established the methodology is applied to a bladder cancer study that motivated this investigation

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

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

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

mixed poisson likelihood regression models for longitudinal interval count data summary in many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event often only the event counts corresponding to the elapsed time intervals between each subject s successive observation times and baseline covariate data are available the intervals may vary substantially in length and number between subjects so that the corresponding vectors of counts are not directly comparable a family of poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure a related empirical bayes estimate of random effect parameters is also described these methods are illustrated by an analysis of dyspepsia data from the national cooperative gallstone study

maximum likelihood estimation for semiparametric regression models with multivariate interval censored data interval censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval we investigate the effects of possibly time dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects and we study nonparametric maximum likelihood estimation under general interval censoring schemes we show that the proposed estimators for the finite dimensional parameters are consistent and asymptotically normal with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood in addition we develop an em algorithm that converges stably for arbitrary datasets finally we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the atherosclerosis risk in communities study

nonparametric comparison for panel count data with unequal observation processes summary this article considers nonparametric comparison of several treatment groups based on panel count data which often occur in among others medical follow up studies and reliability experiments concerning recurrent events for the problem most of the existing procedures require that observation processes are identical across different treatment groups among other requirements we propose a new class of nonparametric test procedures that allow different observation processes the new test statistics are constructed based on the integrated weighted differences between the estimated mean functions of the underlying recurrent event processes the asymptotic distributions of the proposed test statistics are established and their finite sample properties are examined through monte carlo simulations which indicate that the proposed approach works well for practical situations an illustrative example is provided

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality