an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

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

a semiparametric regression cure model with current status data summary this paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event the semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable a sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed under some mild conditions the estimators are shown to be strongly consistent the convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed simulation studies were carried out to investigate the performance of the proposed method and the model is fitted to a dataset from a study of calcification of the hydrogel intraocular lenses a complication of cataract treatment

on a semilinear elliptic neumann problem with asymmetric nonlinearities abstract we consider the neumann problem 1 1 below we extend therange of applicability of the sharp nonresonance condition derived in go om so as in particular allow asymmetric nonlinearities 1 introduction this paper is mainly concerned with the neumann problem i au g u h x inq 1 1 du du 0 on oil here a is the laplacian operator q is a bounded domain of rn n 1 with c1 1 boundary and unit exterior normal v g is a continuous function on r and h is taken in l f2 or in lp q in a previous work go om we showed that if g s 2g s 1 2 lim sup oo s s oo s or s oo then a necessary and sufficient condition for 1 1 to be solvable for any h l f2 is that the range of g be all of k here kx 0 k2 denote the distinct eigenvalues of a on q with neumann boundary condition andg s jo g t dt the surjectivity of g thus provides a nonresonance condi tion at the eigenvalue xx 0 we refer to go om for historical background

existence of multiple nontrivial solutions for semilinear elliptic problems the aim of this paper is to prove the existence of multiple nontrivial solutions to a semilinear elliptic problem at resonance the proofs used here are based on combining the morse theory and the minimax methods

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

asymptotic efficiency in semi parametric models with censoring abstract we consider a regression model subject to bivariate censoring in which the errors are independent of the explanatory variables our objective is to drop the assumption of bivaraite normality and obtain an information bound on asymptotic efficiency when the error distribution is unrestricted except for smoothness and regularity conditions this bound has simple form if there are no exclusion restrictions on the selection equation then positive information requires a restriction on the regression slope parameters and a continuous distribution for a component of the explanatory variables we also consider a binary choice model under the weak assumption that the error distribution has zero median conditional on the explanatory variables here the semi parametric information bound is zero hence although a consistent estimator exists it is not possible to attain covergence at rate 1 n

infinite commutative product formulas for relative extremal projectors abstract loosely speaking a relative extremal projector is a universal projector mapping any appropriate representation onto a certain highest subrepresentation this paper presents a number of infinite product expansions for the relative extremal projector most of which are new even for the extremal projector as an application conditions are given determining when the relative extremal projector descends to a well defined operator on a particular representation the total denominator and related summation formulas are also studied

regression analysis for current status data using the em algorithm we propose new expectation maximization algorithms to analyze current status data under two popular semiparametric regression models the proportional hazards ph model and the proportional odds po model monotone splines are used to model the baseline cumulative hazard function in the ph model and the baseline odds function in the po model the proposed algorithms are derived by exploiting a data augmentation based on poisson latent variables unlike previous regression work with current status data our ph and po model fitting methods are fast flexible easy to implement and provide variance estimates in closed form these techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy copyright 2013 john wiley sons ltd

linear regression with current status data abstract in survival analysis a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates this article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error where the response variable is subject to so called case 1 interval censoring the method uses a constructed random sieve likelihood and constraints combining the benefits of semiparametric likelihood with estimating equations the estimation procedure is implemented and the asymptotic distributions for the estimated regression parameter and for the profile likelihood ratio statistic are obtained in addition some model diagnostics aspects are described finally the small sample operating characteristics of the proposed method is examined via simulations and its usefulness is illustrated on datasets from an animal tumorigenicity study and from a hiv study

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

harish chandra isomorphisms for quantum algebras the center of the quantum algebra is studied especially an analogue of the harish chandra isomorphism is established

nonresonance conditions on the potential for a semilinear dirichlet problem abstract problem u g u h x in a b with u 0 on a b is solved under new nonresonance conditions between the first eigenvalue and the first curve in the fucik spectrum of the associated linear problem

on the existence of mathfrak g mathfrak k modules of finite type let g be a reductive lie algebra over an algebraically closed field of characteristic zero and k be a subalgebra reductive in g we prove that g admits an irreducible g k module m which has finite k multiplicities and which is not a g k 0 module for any proper inclusion of reductive subalgebras k k 0 g if and only if k contains its centralizer in g the main point of the proof is a geometric construction of g k modules which is analogous to cohomological induction for g gl n we show that whenever k contains its centralizer there is an irreducible g k module m of finite type over k such that k coincides with the subalgebra of all g 2 g which act locally finitely on m finally for a root subalgebra k gl n we describe all possibilities for the subalgebra l k of all elements acting locally finitely on some m math subject classification 2000 primary 17b10 secondary 22e46

the profile sampler we consider frequentist inference for the parametric component separately from the nuisance parameter in semiparametric models based on sampling from the posterior of the profile likelihood we prove that this procedure gives a first order correct approximation to the maximum likelihood estimator and consistent estimation of the efficient fisher information for without computing derivatives or using complicated numerical approximations an exact bayesian interpretation is established under a certain data dependent prior the sampler is useful in particular when the nuisance parameter is not estimable at the rate where neither bootstrap validity nor general automatic variance estimation has been theoretically justified even when the nuisance parameter is consistent and the bootstrap is known to be valid the proposed markov chain monte carlo procedure can yield computational savings because maximization of the likelihood is not required the theory is verified for three examples the methods are

regression with interval censored data summary interval censored data result when survival times are not known exactly but are only known to have occurred between intermittent examination times here the accelerated failure time model is treated for interval censored data a class of score statistics that may be used for estimation and confidence procedures is proposed an adaptive procedure based on estimating the optimal member of the class of score statistics is explored

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

nonresonance to the right of the first eigenvalue for the one dimensional p laplacian a quasilinear two point boundary value problem was considered this problem is given by the equation

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

root fernando kac subalgebras of finite type abstract let g be a finite dimensional lie algebra and m be a g module the fernando kac subalgebra of g associated to m is the subset g m g of all elements g g which act locally finitely on m a subalgebra l g for which there exists an irreducible module m with g m l is called a fernando kac subalgebra of g a fernando kac subalgebra of g is of finite type if in addition m can be chosen to have finite jordan holder l multiplicities under the assumption that g is simple i penkov has conjectured an explicit combinatorial criterion describing all fernando kac subalgebras of finite type which contain a cartan subalgebra in the present paper we prove this conjecture for g e 8

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

a flexible computationally efficient method for fitting the proportional hazards model to interval censored data the proportional hazards model ph is currently the most popular regression model for analyzing time to event data despite its popularity the analysis of interval censored data under the ph model can be challenging using many available techniques this article presents a new method for analyzing interval censored data under the ph model the proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function formulating the ph model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility a novel expectation maximization em algorithm is developed for finding the maximum likelihood estimates of the parameters the derivation of the em algorithm relies on a two stage data augmentation involving latent poisson random variables the resulting algorithm is easy to implement robust to initialization enjoys quick convergence and provides closed form variance estimates the performance of the proposed regression methodology is evaluated through a simulation study and is further illustrated using data from a large population based randomized trial designed and sponsored by the united states national cancer institute

nonresonance below the first eigenvalue for a semilinear elliptic problem let be a bounded open subset in hbox i r n with smooth boundary and let f x s be a real valued caratheodory function on upomega times hbox i r we consider the semilinear dirichlet problem

a new bayesian model for survival data with a surviving fraction abstract we consider bayesian methods for right censored survival data for populations with a surviving cure fraction we propose a model that is quite different from the standard mixture model for cure rates we provide a natural motivation and interpretation of the model and derive several novel properties of it first we show that the model has a proportional hazards structure with the covariates depending naturally on the cure rate second we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates prior elicitation is discussed in detail and classes of noninformative and informative prior distributions are proposed several theoretical properties of the proposed priors and resulting posteriors are derived and comparisons are made to the standard mixture model a real dataset from a melanoma clinical trial is discussed in detail

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

nonresonance conditions on the potential for a semilinear elliptic problem abstract we prove the solvability of the dirichlet problem formula for every given h under the following set of assumptions formula and formula and formula here m and m 1 denote two consecutive higher eigenvalues of on h 1 0 and g is the potential of g similar results are also obtained in the case where the nonlinearity interacts with the first eigenvalue 1

efficient estimation in additive hazards regression with current status data summary current status data arise when the exact timing of an event is unobserved and it is only known at a given point in time whether or not the event has occurred recently lin et al 1998 studied the additive semiparametric hazards model for current status data they showed that the analysis of current status data under the additive hazards model reduces to ordinary cox regression under the assumption that a proportional hazards model may be used to describe the monitoring intensity this analysis does not make efficient use of data and in some cases it may not be appropriate to assume a proportional hazards model for the monitoring times we study the semiparametric hazards model for current status data but make use of the semiparametric efficient score function the suggested approach has the advantages that it is efficient in that it reaches the semiparametric information bound and it does not involve any modelling of the monitoring times

indefinite weight nonlinear problems with neumann boundary conditions abstract we present a multiplicity result of positive solutions for the neumann problem associated with a second order nonlinear differential equation of the following form u a t g u 0 where the weight function a t has indefinite sign the only assumption we make for the nonlinear term g u is that its primitive g u presents some oscillations at infinity expressed by the condition involving lim g u u 2 0 lim g u u 2 as an application we obtain multiple radially symmetric solutions for neumann problems associated with u a x g u 0

implementation of estimating function based inference procedures with markov chain monte carlo samplers under a semiparametric or nonparametric setting inferences about the unknown parameter are often made based on a nonsmooth estimating function resampling methods are quite handy for obtaining good approximations to the distribution of the consistent estimator when the estimating equation and its resampled counterparts are not difficult to solve numerically in this article we propose a simple flexible procedure that provides such approximations through the standard markov chain monte carlo sampler without solving any equations more generally the procedure may locate all possible roots of the estimating equation and provides an approximation to the distribution of each root we illustrate our proposed procedure extensively with three examples and evaluate its performance comprehensively through a simulation study

regression with doubly censored current status data data from settings in which an initiating event and a subsequent event occur in sequence are called doubly censored current status data if the time of neither event is observed directly but instead it is determined at a random monitoring time whether either the initiating or subsequent event has yet occurred this paper is concerned with using doubly censored current status data to estimate the regression coefficient in an accelerated failure time model for the length of time between the initiating event and the subsequent event motivated by a problem in the epidemiology of acquired immune deficiency syndrome attention here is focused on a special case the case in which the initiating event given that it has occurred before the monitoring time may be assumed to follow a uniform distribution the main result is that the likelihood in the special case has the same structure as the likelihood in a simpler setting the setting in which the time of the initiating event is known the result allows methods developed for the simpler setting to be applied in the special case the results of the application of the approach to real data are reported

eigenvalue coincidences and k orbits i abstract we study the variety g l consisting of matrices x gl n c such that x and its n 1 by n 1 cutoff x n 1 share exactly l eigenvalues counted with multiplicity we determine the irreducible components of g l by using the orbits of gl n 1 c on the flag variety b of gl n c more precisely let b b be a borel subalgebra such that the orbit gl n 1 c b in b has codimension l then we show that the set y b ad g x x b g l g gl n 1 c is an irreducible component of g l and every irreducible component of g l is of the form y b where b lies in a gl n 1 c orbit of codimension l an important ingredient in our proof is the flatness of a variant of a morphism considered by kostant and wallach and we prove this flatness assertion using an analogue of the steinberg variety

semiparametric estimation of the accelerated failure time model with partly interval censored data summary partly interval censored pic data arise when some failure times are exactly observed while others are only known to lie within certain intervals in this article we consider efficient semiparametric estimation of the accelerated failure time aft model with pic data we first generalize the buckley james estimator for right censored data to pic data then we develop a one step estimator by deriving and estimating the efficient score for the regression parameters we show that under mild regularity conditions the generalized buckley james estimator is consistent and asymptotically normal and the one step estimator is consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound we conduct extensive simulation studies to examine the performance of the proposed estimators in finite samples and apply our methods to data derived from an aids study

additive hazards regression with current status data current status data arise when the only knowledge about the failure time of interest is whether the failure occurs before or after a random monitoring time we propose to analyse such data by the semiparametric additive hazards model which specifies that the hazard function for the failure time associated with a set of possibly time dependent covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates under certain conditions on the monitoring time one can make inferences about the regression parameters of the additive hazards model by using the familiar asymptotic theory and software for the proportional hazards model with right censored data an application to a carcinogenicity experiment is provided

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

representations of kac moody algebras by step algebras representations of a kac moody algebra associated to a semisimple lie algebra g which decompose to a direct sum of finite dimensional representations of the subalgebra g are constructed using a step algebra method the cases g su 2 su 3 are considered in detail

accelerated failure time regression models with a regression model of surviving fraction an application to the analysis of permanent employment in japan abstract accelerated failure time regression models with an additional regression model for the surviving fraction are proposed for the analysis of events that may never occur regardless of censoring for some people in the population risk set the models attempt to estimate simultaneously the effects of covariates on the acceleration deceleration of the timing of a given event and the surviving fraction that is the proportion of the population for which the event never occurs the extended family of the generalized gamma distribution is used for the accelerated failure time regression model the logistic function is used for the regression model of the surviving fraction the models are applied to the data of interfirm job mobility in japan to assess variability in permanent employment among white collar and blue collar employees in firms of different sizes independent from their variability in the timing of interfirm job separations

interval censored survival data with informative examination times parametric models and approximate inference we develop parametric methods for analysing interval censored data when examination and survival times are not independent the hazard function is modelled by introducing individual frailties related to the frequency of examinations model parameters may be obtained by direct maximization of the marginal log likelihood we develop a simpler approximate method in which the frailties are estimated by empirical bayes the two approaches are equivalent asymptotically as the number of examinations on each individual increases simulations suggest that the approximate method is adequate for estimating regression parameters even when the number of examinations on each individual is small the methods are used to estimate age and period effects on hiv incidence in a cohort of repeat attenders at genito urinary clinics in london u k

a proportional hazards model taking account of long term survivors a proportional hazards ph model is modified to take account of long term survivors by assuming the cumulative hazard to be bounded but otherwise unspecified to yield an improper survival function a marginal likelihood is derived under the restriction for type i censoring patterns for a ph model with cure the marginal and the partial likelihood are not the same in the absence of covariate information the estimate of the cure rate based on the marginal likelihood reduces to the value of the kaplan meier estimate at the end of the study an example of low asymptotic efficiency of the partial likelihood as compared to the marginal profile and parametric likelihoods is given an algorithm is suggested to fit the full ph model with cure

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

analysis of clustered interval censored data using a class of semiparametric partly linear frailty transformation models a flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval censored data which arise naturally in complex diseases and dental research this class of models features two nonparametric components resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate the dependence among failure times within a cluster is induced by a shared unobserved frailty term a sieve maximum likelihood estimation method based on piecewise linear functions is proposed the proposed estimators of the regression dependence and transformation parameters are shown to be strongly consistent and asymptotically normal whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence an extensive simulation study is conducted to study the finite sample performance of the proposed estimators we provide an application to a dental study for illustration

a semiparametric regression cure model for interval censored data motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring we present a semiparametric nonmixture cure model for the regression analysis of interval censored time to event data we develop semiparametric maximum likelihood estimation for the model using the expectation maximization method for interval censored data the maximization step for the baseline function is nonparametric and numerically challenging we develop an efficient and numerically stable algorithm via modern convex optimization techniques yielding a self consistency algorithm for the maximization step we prove the strong consistency of the maximum likelihood estimators under the hellinger distance which is an appropriate metric for the asymptotic property of the estimators for interval censored data we assess the performance of the estimators in a simulation study with small to moderate sample sizes to illustrate the method we also analyze a real dataset

proportional odds regression and sieve maximum likelihood estimation summary this paper introduces under a censoring mechanism an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method the procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative kullback leibler risk to select the best approximation the procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree the proposed procedure is implemented for right censored and so called case 2 interval censored data the estimated regression parameters are shown to be asymptotically normal and efficient the small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients

semiparametric probit models with univariate and bivariate current status data summary multivariate current status data are frequently encountered in biomedical and public health studies semiparametric regression models have been extensively studied for univariate current status data but most existing estimation procedures are computationally intensive involving either penalization or smoothing techniques it becomes more challenging for the analysis of multivariate current status data in this article we study the maximum likelihood estimations for univariate and bivariate current status data under the semiparametric probit regression models we present a simple computational procedure combining the expectation maximization algorithm with the pool adjacent violators algorithm for solving the monotone constraint on the baseline function asymptotic properties of the maximum likelihood estimators are investigated including the calculation of the explicit information bound for univariate current status data as well as the asymptotic consistency and convergence rate for bivariate current status data extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes we demonstrate the estimation procedure with two real data examples in the areas of diabetic and hiv research

on assessing the association for bivariate current status data assuming that the two failure times of interest with bivariate current status data follow a bivariate copula model we propose a two stage estimation procedure to estimate the association parameter which is related to kendall s tau asymptotic properties of the proposed semiparametric estimator show that although the first stage marginal estimators have a convergence rate of only n 1 3 the resulting parameter estimator still converges to a normal random variable with the usual n 1 2 rate the variance of the proposed estimator can be consistently estimated simulation results are presented and a community based study of cardiovascular diseases in taiwan provides an illustrative example

existence and localization of solution for second order elliptic bvp in presence of lower and upper solutions without any order abstract we prove an existence and localization result for a solution of a second order elliptic equations with dirichlet and regular oblique derivative boundary conditions the main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behaviour of the right hand member of the equation

on the accelerated failure time model for current status and interval censored data and tianxi cai this paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time model for current status and interval censored data the estimator is constructed by inverting a wald type test for testing a null proportional hazards model a numerically efficient markov chain monte carlo based resampling method is proposed for obtaining simultaneously the point estimator and a consistent estimator of its variance covariance matrix we illustrate our approach with interval censored datasets from two clinical studies extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

nontrivial solutions of semilinear equations at resonance in this paper we prove new existence results concerning nontrivial solutions to semilinear elliptic problem at resonance the methods used here are based on combining the minimax methods and the morse theory

lie algebra modules with finite dimensional weight spaces i let g denote a reductive lie algebra over an algebraically closed field of characteristic zero and let 4 denote a cartan subalgebra of g in this paper we study finitely generated g modules that decompose into direct sums of finite dimensional 4 weight spaces we show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules those we call torsion free modules we also show that if g is a simple lie algebra that admits a torsion free module then g is of type a or c

statistical inference based on non smooth estimating functions summary when the estimating function for a vector of parameters is not smooth it is often rather difficult if not impossible to obtain a consistent estimator by solving the corresponding estimating equation using standard numerical techniques in this paper we propose a simple inference procedure via the importance sampling technique which provides a con sistent root of the estimating equation and also an approximation to its distribution without solving any equations or involving nonparametric function estimates the new proposal is illustrated and evaluated via two extensive examples with real and simulated datasets

smooth semiparametric regression analysis for arbitrarily censored time to event data a general framework for regression analysis of time to event data subject to arbitrary patterns of censoring is proposed the approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models such as the baseline hazard function in the proportional hazards model have densities satisfying mild smoothness conditions densities are approximated by a truncated series expansion that for fixed degree of truncation results in a parametric representation which makes likelihood based inference coupled with adaptive choice of the degree of truncation and hence flexibility of the model computationally and conceptually straightforward with data subject to any pattern of censoring the formulation allows popular models such as the proportional hazards proportional odds and accelerated failure time models to be placed in a common framework provides a principled basis for choosing among them and renders useful extensions of the models straightforward the utility and performance of the methods are demonstrated via simulations and by application to data from time to event studies

semiparametric bayes proportional odds models for current status data with underreporting current status data are a type of interval censored event time data in which all the individuals are either left or right censored for example our motivation is drawn from a cross sectional study which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman we propose a semiparametric bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure the proposed approach has the advantage of being straightforward to implement using a simple and efficient gibbs sampler whereas alternative semiparametric bayes event time models encounter problems for current status data the model is generalized to allow systematic underreporting in a subset of the data and the methods are applied to an epidemiologic study of uterine fibroids

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

a hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data abstract we present a hybrid algorithm for nonparametric maximum likelihood estimation from censored data when the log likelihood is concave the hybrid algorithm uses a composite algorithmic mapping combining the expectation maximization em algorithm and the modified iterative convex minorant icm algorithm global convergence of the hybrid algorithm is proven the iterates generated by the hybrid algorithm are shown to converge to the nonparametric maximum likelihood estimator npmle unambiguously numerical simulations demonstrate that the hybrid algorithm converges more rapidly than either of the em or the naive icm algorithm for doubly censored data the speed of the hybrid algorithm makes it possible to accompany the npmle with bootstrap confidence bands

r matrix and mickelsson algebras for orthosymplectic quantum groups let x1d524 be a complex orthogonal or symplectic lie algebra and x1d524 x1d524 the lie subalgebra of rank rk x1d524 rk x1d524 1 of the same type we give an explicit construction of generators of the mickelsson algebra zq x1d524 x1d524 in terms of chevalley generators via the r matrix of uq x1d524

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

dynamical weyl groups and applications abstract following a preceding paper of tarasov and the second author we define and study a new structure which may be regarded as the dynamical analog of the weyl group for lie algebras and of the quantum weyl group for quantized enveloping algebras we give some applications of this new structure

semiparametric regression analysis of interval censored data with informative dropout interval censored data arise when the event time of interest can only be ascertained through periodic examinations in medical studies subjects may not complete the examination schedule for reasons related to the event of interest in this article we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval censored data specifically we propose a broad class of joint models under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect we consider nonparametric maximum likelihood estimation and develop an em algorithm that involves simple and stable calculations we prove that the resulting estimators of the regression parameters are consistent asymptotically normal and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood in addition we show how to consistently estimate the survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event furthermore we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies finally we provide an application to data on the incidence of diabetes from a major epidemiological cohort study

the analysis of current status data on point processes abstract this article considers the analysis of event count data in which each subject is observed at only one time point and no information is available on subjects between their entry time and observation points this type of data often referred to as current status data arises frequently for example in demography epidemiology and reliability studies statistical methods for the analysis of current status data from point processes are proposed specifically a statistic for testing the equality of the mean functions of point processes is presented and its asymptotic distribution obtained for illustration the proposed method is used to analyze multiple tumor data from a tumorgenicity experiment with focus on the comparison of tumor growth rates in male and female rats the adequacy of the asymptotic distribution of the test statistic is evaluated in a small simulation study power comparisons with the usual parametric model are also obtained finally some possible directions for further research

a nonparametric test for current status data with unequal censoring nonparametric tests for the comparison of different treatments based on current status data are proposed for this problem most methods proposed in the literature require that observation times on all subjects follow the same distribution in other words censoring distributions are identical between the treatment groups in this paper we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given the asymptotic distribution of the test proposed is derived the method proposed is applied to data arising from a tumorigenicity experiment

step algebras of quantum algebras of type a b and d we study the step algebras for the quantum algebras corresponding to the lie algebra pairs and

relative extremal projectors abstract this paper proves the existence of relative extremal projectors an infinite factorization is given as well as a summation formula

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

semiparametric transformation models for survival data with a cure fraction we propose a class of transformation models for survival data with a cure fraction the class of transformation models is motivated by biological considerations and includes both the proportional hazards and the proportional odds cure models as two special cases an efficient recursive algorithm is proposed to calculate the maximum likelihood estimators mles furthermore the mles for the regression coefficients are shown to be consistent and asymptotically normal and their asymptotic variances attain the semiparametric efficiency bound simulation studies are conducted to examine the finite sample properties of the proposed estimators the method is illustrated on data from a clinical trial involving the treatment of melanoma

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

mixture cure survival models with dependent censoring summary the paper is motivated by cure detection among the prostate cancer patients in the national institutes of health surveillance epidemiology and end results programme wherein the main end point e g deaths from prostate cancer and the censoring causes e g deaths from heart diseases may be dependent although many researchers have studied the mixture survival model to analyse survival data with non negligible cure fractions none has studied the mixture cure model in the presence of dependent censoring to account for such dependence we propose a more general cure model that allows for dependent censoring we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time by using a class of archimedean copula models within this framework we consider the parameter estimation the cure detection and the two sample comparison of latency distributions in the presence of dependent censoring when a proportion of patients is deemed cured large sample results by using martingale theory are obtained we examine the finite sample performance of the proposed methods via simulation and apply them to analyse the surveillance epidemiology and end results prostate cancer data