an extended hazard model with longitudinal covariates summary in clinical trials and other medical studies it has become increasingly common to observe an event time of interest and longitudinal covariates simultaneously in the literature joint modelling approaches have been employed to analyze both survival and longitudinal processes and to investigate their association early attention has mostly been placed on developing adaptive and flexible longitudinal processes based on a prespecified survival model most commonly the cox proportional model in this paper we propose a general class of semi parametric hazard regres

joint modelling of accelerated failure time and longitudinal data summary the accelerated failure time model is an attractive alternative to the cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates several complications arise when the covariates are measured intermittently at different time points for different subjects possibly with measurement errors or measurements are not available after the failure time joint modelling of the failure time and longitudinal data offers a solution to such complications we explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors the procedure is based on maximising the joint likelihood function with random effects treated as missing data a monte carlo em algorithm is used to estimate all the unknown parameters including the unknown baseline hazard function the performance of the proposed procedure is checked in simulation studies a case study of reproductive egg laying data for female mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure

wavefront propagation for reaction diffusion systems of pde m i freidlin has introduced probabilistic techniques to study propagation for systems of reaction diffusion pde the motivating idea is that should a reaction diffusion system possess only a single unstable and a single stable equilibrium then the solution u of the system will presumably tend to switch for large times from near the former to near the latter state this paper brings to bear purely pde techniques to this problem especially the theory of viscosity solutions on hamilton jacobi equations due to crandall lions

a bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time to event motivated by a real data example on renal graft failure we propose a new semiparametric multivariate joint model that relates multiple longitudinal outcomes to a time to event to allow for greater flexibility key components of the model are modelled nonparametrically in particular for the subject specific longitudinal evolutions we use a spline based approach the baseline risk function is assumed piecewise constant and the distribution of the latent terms is modelled using a dirichlet process prior formulation additionally we discuss the choice of a suitable parameterization from a practitioner s point of view to relate the longitudinal process to the survival outcome specifically we present three main families of parameterizations discuss their features and present tools to choose between them

semiparametric estimation of an accelerated failure time model with time dependent covariates summary a class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates a class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored these estimates are shown to be consistent and asymptotically normal with variances that can be consistently estimated it is also shown that estimators within this class achieve the semiparametric efficiency bound we consider an accelerated failure time model for time to event data in which the survival distribution is scaled by a factor which may be a function of time dependent covariates these models directly model the effect of covariates on the length of survival this is in contrast to the more commonly used proportional hazards model which models the hazard rate itself in some applications it may be easier to visualize the concept that a treatment intervention or exposure to an environmental contaminant increases or decreases the length of survival by a certain proportion as compared to the concept that the hazard rate is changed for time independent covariates say z z1 zp the class of accelerated failure time models assumes that the survival distribution at time t given a set of covariates z z is given by f t i z f0 h z t the proportionality constant h z can be interpreted as the scale factor by which lifetime is decreased as a function of the covariates z often h z is taken to be log linear or h z exp b z in such cases if z 0 we can interpret fo t as the baseline survival distribution or the survival distribution for individuals with covariates all equal to zero a useful way of envisioning this model is to consider a hypothetical random variable u that corresponds to an individual s survival time if that individual had covariate values all equal to zero this baseline failure time u would be modified for values of the covariate different than zero for example if we denote the actual survival time by t then for an individual with covariate value z we have t e zu the parameters b in this model have a direct interpretation in terms of the increase or decrease in lifespan as a function of the covariates the assumption that u is independent of z in this hypothetical construct induces the probabilistic model

a two part joint model for the analysis of survival and longitudinal binary data with excess zeros many longitudinal studies generate both the time to some event of interest and repeated measures data this article is motivated by a study on patients with a renal allograft in which interest lies in the association between longitudinal proteinuria a dichotomous variable measurements and the time to renal graft failure an interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria 1g day during follow up which introduces a degenerate part in the random effects density for the longitudinal process in this article we propose a two part shared parameter model framework that effectively takes this feature into account and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure

surjectivite de l application restriction a un compact dans des classes de fonctions ultradifferentiables etant donnee m p p 0 une suite de reels strictement positifs on considere la classe de carlemanc p m p resp beurlingb p m p des fonctionsf indefiniment derivables sur n soite un sous ensemble compact de n on peut associer a la classec p m p resp b p m p la classe des jets de whitney sure c e p m p resp b e p m p et on a une application de restriction naturelle dec p m p dansc e p m p resp b p m p dansb e p m p dans ce travail on donne des conditions sur deux suites m p p 0 et m p p 0 pour que l on ait les inclusions suivantes ou ceci est en quelque sorte une generalisation du probleme de prolongement de whitney

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

the singular limit of the allen cahn equation and the fitzhugh nagumo system abstract we consider an allen cahn type equation of the form u t u e 2 f e x t u where e is a small parameter and f e x t u f u e g e x t u a bistable nonlinearity associated with a double well potential whose well depths can be slightly unbalanced given a rather general initial data u 0 that is independent of e we perform a rigorous analysis of both the generation and the motion of interface more precisely we show that the solution develops a steep transition layer within the time scale of order e 2 ln e and that the layer obeys the law of motion that coincides with the formal asymptotic limit within an error margin of order e this is an optimal estimate that has not been known before for solutions with general initial data even in the case where g e 0 next we consider systems of reaction diffusion equations of the form u t u e 2 f e u v v t d v h u v which include the fitzhugh nagumo system as a special case given a rather general initial data u 0 v 0 we show that the component u develops a steep transition layer and that all the above mentioned results remain true for the u component of these systems

a semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error summary a common objective in longitudinal studies is to characterise the relationship between a failure time process and time independent and time dependent covariates timedependent covariates are generally available as longitudinal data collected periodically during the course of the study we assume that these data follow a linear mixed effects model with normal measurement error and that the hazard of failure depends both on the underlying random effects describing the covariate process and other time independent covariates through a proportional hazards relationship a routine assumption is that the random effects are normally distributed however this need not hold in practice within this framework we develop a simple method for estimating the proportional hazards model parameters that requires no assumption on the distribution of the random effects large sample properties are discussed and finite sample performance is assessed and compared to competing methods via simulation

linear continuous operators for the stieltjes moment problem in gelfand shilov spaces we obtain linear continuous operators providing a solution to the stieltjes moment problem in the framework of gelfand shilov spaces of rapidly decreasing smooth functions the construction rests on an interpolation procedure due to r estrada for general rapidly decreasing smooth functions and adapted by s y chung d kim and y yeom to the case of gelfand shilov spaces it requires a linear continuous version of the so called borel ritt gevrey theorem in asymptotic theory

a semiparametric joint model for longitudinal and survival data with application to hemodialysis study in many longitudinal clinical studies the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject s susceptibility to progression of the disease it is of scientific and clinical interest to relate such quantities to a later time to event clinical endpoint such as patient survival this is usually done with a shared parameter model in such models the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject level severity or susceptibility also called frailty in statistical terms in this article we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed effect model and the conditional distribution of the survival data is given by a cox proportional hazard model we allow unknown regression coefficients and time dependent covariates in both models the proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters an idea that originated from correction of covariate measurement error in measurement error models the corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators unlike most published methods for joint modeling the proposed estimation procedure does not rely on distributional assumptions of the frailties the proposed method was studied in simulations and applied to a data set from the hemodialysis study

ultradistributional boundary values of harmonic functions on the sphere abstract we present a theory of ultradistributional boundary values for harmonic functions defined on the euclidean unit ball we also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions to this end we obtain explicit estimates for partial derivatives of spherical harmonics which are of independent interest and refine earlier estimates by calderon and zygmund we apply our results to characterize the support of ultradistributions on the sphere via abel summability of their spherical harmonic expansions

sharp interface limit of the fisher kpp equation we investigate the singular limit as ep to 0 of the fisher equation partial t u ep delta u ep 1 u 1 u in the whole space we consider initial data with compact support plus possibly perturbations very small as vert x vert to infty by proving both generation and motion of interface properties we show that the sharp interface limit moves by a constant speed which is the minimal speed of some related one dimensional travelling waves we obtain an estimate of the thickness of the transition layers we also exhibit initial data lq lq not so small at infinity which do not allow the interface phenomena

on certain extension theorems in the mixed borel setting abstract given two sequences m 1 and m 2 of positive numbers we give necessary and sufficient conditions under which the inclusions m 1 f j 0 j n 0 f d m 2 1 1 m 1 f j 0 j n 0 f d m 2 1 1 hold by means of explicit constructions this answers a question raised by chaumat and chollet math ann 298 1994 7 40 we also consider the case when 1 1 is replaced by 1 1 m as well as the possibility to get ultraholomorphic extensions

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

monte carlo em estimation for time series models involving counts abstract the observations in parameter driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure these models result in very complex likelihoods and even the em algorithm which is usually well suited for problems of this type involves high dimensional integration in this article we discuss a monte carlo em mcem algorithm that uses a markov chain sampling technique in the calculation of the expectation in the e step of the em algorithm we propose a stopping criterion for the algorithm and provide rules for selecting the appropriate monte carlo sample size we show that under suitable regularity conditions an mcem algorithm will with high probability get close to a maximizer of the likelihood of the observed data we also discuss the asymptotic efficiency of the procedure we illustrate our monte carlo estimation method on a time series involving small counts the polio incidence time series previously analyzed by zeger

interface dynamics of the fisher equation with degenerate diffusion abstract we consider a degenerate parabolic reaction diffusion equation with a monostable nonlinearity arising in population dynamics in some suitable scaling limit we prove the generation and propagation of an interface with constant normal velocity in the case that the initial condition has a convex compact support

jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome in many clinical and epidemiologic studies periodically measured disease markers are used to monitor progression to the onset of disease motivated by a study of cd4 counts in men infected with human immunodeficiency virus hiv at risk for acquired immunodeficiency syndrome aids we developed a joint model for analysis of both longitudinal and event time data we use a longitudinal model for continuous data that incorporates a mean structure dependent on covariates a random intercept a stochastic process and measurement error a central component of the longitudinal model is an integrated ornstein uhlenbeck stochastic process which represents a family of covariance structures with a random effects model and brownian motion as special cases the regression model for the event time data is a proportional hazards model that includes the longitudinal marker as a time dependent variable and other covariates a markov chain monte carlo algorithm was developed for fitting the joint model the joint model

log convex sequences and nonzero proximate orders abstract summability methods for ultraholomorphic classes in sectors defined in terms of a strongly regular sequence m m p p n 0 have been put forward by a lastra s malek and the second author 10 and their validity depends on the possibility of associating to m a nonzero proximate order we provide several characterizations of this and other related properties in which the concept of regular variation for functions and sequences plays a prominent role in particular we show how to construct well behaved strongly regular sequences from nonzero proximate orders

dynamics of interfaces in the fisher kpp equation for slowly decaying initial data abstract this paper is concerned with the behavior of solutions of the fisher kpp equation when initial data decay slowly in space first we show by a comparison technique that the motion of an interface or a thin transition layer can be approximated as a level set of a first order pde of hamilton jacobi type then by the method of characteristics it is shown that various but not all motion of interfaces can be observed by taking initial data appropriately finally we study the large time behavior of solutions especially the existence of similarly expanding interfaces

convergence to a propagating front in a degenerate fisher kpp equation with advection abstract we consider a fisher kpp equation with density dependent diffusion and advection arising from a chemotaxis growth model we study its behavior as a small parameter related to the thickness of a diffuse interface tends to zero we analyze for small times the emergence of transition layers induced by a balance between reaction and drift effects then we investigate the propagation of the layers convergence to a free boundary limit problem is proved and a sharp estimate of the thickness of the layers is provided

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented