proportional means regression for censored medical costs summary the semiparametric proportional means model specifies that the mean function for the cumulative medical cost over time conditional on a set of covariates is equal to an arbitrary baseline mean function multiplied by an exponential regression function we demonstrate how to estimate the vector valued regression parameter using possibly censored lifetime costs the estimator is consistent and asymptotically normal with an easily estimable covariance matrix simulation studies show that the proposed methodology is appropriate for practical use an application to aids is provided

marcinkiewicz zygmund inequalities and interpolation by spherical harmonics abstract we find necessary density conditions for marcinkiewicz zygmund inequalities and interpolation for spaces of spherical harmonics in s d with respect to the l p norm moreover we prove that there are no complete interpolation families for p 2

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

estimating medical costs with censored data incompleteness of follow up data is a common problem in estimating medical costs naive analysis using summary statistics on the collected data can result in severely misleading statistical inference this paper focuses on the problem of estimating the mean medical cost from a sample of individuals whose medical costs may be right censored a class of weighted estimators which account appropriately for censoring are introduced our estimators are shown to be consistent and asymptotically normal with easily estimated variances the efficiency of these estimators is studied with the goal of finding as efficient an estimator for the mean medical cost as is feasible extensive simulation studies are used to show that our estimators perform well in finite samples even with heavily censored data for a variety of circumstances the methods are applied to a set of cost data from a cardiology trial conducted by the duke university medical center extensions to other censored data problems are also discussed

temporal process regression summary we consider regression for response and covariates which are temporal processes observed over intervals a functional generalised linear model is proposed which includes extensions of standard models in multi state survival analysis simple nonparametric esti mators of time indexed parameters are developed using working independence estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes the procedure does not require smoothing or a markov assumption unlike approaches based on transition intensities the usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy the estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters providing novel goodness of fit tests the methodology s practical utility is illustrated in a data analysis

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

bootstrap confidence intervals for medical costs with censored observations medical costs data with administratively censored observations often arise in cost effectiveness studies of treatments for life threatening diseases mean of medical costs incurred from the start of a treatment until death or a certain time point after the implementation of treatment is frequently of interest in many situations due to the skewed nature of the cost distribution and non uniform rate of cost accumulation over time the currently available normal approximation confidence interval has poor coverage accuracy in this paper we propose a bootstrap confidence interval for the mean of medical costs with censored observations in simulation studies we show that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution when there is light censoring on medical costs 25 per cent we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy for heavily censored cost data censoring rate 30 per cent with larger sample sizes n 200 the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy we also illustrate the use of our methods in a real example

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

model checking techniques based on cumulative residuals depuis longtemps on utilise les residus pour apprecier graphiquement et muneriquement l adequation de modeles de regression l analyse conventionnelle des residus fondee sur les graphes des residus bruts ou des courbes lissees est eminemment subjective tandis que la plupart des tests numeriques d ajustement informent peu sur la nature de l inadequation nous developpons des techniques d examen d un modele objectives et informatives qui reposent soit sur les sommes des residus cumulees selon certaines coordonnees comme une covariable on le predicteur lineaire soit sur des regroupements partiels sommes ou moyennes mobiles selon ces coordonnees pour une grande variete de modeles statistiques et de structures des observations dont les modeles lineaires generalises sur observations independantes ou correlees les distributions de ces processus stochastiques sous le modele postule peuvent etre approchees par des processus gaussiens centres faciles a simuler on pent done comparer graphiquement et numeriquement chaque processus observe a une serie de realisations du ment chaque processus observe a une serie de realisations du processus gaussien ces comparaisons permettent d evaluer objectivement dans quelle mesure une tendance observee sur un graphique serait attribuable a une mauvaise specification du modele plutot qu aux fluctuations d echantillonnage ces techniques sont particulierement utiles pour l examen de la fonction de lien ou de la forme fonctionnelle d une covariable plusieurs exemples medicaux illustrent cette approche

efficient estimation of the distribution of quality adjusted survival time quality of life is an important aspect in evaluation of clinical trials of chronic diseases such as cancer and aids quality adjusted survival analysis is a method that combines both the quantity and quality of a patient s life into one single measure in this paper we discuss the efficiency of weighted estimators for the distribution of quality adjusted survival time using the general representation theorem for missing data processes we are able to derive an estimator that is more efficient than the one proposed in zhao and tsiatis 1997 biometrika 84 339 348 simulation experiments are conducted to assess the small sample properties of this estimator and to compare it with the semiparametric efficiency bound the value of this estimator is demonstrated from an application of the method to a data set obtained from a breast cancer clinical trial

probabilistic index models summary we present a semiparametric statistical model for the probabilistic index which can be defined as p y y a where y and y a are independent random response variables associated with covariate patterns x and x a respectively a link function defines the relationship between the probabilistic index and a linear predictor asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory the model is illustrated with several examples and the estimation theory is validated in a simulation study

empirical likelihood confidence intervals for nonparametric density estimation summary we suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x this suggestion arises from a simulation study which shows that confidence intervals produced by the kernel based percentle t bootstrap do not have the coverage claimed by the theory this coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by the percentile t method empirical likelihood avoids this conflict by studentising internally we show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy of the same order of magnitude as the bootstrap and which are also empirically more accurate

semiparametric modeling and estimation of the terminal behavior of recurrent marker processes before failure events abstractrecurrent event processes with marker measurements are mostly and largely studied with forward time models starting from an initial event interestingly the processes could exhibit important terminal behavior during a time period before occurrence of the failure event a natural and direct way to study recurrent events prior to a failure event is to align the processes using the failure event as the time origin and to examine the terminal behavior by a backward time model this article studies regression models for backward recurrent marker processes by counting time backward from the failure event a three level semiparametric regression model is proposed for jointly modeling the time to a failure event the backward recurrent event process and the marker observed at the time of each backward recurrent event the first level is a proportional hazards model for the failure time the second level is a proportional rate model for the recurrent events occurring before the failure event and the thi

semi parametric regression models for cost effectiveness analysis improving the efficiency of estimation from censored data in a cost effectiveness analysis using clinical trial data estimates of the between treatment difference in mean cost and mean effectiveness are needed several methods for handling censored data have been suggested one of them is inverse probability weighting and has the advantage that it can also be applied to estimate the parameters from a linear regression of the mean such regression models can potentially estimate the treatment contrast more precisely since some of the residual variance can be explained by baseline covariates the drawback however is that inverse probability weighting may not be efficient using existing results on semi parametric efficiency this paper derives the semi parametric efficient parameter estimates for regression of mean cost mean quality adjusted survival time and mean survival time the performance of these estimates is evaluated through a simulation study applying both the new estimators and the inverse probability weighted estimators to the results of the evaluate trial showed that the new estimators achieved a halving of the variance of the estimated treatment contrast for cost some practical suggestions for choosing an estimator are offered

polynomial interpolation and marcinkiewicz zygmund inequalities on the unit circle abstract the objective of this paper is to derive an intimate relationship among three important mathematical tools namely polynomial interpolation marcinkiewicz zygmund inequalities and a p weights in particular it is shown that minimum separation of sample points on the unit circle together with certain uniform a p weights generated by these sample points constitute a necessary and sufficient condition for the validity of the marcinkiewicz zygmund inequality evaluated at these points which in turn is equivalent to the jackson type estimate using the popov andreev module of continuity of polynomial interpolation again at these sample points

estimating medical costs from incomplete follow up data estimation of the average total cost for treating patients with a particular disease is often complicated by the fact that the survival times are censored on some study subjects and their subsequent costs are unknown the naive sample average of the observed costs from all study subjects or from the uncensored cases only can be severely biased and the standard survival analysis techniques are not applicable to minimize the bias induced by censoring we partition the entire time period of interest into a number of small intervals and estimate the average total cost either by the sum of the kaplan meier estimator for the probability of dying in each interval multiplied by the sample mean of the total costs from the observed deaths in that interval or by the sum of the kaplan meier estimator for the probability of being alive at the start of each interval multiplied by an appropriate estimator for the average cost over the interval conditional on surviving to the start of the interval the resultant estimators are consistent if censoring occurs solely at the boundaries of the intervals in addition the estimators are asymptotically normal with easily estimated variances extensive numerical studies show that the asymptotic approximations are adequate for practical use and the biases of the proposed estimators are small even when censoring may occur in the interiors of the intervals an ovarian cancer study is provided

quantifying the totality of treatment effect with multiple event time observations in the presence of a terminal event from a comparative clinical study to evaluate the totality of one treatment s benefit risk profile relative to an alternative treatment via a longitudinal comparative clinical study the timing and occurrence of multiple clinical events are typically collected during the patient s follow up these multiple observations reflect the patient s disease progression burden over time the standard practice is to create a composite endpoint from the multiple outcomes the timing of the occurrence of the first clinical event to evaluate the treatment via the standard survival analysis techniques by ignoring all events after the composite outcome this type of assessment may not be ideal various parametric or semiparametric procedures have been extensively discussed in the literature for the purposes of analyzing multiple event time data many existing methods were developed based on extensive model assumptions when the model assumptions are not plausible the resulting inferences for the treatment effect may be misleading in this article we propose a simple nonparametric inference procedure to quantify the treatment effect which has an intuitive clinically meaningful interpretation we use the data from a cardiovascular clinical trial for heart failure to illustrate the procedure a simulation study is also conducted to evaluate the performance of the new proposal

survival models for cost data the forgotten additive approach the usage of the aalen additive approach is proposed to model cost data using a monte carlo simulation in a wide set of scenarios we showed that the aalen model is performing well and can be a reasonable alternative to the standard gamma regression models in addition with reference to the costami trial data we highlighted the ability of the aalen model to offer additional information about the relationships between costs and specific covariates as compared with standard regression techniques

regression analysis of incomplete medical cost data the accumulation of medical cost over time for each subject is an increasing stochastic process defined up to the instant of death the stochastic structure of this process is complex in most applications the process can only be observed at a limited number of time points furthermore the process is subject to right censoring so that it is unobservable after the censoring time these special features of the medical cost data especially the presence of death and censoring pose major challenges in the construction of plausible statistical models and the development of the corresponding inference procedures in this paper we propose several classes of regression models which formulate the effects of possibly time dependent covariates on the marginal mean of cost accumulation in the presence of death or on the conditional means of cost accumulation given specific survival patterns we then develop estimating equations for these models by combining the approach of generalized estimating equations for longitudinal data with the inverse probability of censoring weighting technique the resultant estimators are shown to be consistent and asymptotically normal with simple variance estimators simulation studies indicate that the proposed inference procedures behave well in practical situations an application to data taken from a large cancer study reveals that the medicare enrollees who are diagnosed with less aggressive ovarian cancer tend to accumulate medical cost at lower rates than those with more aggressive disease but tend to have higher lifetime costs because they live longer

estimating mean cost using auxiliary covariates we study the estimation of mean medical cost when censoring is dependent and a large amount of auxiliary information is present under missing at random assumption we propose semiparametric working models to obtain low dimensional summarized scores an estimator for the mean total cost can be derived nonparametrically conditional on the summarized scores we show that when either the two working models for cost survival process or the model for censoring distribution is correct the estimator is consistent and asymptotically normal small sample performance of the proposed method is evaluated via simulation studies finally our approach is applied to analyze a real data set in health economics

semiparametric estimation of marginal mark distribution in many applications the outcome of interest is a mark such that its observation is contingent upon occurrence of an event with incomplete follow up data the marginal mark distribution is however nonparametrically nowhere identifiable in many practical situations to address this problem we suggest a semiparametric model that postulates a normal copula for the association between the mark and survival time but leaves the marginals unspecified we show identifiability of the marginal mark distribution under this model and propose an inference procedure the estimated marginal distribution function is consistent and asymptotically normal and it provides a basis for estimating summaries of the mark furthermore we propose graphical model checking methods and kolmogorov smirnov type goodness of fit tests simulation studies demonstrate that the inference procedure performs well in practical settings the method is applied to the estimation of lifetime medical cost in a lung cancer trial

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

classical bounded and almost periodic solutions to quasilinear first order hyperbolic systems in a strip abstract we consider boundary value problems for quasilinear first order one dimensional hyperbolic systems in a strip the boundary conditions are supposed to be of a smoothing type in the sense that the l 2 generalized solutions to the initial boundary value problems become eventually c 2 smooth for any initial l 2 data we investigate small global classical solutions and obtain the existence and uniqueness result under the condition that the evolution family generated by the linearized problem has exponential dichotomy on r we prove that the dichotomy survives under small perturbations in the leading coefficients of the hyperbolic system assuming that the coefficients of the hyperbolic system are almost periodic we prove that the bounded solution is almost periodic also

joint regression analysis of survival and quality adjusted survival summary in this paper a semiparametric bivariate linear regression model for survival and quality adjusted survival is investigated even with a parametric specification for the joint distribution maximum likelihood is not applicable because of induced informative censoring we propose inference procedures based on estimating functions the estimators are consistent and asymptotically normal hypothesis tests and confidence intervals may be constructed with easy to implement resampling techniques simultaneous regression modeling of survival and quality adjusted survival has not been studied formally our methodology gives parameter estimates that are highly interpretable in the context of a cost effectiveness analysis the usefulness of the proposal is illustrated with a breast cancer dataset

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

smooth quantile ratio estimation in a study of health care expenditures attributable to smoking we seek to compare the distribution of medical costs for persons with lung cancer or chronic obstructive pulmonary disease cases to those without controls using a national survey which includes hundreds of cases and thousands of controls the distribution of costs is highly skewed toward larger values making estimates of the mean from the smaller sample dependent on a small fraction of the biggest values one approach to deal with the smaller sample is to rely on a simple parametric model such as the log normal but this makes the undesirable assumption that the distribution of the log expenditures is symmetric we propose a novel approach to estimate the mean difierence of two highly skewed distributions which we call smooth quantile ratio estimation square square is obtained by smoothing over percentiles the ratio of the cost quantiles of the cases and controls square deflnes a large class of estimators of including 1 the sample mean difference 2 the maximum likelihood estimate under log normal samples and 3 l estimates we detail asymptotic properties of square such as consistency and asymptotic normality and also provide a closed form expression for the asymptotic variance through a simulation study we show that square has lower mean squared error than several competitors including the sample mean difierence and log normal parametric estimates in several realistic situations we apply square to the 1987 national medicare expenditure survey to estimate the difierence in medical expenditures between persons sufiering from the smoking attributable diseases lung cancer and chronic obstructive pulmonary disease and persons without these diseases software in r ihaka and gentleman 1996 for the implementation of square and of all its special cases and the cost data used in this paper are available at http biostat jhsph edu fdominic square html

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

the generalized marcinkiewicz zygmund inequality for trigonometric polynomials abstract the well known marcinkiewicz zygmund inequality 0 2x t x p dx 1 p a p 1 n k 0 2n t 2k 2n 1 p 1 p 1 where t is a trigonometric polynomial of degree n and ap depends on p only will be generalized to have the right hand side containing the derivative values as well the results will then be applied to prove the mean convergence of the hermite interpolation by trigonometric polynomials on equidistant nodes

a consistent estimator for the distribution of quality adjusted survival time summary quality adjusted survival analysis is a new approach to therapy evaluation in clinical trials it has received much attention recently because of its ability to take patients quality of life into consideration in this paper we present a method that enables us to calculate the survival distribution of quality adjusted lifetime using martingale theory for counting processes we can show that our estimator is asymptotically consistent normally distributed and its asymptotic variance estimate can be obtained analytically simulation experiments are conducted to compare our estimator with the true underlying distribution for two cases that are of practical importance

smoothed empirical likelihood confidence intervals for quantiles standard empirical likelihood confidence intervals for quantiles are identical to sign test intervals they have relatively large coverage error of size n 1 2 even though they are two sided intervals we show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order n 1 and may be bartlett corrected to produce intervals with an error of order only n 2 necessary and sufficient conditions on the smoothing parameter in order for these sizes of error to be attained are derived the effects of smoothing on the positions of endpoints of the intervals are analysed and shown to be only of second order

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

empirical likelihood inference for the area under the roc curve for a continuous scale diagnostic test the most commonly used summary index of the receiver operating characteristic curve roc is the area under the curve auc that measures the accuracy of the diagnostic test in this article we propose an empirical likelihood el approach for the inference on the auc first we define an el ratio for the auc and show that its limiting distribution is a scaled chi square distribution we then obtain an el based confidence interval for the auc using the scaled chi square distribution this el inference for the auc can be extended to stratified samples and the resulting limiting distribution is a weighted sum of independent chi square distributions additionally we conduct simulation studies to compare the relative performance of the proposed el based interval with the existing normal approximation based intervals and bootstrap intervals for the auc

empirical likelihood based confidence intervals for mean medical cost with censored data in this paper we propose empirical likelihood methods based on influence function and jackknife techniques for constructing confidence intervals for mean medical cost with censored data we conduct a simulation study to compare the coverage probabilities and interval lengths of our proposed confidence intervals with that of the existing normal approximation based confidence intervals and bootstrap confidence intervals the proposed methods have better finite sample performances than existing methods finally we illustrate our proposed methods with a relevant example

nonparametric estimation of the joint distribution of survival time and mark variables summary in many applications variables of interest are marks of the endpoint which are not observed when the survival time is censored this paper focuses on nonparametric estimation of the joint distribution and summaries of survival time and mark variables we establish a representation of the joint distribution function through the cumulative markspecific hazard function which is analogous to the product integral representation of univariate survival function we identify a basic data structure common to various applications propose nonparametric estimators and show that they maximise the likelihood we formulate the problem in the marked point process framework and study both finite and large sample properties of the estimators we show that the joint distribution function estimator is nearly unbiased uniformly strongly consistent and asymptotically normal we also derive asymptotic variances for the estimators and propose sample based variance estimates numerical studies demonstrate that both the estimators and their variance estimates perform well for practical sample sizes we outline an application strategy

confidence bands for survival curves under the proportional hazards model summary in this paper we show how to construct simultaneous confidence bands for the subjectspecific survival curve under the cox proportional hazards model the idea is to approximate the distribution of the normalized cumulative hazard estimator by a zero mean gaussian process whose distribution can be easily generated through simulation numerical studies indicate that the proposed bands are appropriate for practical use a liver disease example is presented

on perturbations of delay differential equations with periodic orbits abstract equations of retarded type and simple neutral type equations are considered the study concerns both autonomous and non autonomous perturbations of an autonomous equation which possesses a non trivial periodic orbit the main tool is a local coordinate system around the periodic orbit which is obtained from the phase space decomposition via floquet multipliers under the assumption that the perturbation function is lipschitz the existence of an integral manifold with periodic structure for the system in the new coordinates is shown this implies that under autonomous perturbations periodic orbits are continued furthermore we give a description of the flow on the center manifold of the periodic orbit

plausibility functions and exact frequentist inference in the frequentist program inferential methods with exact control on error rates are a primary focus the standard approach however is to rely on asymptotic approximations which may not be suitable this article presents a general framework for the construction of exact frequentist procedures based on plausibility functions it is shown that the plausibility function based tests and confidence regions have the desired frequentist properties in finite samples no large sample justification needed an extension of the proposed method is also given for problems involving nuisance parameters examples demonstrate that the plausibility function based method is both exact and efficient in a wide variety of problems

exponential dichotomies of linear dynamic equations on measure chains under slowly varying coefficients unifying ordinary differential and difference equations we consider linear dynamic equations on measure chains or time scales which possess an exponential dichotomy uniformly in a parameter and show that this dichotomy is robust if the mentioned parameter changes slowly in time here the equations can be infinite dimensional and are not assumed to be invertible

a confidence interval for the median survival time a nonparametric asymptotic confidence interval for the median survival time is developed for the case where data are subject to arbitrary right censoring this is accomplished by inverting a generalization of the sign test for censored data a simulation study shows that this nonparametric confidence interval performs well for a variety of underlying survival functions the procedure is applied to data from a clinical trial that compared f our dosage regimens of 5 uorouracil

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

constrained empirical likelihood confidence regions in nonignorable covariate missing data problems missing covariates in regression analysis are a pervasive problem in medical social and economic researches we study empirical likelihood confidence regions for unconstrained and constrained regression parameters in a nonignorable covariate missing data problem for an assumed conditional mean regression model we assume that some covariates are fully observed but other covariates are missing for some subjects by exploitation of a probability model of missingness and a working conditional score model from a semiparametric perspective we build a system of unbiased estimating equations where the number of equations exceeds the number of unknown parameters based on the proposed estimating equations we introduce unconstrained and constrained empirical likelihood ratio statistics to construct empirical likelihood confidence regions for the underlying regression parameters without and with constraints we establish the asymptotic distributions of the proposed empirical likelihood ratio statistics simulation results show that the proposed empirical likelihood methods have a better finite sample performance than other competitors in terms of coverage probability and interval length finally we apply the proposed empirical likelihood methods to the analysis of a data set from the us national health and nutrition examination survey

a survey on mean convergence of interpolatory processes abstract a detailed account of what happened in the theory of mean convergence of lagrange and hermite fejer type interpolation in the last fifty five years is given starting from the classical result of erd s and turan hopefully all important developments are considered in some cases with an indication of the method of proof even some yet unpublished results are included a list of references helps to orientate those interested in the details

the two sample problem with induced dependent censorship summary induced dependent censorship is a general phenomenon in health service evaluation studies in which a measure such as quality adjusted survival time or lifetime medical cost is of interest we investigate the two sample problem and propose two classes of nonparametric tests based on consistent estimation of the survival function for each sample the two classes of test statistics examine the cumulative weighted difference in hazard functions and in survival functions we derive a unified asymptotic null distribution theory and inference procedure the tests are applied to trial v of the international breast cancer study group and show that long duration chemotherapy significantly improves time without symptoms of disease and toxicity of treatment as compared with the short duration treatment simulation studies demonstrate that the proposed tests with a wide range of weight choices perform well under moderate sample sizes

evaluating utility measurement from recurrent marker processes in the presence of competing terminal events abstractin follow up studies utility marker measurements are usually collected upon the occurrence of recurrent events until a terminal event such as death takes place in this article we define the recurrent marker process to characterize utility accumulation over time for example with medical cost and repeated hospitalizations being treated as marker and recurrent events respectively the recurrent marker process is the trajectory of cumulative cost which stops to increase after death in many applications competing risks arise as subjects are at risk of more than one mutually exclusive terminal event such as death from different causes and modeling the recurrent marker process for each failure type is often of interest however censoring creates challenges in the methodological development because for censored subjects both failure type and recurrent marker process after censoring are unobserved to circumvent this problem we propose a nonparametric framework for the recurrent marker proce

jackknife empirical likelihood empirical likelihood has been found very useful in many different occasions however when applied directly to some more complicated statistics such as u statistics it runs into serious computational difficulties in this paper we introduce a so called jackknife empirical likelihood jel method the new method is extremely simple to use in practice in particular the jel is shown to be very effective in handling one and two sample u statistics the jel can be potentially useful for other nonlinear statistics

a simple nonparametric estimator of the bivariate survival function under univariate censoring summary in the presence of univariate censoring the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at risk probability to the survival function of the censoring time the use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve the estimator is strongly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied

a perturbation theorem for exponential dichotomies suppose the linear equation x a t x has an exponential dichotomy and suppose b t is close to a t in the following sense on any interval of length 2t b t is close to some translate a t of a t actually the conditions in the paper are slightly weaker than this then if t is sufficiently large the equation y b t y also has an exponential dichotomy this generalises the usual roughness theorem for exponential dichotomies

penalized high dimensional empirical likelihood we propose penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models by using an appropriate penalty function we showthat penalized empirical likelihood has the oracle property that is with probability tending to 1 penalized empirical likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance the advantage of penalized empirical likelihood as a nonparametric likelihood approach is illustrated by testing hypotheses and constructing confidence regions numerical simulations confirm our theoretical findings

on the compuation of lyapunov exponents for continuous dynamical systems in this paper we consider discrete and continuous qr algorithms for computing all of the lyapunov exponents of a regular dynamical system we begin by reviewing theoretical results for regular systems and present general perturbation results for lyapunov exponents we then present the algorithms give an error analysis of them and describe their implementation finally we give several numerical examples and some conclusions

statistical methods for multivariate interval censored recurrent events multi type recurrent event data arise when two or more different kinds of events may occur repeatedly over a period of observation the scientific objectives in such settings are often to describe features of the marginal processes and to study the association between the different types of events interval censored multi type recurrent event data arise when the precise event times are unobserved but intervals are available during which the events are known to have occurred this type of data is common in studies of patients with advanced cancer for example where the events may represent the development of different types of metastatic lesions which are only detectable by conducting bone scans of the entire skeleton in this setting it is of interest to characterize the incidence of the various types of bone lesions to estimate the impact of treatment and other covariate effects on the development of new lesions and to understand the relationship between the processes generating the bone lesions we develop joint models for multi type interval censored recurrent events which accommodate dependencies between different types of events and enable one to examine the covariate effects via regression however since the marginal likelihood resulting from the multivariate random effect model is intractable we describe a gibbs sampling algorithm to facilitate model fitting and inference we use generalized estimating equations for estimation and inference based on marginal models the finite sample properties of the marginal approach are studied via simulation the estimates of both the regression coefficients and the variance covariance parameters are shown to have negligible bias and 95 per cent confidence intervals based on the asymptotic variance formula are shown to have excellent empirical coverage probabilities in all of the settings considered the application of these methods to data from a trial of women with advanced breast cancer provides insight into the clinical course of bone metastases in this population

median regression with censored cost data because of the skewness of the distribution of medical costs we consider modeling the median as well as other quantiles when establishing regression relationships to covariates in many applications the medical cost data are also right censored in this article we propose semiparametric procedures for estimating the parameters in median regression models based on weighted estimating equations when censoring is present numerical studies are conducted to show that our estimators perform well with small samples and the resulting inference is reliable in circumstances of practical importance the methods are applied to a dataset for medical costs of patients with colorectal cancer

double robust estimator of average causal treatment effect for censored medical cost data in observational studies estimation of average causal treatment effect on a patient s response should adjust for confounders that are associated with both treatment exposure and response in addition the response such as medical cost may have incomplete follow up in this article a double robust estimator is proposed for average causal treatment effect for right censored medical cost data the estimator is double robust in the sense that it remains consistent when either the model for the treatment assignment or the regression model for the response is correctly specified double robust estimators increase the likelihood the results will represent a valid inference asymptotic normality is obtained for the proposed estimator and an estimator for the asymptotic variance is also derived simulation studies show good finite sample performance of the proposed estimator and a real data analysis using the proposed method is provided as illustration copyright 2016 john wiley sons ltd

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

on roughness of exponential dichotomy we present new perturbation theorems on the roughness of exponential dichotomy which improve previous results the proofs given here are also much simpler compared with previous ones the new results provide significant improvements of existing results in the case where the operator a t is unbounded for t j this is precisely the situation that is of interest from the point of view of the applications in lobe dynamics the results are also valid in banach spaces and useful for general purposes

qualms about bootstrap confidence intervals abstract the percentile method and bias corrected percentile method of efron 1981 1982 are discussed when these methods are used to construct nonparametric confidence intervals for the variance of a normal distribution the coverage probabilities are substantially below the nominal level for small to moderate samples this is due to the inapplicability of assumptions underlying the methods these assumptions are difficult or impossible to check in the complicated situations for which the bootstrap is intended therefore bootstrap confidence intervals should be used with caution in complex problems

exponential dichotomy on the real line svd and qr methods abstract in this work we show when and how techniques based on the singular value decomposition svd and the qr decomposition of a fundamental matrix solution can be used to infer if a system enjoys or not exponential dichotomy on the whole real line

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

empirical likelihood confidence intervals for local linear smoothers summary empirical likelihood is considered in conjunction with the local linear smoother to construct confidence intervals for a nonparametric regression function with bounded support the coverage error of the empirical likelihood confidence intervals is evaluated and is shown to be of the same order throughout the support of the regression function this is a significant improvement over confidence intervals based directly on the asymptotic normal distribution of the local linear estimator which have a larger order of coverage error near the boundary this improvement is attributable to the natural variance estimator that empirical likelihood implicitly chooses for the local linear smoother

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

estimating the mean of an increasing stochastic process at a censored stopping time abstract data often come in the form of a longitudinal series say n whose observation has been stopped either by a terminal event u e g death or censoring event c e g lost to follow up when n is not deterministic it is generally not possible to use standard survival analysis tools e g the kaplan meier estimator to consistently estimate functionals of the distribution of n u because of induced informative censoring various seemingly unrelated estimators recently have been proposed to handle this difficulty within the context of specific problems ranging from the analysis of quality adjusted survival data to recurrent event data to lifetime medical cost data in this article i consider a general framework containing each of these specific examples as a special case propose a class of estimators for the mean of the stopped longitudinal process and establish the asymptotic properties of this class of estimators connections between the aforementioned estimators are established

on lagrange interpolation at disturbed roots of unity let z nk e itnk 0 t n0 0 such that l n f f p 0 f 1 n whenever n p n 1 it must be emphasized that p necessarily depends on p in the sense that there exists a family z nk k 0 n with n 2 n 1 and such that l n f f 2 o f 1 n for all f a but sup l n f p f a f 1 diverges for sufficiently large values of p