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

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

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

on the cohen macaulay type of s lines in an 1 abstract let a be the coordinate ring of s lines through the origin in a n 1 k we discuss what it means for these lines to be in sufficiently general position and then with this restriction on the lines we attempt to verify our belief that the cohen macaulay type of a depends only on s and n we characterize those s and n for which a is a gorenstein ring i e of c m type 1 and explicitly calculate the cohen macaulay type in several other cases we then extend some of our results to the case of an arbitrary reduced curve whose tangent cone consists of lines in sufficiently general position finally we calculate the hubert samuel polynomials of the curves we have been considering

weak galerkin finite element methods for darcy flow anisotropy and heterogeneity this paper presents a family of weak galerkin finite element methods wgfems for darcy flow computation the wgfems are new numerical methods that rely on the novel concept of discrete weak gradients the wgfems solve for pressure unknowns both in element interiors and on the mesh skeleton the numerical velocity is then obtained from the discrete weak gradient of the numerical pressure the new methods are quite different than many existing numerical methods in that they are locally conservative by design the resulting discrete linear systems are symmetric and positive definite and there is no need for tuning problem dependent penalty factors we test the wgfems on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in darcy flow

the poincare series of the module of derivations of affine monomial curves abstract let a be a graded k algebra and m be a finitely generated a module the poincare series p m a z is the formal power series i dim k tor i a k m z i we study the poincare series of der k k s the module of derivations of a numerical semigroup ring k s and we relate it to the poincare series of k over k s and to the type of s we then use this in order to determine the poincare series of der k k s or at least its rationality for some classes of examples we finally give an example of a non rational p der k k s k s z

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

on a conjecture by wilf about the frobenius number given coprime positive integers a 1 cdots a d the frobenius number f is the largest integer which is not representable as a non negative integer combination of the a i let g denote the number of all non representable positive integers wilf conjectured that d ge frac f 1 f 1 g we prove that for every fixed value of lceil frac a 1 d rceil the conjecture holds for all values of a 1 which are sufficiently large and are not divisible by a finite set of primes we also propose a generalization in the context of one dimensional local rings and a question on the equality d frac f 1 f 1 g

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

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

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

invariants associated with ideals in one dimensional local domains let r be a one dimensional local noetherian domain with maximal ideal m quotient field k and residue field r m k we assume that the integral closure r of r in its quotient field k is a dvr and a finite r module we assume also that the field k is isomorphic to the residue field of r for i a proper ideal of r denote the inverse of i by i that is i is the set r ki of elements of k that multiply i into r we investigate two numerical invariants associated to a proper ideal i of r that have previously come up in the literature from various points of view the two invariants are 1 the difference between the composition lengths of i r and r i and 2 the difference between the product when the composition length of r i is multiplied by the composition length of m r and the length of i r we show that these two differences can be expressed in terms of the type sequence of r a finite sequence of positive integers related to the natural valuation inherited from r

accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities the accuracy of the darcy velocity flux and stream function computed from lowest order triangle based control volume and mixed finite element approximations to the two dimensional pressure equation is considered the control volume finite element method similar to integrated finite difference methods and analogous to the interpolation of galerkin finite element results over control volumes is shown to yield a conservative velocity field and smooth streamlines the streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method which approximates the pressure and velocity variables separately it is shown that for systems with only moderate degrees of heterogeneity the control volume finite element method is the more computationally efficient alternative i e it provides more accurate flow results for a given number of unknowns for more variable or discontinuous permeability fields by contrast such as sand shale systems the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns

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

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

a stable weak galerkin finite element method for stokes problem abstract we study the weak galerkin finite element method for stokes problem a new weak galerkin finite element velocity pressure space pair is presented which satisfies the discrete inf sup condition based on this space pair we establish a stable weak galerkin approximation scheme without adding any stability term or penalty term then we further derive the optimal error estimates for velocity and pressure approximations respectively numerical experiments are provided to illustrate the theoretical analysis

a locally conservative finite element method based on piecewise constant enrichment of the continuous galerkin method this paper presents a locally conservative finite element method based on enriching the approximation space of the continuous galerkin method with elementwise constant functions the proposed method has a smaller number of degrees of freedom than the discontinuous galerkin method numerical examples on coupled flow and transport in porous media are provided to illustrate the advantages of this method we also present a theoretical analysis of the method and establish optimal convergence of numerical solutions

one dimensional local rings of maximal and almost maximal length let a m k denote a one dimensional cohen macaulay local ring with maximal ideal m and residue class field k we assume a is a reduced excellent local ring which has a canonical module a with no loss of generality we can also assume k is infinite let denote the integral closure of a in its total quotient ring q and let b denote the conductor of a in a has maximal length if la aa la ab t a here t a denotes the cohen macaulay type of a and la denotes the length of the a module a has almost maximal length if la aa la ab t a 1 the two main results of this paper are as follows a has maximal length if and only if either a is gorenstein or there exists an x m and a positive integer p such that m x b andba xpa let e a denote the multiplicity of a then a has almost maximal length and 1 t a e a if and only if there exists a transversal x of m such that m x b and la bxpa 1 here p min i xi b these two theorems generalize more specific results for semigroup rings obtained in brown and curtis numerical semigroups of maximal and almost maximal length semigroup forum vol 42 springer verlag berlin new york 1991 219 235

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

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

a weak galerkin finite element method for second order elliptic problems this paper introduces a finite element method by using a weakly defined gradient operator over generalized functions the use of weak gradients and their approximations results in a new concept called discrete weak gradients which is expected to play an important role in numerical methods for partial differential equations this article intends to provide a general framework for managing differential operators on generalized functions as a demonstrative example the discrete weak gradient operator is employed as a building block in the design of numerical schemes for a second order elliptic problem in which the classical gradient operator is replaced by the discrete weak gradient the resulting numerical scheme is called a weak galerkin wg finite element method it can be seen that the weak galerkin method allows the use of totally discontinuous functions in the finite element procedure for the second order elliptic problem an optimal order error estimate in both a discrete h 1 and l 2 norms are established for the corresponding weak galerkin finite element solutions a superconvergence is also observed for the weak galerkin approximation

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

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

a comparative study on the weak galerkin discontinuous galerkin and mixed finite element methods this paper presents a comparative study on the newly introduced weak galerkin finite element methods wgfems with the widely accepted discontinuous galerkin finite element methods dgfems and the classical mixed finite element methods mfems for solving second order elliptic boundary value problems we examine the differences similarities and connection among these methods in scheme formulations implementation strategies accuracy and computational cost the comparison and numerical experiments demonstrate that wgfems are viable alternatives to mfems and hold some advantages over dgfems due to their properties of local conservation normal flux continuity no need for penalty factor and definiteness of discrete linear systems

estimation of penalty parameters for symmetric interior penalty galerkin methods this paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty galerkin methods in particular we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements numerical examples in all dimensions and for different polynomial degrees are presented we show the numerical effects of loss of coercivity

locally conservative fluxes for the continuous galerkin method the standard continuous galerkin cg finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations a much needed quantity in many applications we show how to overcome this shortcoming by using a two step postprocessing the first step is the computation of a numerical flux trace defined on element interfaces and is motivated by the structure of the numerical traces of discontinuous galerkin methods this computation is nonlocal in that it requires the solution of a symmetric positive definite system but the system is well conditioned independently of mesh size so it can be solved at asymptotically optimal cost the second step is a local element by element postprocessing of the cg solution incorporating the result of the first step this leads to a conservative flux approximation with continuous normal components this postprocessing applies for the cg method in its standard form or for a hybridized version of it we present the hybridized version since it allows easy handling of variable degree polynomials and hanging nodes furthermore we provide an a priori analysis of the error in the postprocessed flux approximation and display numerical evidence suggesting that the approximation is competitive with the approximation provided by the raviart thomas mixed method of corresponding degree

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