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

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

separability of sequential isomorphisms on quantum effects in multipartite systems in the paper we study separability of sequential isomorphisms on quantum effects in multipartite systems first we obtain necessary and sufficient conditions for separable sequential isomorphisms in bipartite systems secondly in finite dimensional bipartite systems separability of sequential endomorphisms on quantum effects is discussed furthermore we extend these conclusions to the multipartite case finally applying our results an equivalent characterization of local unitary operations is given

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

the nth root of sequential effect algebras in 2005 gudder int j theor phys 44 2219 2005 presented 25 problems of sequential effect algebras the 20th problem asked in a sequential effect algebra if the square root of some element exists is it unique in this paper we show that for each given positive integer n 1 there is a sequential effect algebra such that the nth root of its some element c is not unique and the nth root of c is not the kth root of c k n thus we answer the problem negatively

sequential quantum measurements a quantum effect is an operator a on a complex hilbert space h that satisfies 0 a i we denote the set of quantum effects by e h the set of self adjoint projection operators on h corresponds to sharp effects and is denoted by p h we define the sequential product of a b e h by a b a1 2ba1 2 the main purpose of this article is to study some of the algebraic properties of the sequential product many of our results show that algebraic conditions on a b imply that a and b commute for the usual operator product for example if a b satisfies certain distributive or associative laws then ab ba moreover if a b p h then ab ba and a b b or b a b if and only if ab ba b a natural definition of stochastic independence is introduced and briefly studied

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

generalized infimum and sequential product of quantum effects the quantum effects for a physical system can be described by the set e h of positive operators on a complex hilbert space h that are bounded above by the identity operator i for a b e h the operation of sequential product a b a1 2ba1 2 was proposed as a model for sequential quantum measurements a nice investigation of properties of the sequential product has been carried over gudder s and nagy g sequential quantum measurements j math phys 42 5212 2001 in this note we extend some results of this reference in particular a gap in the proof of theorem 3 2 in this reference is overcome in addition some properties of generalized infimum a b are studied

a uniqueness problem of the sequence product on operator effect algebra cal e h a quantum effect is an operator on a complex hilbert space h that satisfies 0 a i we denote the set of all quantum effects by in this paper we prove theorem 4 3 the theory of the sequential product on which shows in fact that there are sequential products on which are not of the generalized luders form this result answers gudder s open problem negatively

association schemes based on maximal totally isotropic subspaces in singular pseudo symplectic spaces this paper provides some new families of symmetric association schemes based on maximal totally isotropic subspaces in singular pseudo symplectic spaces all intersection numbers of these schemes are computed

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

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

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

suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs abstract as one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper we determine all the suborbits of a point stabilizer in the orthogonal group on the last subconstituent and calculate the length of each suborbit moreover we discuss the quasi strongly regular graphs and the association schemes based on the last subconstituent respectively

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

sequential endomorphisms of finite dimensional hilbert space effect algebras we describe the structure of all continuous sequential endomorphisms of the effect algebra of a finite dimensional hilbert space

characterizing sequential isomorphisms on hilbert space effect algebras let be any sequential product on the hilbert space effect algebra with and be a bijective map we show that if satisfies ab a b for then there is either a unitary or an anti unitary operator u such that a uau for every let be a borel function satisfying g 0 0 g 1 1 and let us define a binary operation g on by a gb a1 2 g a bg a a1 2 where t denotes the conjugate of the operator t we also show that a bijective map satisfies a gb a g b for if and only if there is either a unitary or an anti unitary operator u such that a uau for every

entropy preserving maps on quantum states abstract in the paper we give a characterization of surjective maps on quantum states preserving quantum entropy of convex combinations let s h be the set of all quantum states positive operators with the unit trace on a complex hilbert space h with dim h n and s the quantum entropy of the quantum state for arbitrary a surjective map s h s h we claim that preserves quantum entropy of convex combinations of quantum states i e satisfies s t 1 t s t 1 t for arbitrary s h and t 0 1 if and only if there exists a unitary or anti unitary operator u on h such that u u for all s h

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

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

suborbits of a point stabilizer in the unitary group on the last subconstituent of hermitean dual polar graphs let be a dual polar graph in a unitary space it is well known that a point stabilizer in the unitary group is transitive on the last subconstituent of in this paper we determine all the suborbits of this action calculate its rank and the length of each suborbit note that the induced subgraph on is quasi strongly regular as an application of our results all its parameters are computed

sequential product on standard effect algebra cal e h a quantum effect is an operator a on a complex hilbert space h that satisfies is the set of all quantum effects on h in 2001 professors gudder and nagy studied the sequential product for in 2005 professor gudder asked is the only sequential product on recently liu and wu have presented an example to show that the answer is negative in this paper first we characterize some algebraic properties of the abstract sequential product on second we present a general method for constructing sequential products on and finally we study some properties of the sequential products constructed by the method

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 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

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

subconstituents of dual polar graph in finite classical space iii abstract let f q be the finite field with q elements denote by the dual polar graph of 2 dimensional orthogonal space over f q where 0 1 or 2 for any vertex p of all subconstituents i p 1 i of are studied and it is proved that i p is isomorphic to i q i where i is a subgraph of the graph of i i matrices over f q moreover some properties of the graph i are also studied in particular it is shown that i is edge regular furthermore both 2 1 and 3 1 are distance regular with intersection arrays q 2 1 q 2 q 1 1 q q 2 1 and q 3 1 q 3 q q 3 q 2 1 1 q q 2 1 respectively

a generalization of the formulas for intersection numbers of dual polar association schemes and their applications dual polar association schemes form an important family of association schemes whose intersection numbers were computed in wan et al studies in finite geometry and the construction of incomplete block designs science press beijing 1966 in chinese in this paper we generalize the formulas for the intersection numbers and introduce their applications to pooling designs cartesian authentication codes and vertex transitive graphs

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

on the standard k loop structure of positive invertible elements in a c algebra abstract we investigate the algebraic properties of the operation a b a b a on the set of all positive invertible elements of a c algebra a we show that its commutativity associativity and distributivity are each equivalent to the commutativity of a we present abstract characterizations of the operation and a few related ones too

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

characterization of the sequential product on quantum effects we present a characterization of the standard sequential product of quantum effects the characterization is in terms of algebraic continuity and duality conditions that can be physically motivated

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