a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

remarks on generalized quasi equilibrium problems our main aim in this paper is to obtain fundamental existence theorems of quasi equilibrium problems and generalized quasi equilibrium problems of multivalued functions we use a continuous selection theorem to show that the existence theorems of generalized quasi equilibrium problems are simple consequences of the corresponding quasi equilibrium problems we use a generalization of himmelberg s theorem due to the third author for not necessary locally convex topological vector spaces to prove the existence theorems of quasi equilibrium problems for multivalued functions

on convergence of block centered finite differences for elliptic problems we consider linear selfadjoint elliptic problems with neumann boundary conditions in rectangular domains we demonstrate that with sufficiently smooth data the discrete l 2 norm errors for tensor product block centered finite differences in both the approximate solution and its first derivatives are second order for all nonuniform grids extensions to nonselfadjoint and parabolic problems are discussed

existence of solutions for generalized equilibrium problem in g convex space in this paper we introduce and study a kind of generalized equilibrium problem in a g convex space by means of the fixed point theorems we obtain some existence theorems of solutions for the generalized equilibrium problems

analysing competing risks data with transformation models we present a flexible class of marginal models for the cumulative incidence function the semiparametric transformation model is utilized in a decomposition for the marginal failure probabilities which extends previous work on farewell s cure model novel estimation inference and prediction procedures are developed with large sample properties derived from the theory of martingales and u statistics a small simulation study demonstrates that the methods are appropriate for practical use the methods are illustrated with a thorough analysis of a prostate cancer clinical trial simple graphical displays are used to check for the goodness of fit

extended hazard regression for censored survival data with covariates a spline approximation for the baseline hazard function a regression model for censored survival data with covariates is introduced and termed extended hazard regression ehr ehr includes the proportional hazards ph and the accelerated failure time aft models as special cases by approximating the baseline hazard function with quadratic splines we develop a maximum likelihood estimation procedure to provide a simultaneous estimate of both the hazard function and the regression coefficients the aft and ph assumptions can then be compared by likelihood ratio tests within the more general ehr model several examples based on artificial and real data are discussed

decoupling mixed finite elements on hierarchical triangular grids for parabolic problems in this paper we propose a numerical method for the solution of time dependent flow problems in mixed form such problems can be efficiently approximated on hierarchical grids obtained from an unstructured coarse triangulation by using a regular refinement process inside each of the initial coarse elements if these elements are considered as subdomains we can formulate a non overlapping domain decomposition method based on the lowest order raviart thomas elements properly enhanced with lagrange multipliers on the boundaries of each subdomain excluding the dirichlet edges a suitable choice of mixed finite element spaces and quadrature rules yields a cell centered scheme for the pressures with a local 10 point stencil the resulting system of differential algebraic equations is integrated in time by the crank nicolson method which is known to be a stiffly accurate scheme as a result we obtain independent subdomain linear systems that can be solved in parallel the behavior of the algorithm is illustrated on a variety of numerical experiments

on some mixed finite element methods with numerical integration in this paper a new family of mixed finite volume methods is analyzed for the approximation of a reaction diffusion problem all the methods are obtained starting from the dual mixed formulation of the problem and then employing the lowest order raviart thomas finite element spaces plus a suitable quadrature formula for the mass matrix this allows for the use of different averages of the inverse diffusion coefficient to enforce the constitutive law for the fluxes at the interelement boundary in a finite volume fashion the soundness of the methods is supported by an error analysis which shows optimal cal o h convergence rate with respect to the standard mixed finite element norm in the case of both smooth and piecewise smooth coefficients numerical results on test problems with both smooth and nonsmooth coefficients support the theoretical estimates

efficient semiparametric estimation of short term and long term hazard ratios with right censored data the proportional hazards assumption in the commonly used cox model for censored failure time data is often violated in scientific studies yang and prentice 2005 proposed a novel semiparametric two sample model that includes the proportional hazards model and the proportional odds model as sub models and accommodates crossing survival curves the model leaves the baseline hazard unspecified and the two model parameters can be interpreted as the short term and long term hazard ratios inference procedures were developed based on a pseudo score approach although extension to accommodate covariates was mentioned no formal procedures have been provided or proved furthermore the pseudo score approach may not be asymptotically efficient we study the extension of the short term and long term hazard ratio model of yang and prentice 2005 to accommodate potentially time dependent covariates we develop efficient likelihood based estimation and inference procedures the nonparametric maximum likelihood estimators are shown to be consistent asymptotically normal and asymptotically efficient extensive simulation studies demonstrate that the proposed methods perform well in practical settings the proposed method successfully captured the phenomenon of crossing hazards in a cancer clinical trial and identified a genetic marker with significant long term effect missed by using the proportional hazards model on age at onset of alcoholism in a genetic study

an efficient cell centered multigrid method for problems with discontinuous coefficients on semi structured triangular grids this paper is focused on the numerical solution of elliptic equations with discontinuous coefficients in particular the design of efficient geometric multigrid methods for cell centered finite volume schemes for this kind of problems is dealt with in this work we propose a block wise multigrid algorithm on semi structured triangular grids for solving piecewise constant diffusivity problems on relatively complex domains appropriate novel smoothers for cell centered discretizations are considered on each structured patch of the mesh the difficulties appearing when highly varying coefficients occur are overcome by the use of a modified galerkin coarse grid approximation numerical experiments are presented to illustrate the good behavior of the proposed multigrid method which achieves an h independent convergence rate

discretization schemes on triangular grids abstract physical applications posed on irregular domains have caused difficulties in the use of many otherwise effective discretization schemes in two dimensional examples we consider discretization schemes on triangles to approximate irregular domains although finite element mixed finite element and finite volume schemes for triangles are well understood efficient solvers are essential for their effective use in this paper we consider certain cell centered finite difference schemes on triangles both for their theoretical properties on regular grids and as effective preconditioners for other discretization schemes for more general triangulations two cell centered finite difference schemes four point star stencils are derived from the simplification of the lowest order raviart thomas mixed finite element discretization on certain triangular grids optimal and superconvergence error estimates for both the solution and the gradient of the solution are established the accuracy of these schemes is also discussed in the case of discontinuous coefficients computational experiments verify the error estimates finally the use of these methods as preconditioners is also discussed

on some equilibrium problems for multimaps abstract in this paper we first establish the continuity property for multimaps and generalized berge s theorem for multimaps then we apply these results and the fan browder fixed point theorem to establish the existence theorems of quasi equilibrium problems and generalized quasi equilibrium problems for multimaps

nash type equilibrium theorems and competitive nash type equilibrium theorems abstract in this paper we consider two types of equilibrium problems we study the constrained nash type equilibrium problems with multivalued payoff functions we also study the competitive nash type equilibrium problems with multivalued payoff functions in these two equilibrium problems we want to find a strategy combination such that each player wishes to find a minimal loss from his multivalued payoff function we use a fixed point theorem of park to prove the existence results of these two types of equilibrium problems

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

a mixture model combining logistic regression with proportional hazards regression summary a model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event the proposed model is a semiparametric generalization of a parametric model due to farewell 1982 estimates of the regression parameters are obtained by maximizing a monte carlo approximation of a marginal likelihood and the em algorithm is used to estimate the baseline survivor function we present some simulation results to verify the validity of the suggested estimation procedure it appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions

semiparametric regression analysis for clustered failure time data inference procedures based on the partial likelihood function for the cox proportional hazards model have been generalised to the case in which the data consist of a large number of independent small groups of correlated failure time observations lee wei amato 1992 liang self chang 1993 cai prentice 1997 however the cox model may not fit the data well a class of linear transformation models which includes the proportional hazards and odds models as special cases has been studied extensively for univariate event times in this paper statistical methods to analyse such correlated observations are proposed for these models we use the data from a recent study of the genetic aetiology of alcoholism to illustrate the new procedures for estimation prediction and model selection

on the constrained equilibrium problems with finite families of players in this paper we consider the equilibrium problem with finite number of families of players such that each family may not have the same number of players and finite number of families of constrained correspondences on the strategy sets we also consider the case with two finite families of constrained correspondences on the strategies sets we demonstrate an example of our equilibrium problem we derive a fixed point theorem for a family of multimaps and a coincidence theorem for two families of multimaps by using these results we establish the existence of a solution of our equilibrium problems the results of this paper generalize some known results in the literature

on generalized vector equilibrium problems abstract in this paper we study the generalized vector equilibrium problems in real hausdorff topological vector space settings the concepts of weak solutions and strong solutions are introduced several new results of existence for the weak solutions and strong solutions of generalized vector equilibrium problems are derived the new results extend and modify various existence theorems for similar problems

estimating the proportion of immunes in a censored sample summary an estimator for the proportion of immunes in a population is proposed when a sample of censored failure times is available our suggestion is to use one minus the maximum observed value of the kaplan meier empirical distribution function this estimator is shown to be consistent and asymptotically normal under modest conditions on the censoring mechanism simulations suggest that the estimator is approximately normal for quite small sample sizes provided the immune proportion is not too close to zero a simple nonparametric statistic is proposed to test whether the assumptions of the analysis are likely to be valid

cure rate quantile regression for censored data with a survival fraction censored quantile regression offers a valuable complement to the traditional cox proportional hazards model for survival analysis survival times tend to be right skewed particularly when there exists a substantial fraction of long term survivors who are either cured or immune to the event of interest for survival data with a cure possibility we propose cure rate quantile regression under the common censoring scheme that survival times and censoring times are conditionally independent given the covariates in a mixture formulation we apply censored quantile regression to model the survival times of susceptible subjects and logistic regression to model the indicators of whether patients are susceptible we develop two estimation methods using martingale based equations one approach fully uses all regression quantiles by iterating estimation between the cure rate and quantile regression parameters and the other separates the two via a nonparametric kernel smoothing estimator we establish the uniform

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

generalized vector quasi equilibrium problems with applications to common fixed point theorems and optimization problems abstract in this paper we first establish the existence theorems of generalized vector quasi equilibrium problems from these results we establish the existence theorems of common fixed point theorems for two multivalued maps and mathematical programs with an equilibrium constraint as applications

an analysis of monotonicity conditions in the mixed hybrid finite element method on unstructured triangulations in this paper we consider the mixed hybrid finite element method on unstructured triangular grids and evaluate its monotonicity properties by using a non standard set of basis functions for the velocity approximation space the mixed hybrid discretization of the steady state diffusion equation produces a system matrix that depends only on the inner product of the outward normals to the edges of the triangulation and not on the choice of the velocity space basis this property is used to study the characteristics of the system matrix it is well known that this matrix is of type m if the angles of the triangulation are not bigger than 2 an m matrix has a nonnegative inverse i e all the elements are nonnegative this implies the existence of a discrete maximum principle and thus monotonicity of the discretization we show that when the triangulation is of delaunay type and satisfies the property that no circumcenters of boundary elements with dirichlet conditions lie outside the domain the inverse of the final matrix is always positive even in the presence of obtuse angles

semiparametric efficient estimation for a class of generalized proportional odds cure models we present a mixture cure model with the survival time of the uncured group coming from a class of linear transformation models which is an extension of the proportional odds model this class of model first proposed by dabrowska and doksum 1988 which we term generalized proportional odds model is well suited for the mixture cure model setting due to a clear separation between long term and short term effects a standard expectation maximization algorithm can be employed to locate the nonparametric maximum likelihood estimators which are shown to be consistent and semiparametric efficient however there are difficulties in the m step due to the nonparametric component we overcome these difficulties by proposing two different algorithms the first is to employ an majorize minimize mm algorithm in the m step instead of the usual newton raphson method and the other is based on an alternative form to express the model as a proportional hazards frailty model the two new algorithms are compared

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

existence and algorithms for the bilevel new generalized mixed equilibrium problems in banach spaces abstract in this paper we introduce and analyze the new generalized mixed equilibrium problems ngmep and the bilevel new generalized mixed equilibrium problems bngmep in banach spaces first by using a minimax inequality some new existence theorems of the solution and the behavior of solution set for the ngmep and the bngmep are obtained in both arbitrary banach spaces with the coercive conditions and a reflexive banach space without the coercive conditions next by using auxiliary principle technique some new iterative algorithms for solving the ngmep and the bngmep are suggested and analyzed the strong convergence of the iterative sequences generated by the algorithms are also proved in both arbitrary banach spaces with the coercive conditions and a reflexive banach space without the coercive conditions these results are new and generalize some recent results in this field

an expectation maximization algorithm for fitting the generalized odds rate model to interval censored data the generalized odds rate model is a class of semiparametric regression models which includes the proportional hazards and proportional odds models as special cases there are few works on estimation of the generalized odds rate model with interval censored data because of the challenges in maximizing the complex likelihood function in this paper we propose a gamma poisson data augmentation approach to develop an expectation maximization algorithm which can be used to fit the generalized odds rate model to interval censored data the proposed expectation maximization algorithm is easy to implement and is computationally efficient the performance of the proposed method is evaluated by comprehensive simulation studies and illustrated through applications to datasets from breast cancer and hemophilia studies in order to make the proposed method easy to use in practice an r package icgor was developed copyright 2016 john wiley sons ltd

semiparametric models a generalized self consistency approach in semiparametric models the dimension d of the maximum likelihood problem is potentially unlimited conventional estimation methods generally behave like o d 3 a new o d estimation procedure is proposed for a large class of semiparametric models potentially unlimited dimension is handled in a numerically efficient way through a nelson aalen like estimator discussion of the new method is put in the context of recently developed minorization maximization algorithms based on surrogate objective functions the procedure for semiparametric models is used to demonstrate three methods to construct a surrogate objective function using the difference of two concave functions the em way and the new quasi em qem approach the qem approach is based on a generalization of the em like construction of the surrogate objective function so it does not depend on the missing data representation of the model like the em algorithm the qem method has a dual interpretation a result of merging the idea of surrogate maximization with the idea of imputation and self consistency the new approach is compared with other possible approaches by using simulations and analysis of real data the proportional odds model is used as an example throughout the paper

multiple imputation for cure rate quantile regression with censored data summary the main challenge in the context of cure rate analysis is that one never knows whether censored subjects are cured or uncured or whether they are susceptible or insusceptible to the event of interest considering the susceptible indicator as missing data we propose a multiple imputation approach to cure rate quantile regression for censored data with a survival fraction we develop an iterative algorithm to estimate the conditionally uncured probability for each subject by utilizing this estimated probability and bernoulli sample imputation we can classify each subject as cured or uncured and then employ the locally weighted method to estimate the quantile regression coefficients with only the uncured subjects repeating the imputation procedure multiple times and taking an average over the resultant estimators we obtain consistent estimators for the quantile regression coefficients our approach relaxes the usual global linearity assumption so that we can apply quantile regression to any particular quantile of interest we establish asymptotic properties for the proposed estimators including both consistency and asymptotic normality we conduct simulation studies to assess the finite sample performance of the proposed multiple imputation method and apply it to a lung cancer study as an illustration

semiparametric regression on cumulative incidence function with interval censored competing risks data many biomedical and clinical studies with time to event outcomes involve competing risks data these data are frequently subject to interval censoring this means that the failure time is not precisely observed but is only known to lie between two observation times such as clinical visits in a cohort study not taking into account the interval censoring may result in biased estimation of the cause specific cumulative incidence function an important quantity in the competing risks framework used for evaluating interventions in populations for studying the prognosis of various diseases and for prediction and implementation science purposes in this work we consider the class of semiparametric generalized odds rate transformation models in the context of sieve maximum likelihood estimation based on b splines this large class of models includes both the proportional odds and the proportional subdistribution hazard models i e the fine gray model as special cases the estimator for the regression parameter is shown to be consistent asymptotically normal and semiparametrically efficient simulation studies suggest that the method performs well even with small sample sizes as an illustration we use the proposed method to analyze data from hiv infected individuals obtained from a large cohort study in sub saharan africa we also provide the r function ciregic that implements the proposed method and present an illustrative example copyright 2017 john wiley sons ltd

stability and error analysis of mixed finite volume methods for advection dominated problems abstract we consider a convection diffusion reaction problem and we analyze a stabilized mixed finite volume scheme introduced in 1 the scheme is presented in the format of discontinuous galerkin methods and error bounds are given proving o h convergence in the l 2 norm for the scalar variable which is approximated with piecewise constant elements

existence results for stampacchia and minty type implicit variational inequalities with multivalued maps abstract stampacchia and minty type generalized implicit variational inequality problems are considered we extended the notion of dense pseudomonotonicity for multivalued maps and established several existence results for solutions of these problems in the setting of segment dense sets we also studied the existence of solutions of minty type generalized implicit quasi variational inequality problems some particular cases are also studied it is shown that our results contain several existing results in the literature as special cases

a generalized f mixture model for cure rate estimation cure rate estimation is an important issue in clinical trials for diseases such as lymphoma and breast cancer and mixture models are the main statistical methods in the last decade mixture models under different distributions such as exponential weibull log normal and gompertz have been discussed and used however these models involve stronger distributional assumptions than is desirable and inferences may not be robust to departures from these assumptions in this paper a mixture model is proposed using the generalized f distribution family although this family is seldom used because of computational difficulties it has the advantage of being very flexible and including many commonly used distributions as special cases the generalised f mixture model can relax the usual stronger distributional assumptions and allow the analyst to uncover structure in the data that might otherwise have been missed this is illustrated by fitting the model to data from large scale clinical trials with long follow up of lymphoma patients computational problems with the model and model selection methods are discussed comparison of maximum likelihood estimates with those obtained from mixture models under other distributions are included

a block finite difference scheme for second order elliptic problems with discontinuous coefficients a block finite element difference scheme is derived from the next to the lowest order raviart thomas mixed quadrilateral finite element method by using some numerical quadratures element wise this finite difference scheme is much simpler than the mixed finite element method itself with the same order of accuracy superconvergence error estimates of order o h 3 for both the pressure and the darcy velocity are established even for certain discontinuous coefficients numerical experiments are presented to confirm the analysis at the end of this paper

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

superconvergence of the velocity along the gauss lines in mixed finite element methods superconvergence for the velocity along the gauss lines is derived for the mixed finite element method for the second order elliptic equation in rectangular domains these estimates are based on the rectangular finite elements of raviart thomas type

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