bases axioms and circuits axioms for fuzzifying matroids abstract this paper shows that weighted graphs are examples of fuzzifying matroids axioms of bases and that of circuits are established for fuzzifying matroids

analysis of proportional mean residual life model with latent variables end stage renal disease esrd is one of the most serious diabetes complications numerous studies have been devoted to revealing the risk factors of the onset time of esrd in this article we propose a proportional mean residual life mrl model with latent variables to assess the effects of observed and latent risk factors on the mrl function of esrd in a cohort of chinese type 2 diabetic patients the proposed model generalizes the conventional proportional mrl model to accommodate the latent risk factor that cannot be measured by a single observed variable we employ a factor analysis model to characterize the latent risk factors via multiple observed variables we develop a borrow strength estimation procedure which incorporates the expectation maximization algorithm and an extended estimating equation approach the asymptotic properties of the proposed estimators are established simulation shows that the performance of the proposed methodology is satisfactory the application to the study of type 2 diabetes reveals insights into the prevention of esrd copyright 2016 john wiley sons ltd

nonparametric analysis of covariance for censored data the fully nonparametric model for nonlinear analysis of covariance proposed in akritas et al 2000 is considered in the context of censored observations under this model the distributions for each factor level combination and covariate value are not restricted to comply to any parametric or semiparametric model the data can be continuous or ordinal categorical the possibility of different shapes of covariate effect in different factor level combinations is also allowed this generality is useful whenever modelling assumptions such as additive risks proportional hazards or proportional odds appear suspect test statistics are obtained for the nonparametric hypotheses of no main effect and of no interaction effect which adjusts for the presence of a covariate they are quadratic forms based on averages over the covariate values of beran estimators of the conditional distribution of the survival time given each covariate value the derivation of the asymptotic chi 2 distribution of the test statistics uses a recently obtained asymptotic representation of the bekan estimator as average of independent random variables a real data set is analysed and results of simulation studies are reported

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

closure axioms for a class of fuzzy matroids and co towers of matroids this paper represents an attempt to define a closure operator which can determine geotschel and voxman fuzzy matroid gv fuzzy matroid for short and presents an application of the notion co tower in gv fuzzy matroids two bijections are obtained for a given finite set x one is from a x email protected 0 1 x x d is a closed singular gv fuzzy matroid or a closed proper single gv fuzzy matroid to b x the set of all triples of operators on x satisfying some fuzzy closure axioms the other is from fm x the set of all systems of gv independent fuzzy sets on x to m c x the set of all co tower structures on x the first bijection shows that a triple of operators on x satisfying some fuzzy closure axioms can determine a closed singular gv fuzzy matroid or a closed proper single gv fuzzy matroid and the second shows that a co tower structure on x can determine a gv fuzzy matroid as a result it is proved that the category fm of all gv fuzzy matroids and continuous mappings is isomorphic to the category m c of all co towers in m the category of all matroids and continuous mappings and continuous mappings

axioms for bases of closed regular fuzzy matroids this paper represents an attempt to define a set of bases which can determine a closed regular fuzzy matroid and to study some properties of section fuzzy matroids elementary section fuzzy matroids and elementary fuzzy matroids axioms for bases of both elementary fuzzy matroids and closed regular fuzzy matroids are presented respectively it is proved that the set of bases of all closed regular fuzzy matroids on a set equipped with a suitable order is order isomorphic to the set of systems of independent sets of all closed regular fuzzy matroids on this set equipped with the inclusion order

regression analysis of additive hazards model with latent variables we propose an additive hazards model with latent variables to investigate the observed and latent risk factors of the failure time of interest each latent risk factor is characterized by correlated observed variables through a confirmatory factor analysis model we develop a hybrid procedure that combines the expectation maximization em algorithm and the borrow strength estimation approach to estimate the model parameters we establish the consistency and asymptotic normality of the parameter estimators various nice features including finite sample performance of the proposed methodology are demonstrated by simulation studies our model is applied to a study concerning the risk factors of chronic kidney disease for type 2 diabetic patients supplementary materials for this article are available online

two sample goodness of fit tests for additive risk models with censored observations summary the additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates we propose two different test procedures for checking the adequacy of two sample additive risk models for randomly censored observations one is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk the test statistics are shown to be asymptotically normal under appropriate regularity conditions and consistent under any model misspecifications finally two real examples are provided along with results of a simulation study

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

additive risk models for survival data with high dimensional covariates as a useful alternative to cox s proportional hazard model the additive risk model assumes that the hazard function is the sum of the baseline hazard function and the regression function of covariates this article is concerned with estimation and prediction for the additive risk models with right censored survival data especially when the dimension of the covariates is comparable to or larger than the sample size principal component regression is proposed to give unique and numerically stable estimators asymptotic properties of the proposed estimators component selection based on the weighted bootstrap and model evaluation techniques are discussed this approach is illustrated with analysis of the primary biliary cirrhosis clinical data and the diffuse large b cell lymphoma genomic data it is shown that this methodology is numerically stable and effective in dimension reduction while still being able to provide satisfactory prediction and classification results

estimation for a semimartingale regression model using the method of sieves estimation by the method of sieves for a semimartingale regression model introduced by aalen 1980 is studied it is of interest to estimate functions which describe the influence of the covariates over time an estimator for these functions is introduced and conditions which ensure consistency of the estimator in l 2 norm are given applications to diffusion processes and point processes with censored data are also discussed

fuzzy matroid structures abstract this paper is a continuation of our study of fuzzy matroids we examine the fuzzy counterparts of matroid sums dual and products

bases of fuzzy matroids in this paper we continue our study of fuzzy matroids we define the notion of a basis for a fuzzy matroid and investigate which properties of crisp matroid bases carry over to the fuzzy case

confidence bands for cumulative incidence curves under the additive risk model in the context of competing risks the cumulative incidence function is often used to summarize the cause specific failure time data as an alternative to the proportional hazards model the additive risk model is used to investigate covariate effects by specifying that the subject specific hazard function is the sum of a baseline hazard function and a regression function of covariates based on such a formulation we present an approach to constructing simultaneous confidence intervals for the cause specific cumulative incidence function of patients with given risk factors a melanoma data set is used for the purpose of illustration

estimation of the survival function for gray s piecewise constant time varying coefficients model gray s extension of cox s proportional hazards ph model for right censored survival data allows for a departure from the ph assumption via introduction of time varying regression coefficients tvc using penalized splines gray s work focused on estimation inference and residual analyses but no estimator for the survival function has been proposed we derive a survival function estimator for one important member of the class of tvc models a piecewise constant time varying coefficients pc tvc model we also derive an estimate for the confidence limits of the survival function accuracy in estimating underlying survival times and survival quantiles is assessed for both cox s and gray s pc tvc model using a simulation study featuring scenarios violating the ph assumption finally an example of the estimated survival functions and the corresponding confidence limits derived from cox s ph and gray s pc tvc model respectively is presented for a liver transplant data set in the second part of the thesis we examine the effect of model misspecification for two classes of regression models for right censored survival data additive and multiplicative models for the conditional hazard rate a particular attention is given to data exhibiting time varying regression coefficients the class of multiplicative models is represented by cox ph model and gray s tvc model respectively and for additive models we use aalen s linear model both gray s tvc model and aalen s linear model incorporate time varying coefficients a simulation study is performed to cross analyze survival data which follows either a multiplicative or an additive model for the conditional hazard rate the effect of misspecifying the true model for the conditional hazard rate is assessed by looking at the power of the individual models to detect an existing effect bias and mean square error observed for each conditional model based estimator of survival we also show that aalen s model formulae is a first order taylor series approximation of that of gray s model which explains the comparably higher flexibility on part of the aalen s model as compared to the cox ph when the gray s tvc model for the data is misspecified

completeness of superintegrability in two dimensional constant curvature spaces we classify the hamiltonians h px2 py2 v x y of all classical superintegrable systems in two dimensional complex euclidean space with two additional second order constants of the motion we similarly classify the superintegrable hamiltonians h j12 j22 j32 v x y z on the complex two sphere where x2 y2 z2 1 this is achieved in all generality using properties of the complex euclidean group and the complex orthogonal group

estimation of excess risk from case control data using aalen s linear regression model we introduce methods for statistical inference in aalen s non parametric linear regression model of disease incidence aalen 1989 statistics in medicine 8 907 925 from nested case control data these methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history the methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case control samples from the colorado plateau uranium miners cohort language en

a sieve estimator for the covariance of a gaussian process on considere l estimation du maximum de vraisemblance de la covariance r d un processus gaussien de moyenne nulle avec aucune hypothese sur la covariance ou sur l ensemble des parametres temps on montre que la fonction de vraisemblance est presque surement non bornee en general et on construit un estimateur r

analysis of additive risk model with high dimensional covariates using partial least squares in this paper we construct a partial additive regression par model to predict the survival times of cancer patients based on microarray gene expression data with right censoring the area under time dependent receiver operating characteristic curve is used as a model evaluation criterion we conduct a simulation study to compare the proposed method with other methods i e partial cox regression and supervised principal component analysis two data sets of breast cancer and diffuse large b cell lymphoma are analyzed to illustrate our procedure the outcome indicates great predictive performance on both dimension reduction and predictive performance of the proposed par model

functional association models for multivariate survival processes we consider multivariate temporal processes that are continuously observed within overlapping time windows the intended application is in censored multistate and multivariate survival settings where point processes are continuously observed these data differ from other functional data like longitudinal data which are discretely observed at irregular times existing functional approaches to survival processes use intensity models which require smoothing and depend critically on the choice of smoothing parameters similarly to discretely observed data in this article we study functional mean and association regression models for the point processes with unspecified time varying coefficients the continuous observation scheme is exploited the coefficients may be estimated nonparametrically by extending generalized estimating equations to continuously observed data the estimators automatically converge at the parametric rate without smoothing unlike with discretely observed data uniform consistenc

fuzzy bases of fuzzy independent set systems abstract compactness closeness and sc are conditions to ensure the existence of fuzzy bases for polymatroids g v fuzzy matroids and h fuzzy matroids respectively in this work relations of these three conditions with different fuzzy independent systems are studied furthermore the equivalence of compactness closeness and sc for g v fuzzy matroids is proved and the existence of fuzzy bases of h fuzzy matroids is verified finally it has been pointed out that h fuzzy matroids and e fuzzy matroids induced from polymatroids are the same and the question whether an h fuzzy matroid is a fuzzy pre matroid is solved

partially linear additive hazards regression with varying coefficients please see the supplementary materials for a correction to this article to explore the nonlinear interactions between some covariates and an exposure variable we propose the partially linear additive hazards model for survival data in a semiparametric setting we construct a local pseudoscore function to estimate the varying and constant coefficients and establish the asymptotic normality of the proposed estimators moreover we develop the weak convergence property for the local estimator of the baseline cumulative hazard function we conduct simulation studies to empirically examine the finite sample performance of the proposed methods and use real data from a breast cancer study for illustration

on fuzzification of matroids in this paper we propose one possible fuzzification of matroids which entends the independence axioms of matroids from set systems to fuzzy set systemsand preserves most basic properties of matroids by representing a fuzzy subset of a finite set e as a subset of e 0 1 we obtain fuzzy matroids by fuzzifying independence spaces on e 0 1 alternatively by representing fuzzy subsets of e as functions from e into 0 1 we can obtain fuzzy matroids from polymatroids associated with real rank functions we also investigate the duality for fuzzy matroids

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

additive and multiplicative models for relative survival rates the relative survival rate is the ratio of the overall survival rate to that expected for demographically similar individuals in a reference population it is commonly used to estimate the effect of a particular disease on mortality when the cause of death is not reliably known the effect of the disease on the underlying hazards may be multiplicative or additive the former case has been considered elsewhere but seems biologically less plausible than the latter both models are examined in this paper the effect of the disease is assumed to be constant throughout the follow up period or to be piecewise constant within k follow up intervals maximum likelihood estimates and related statistics are presented as are simpler statistics based on moment estimators of the disease effect the moment based statistic for testing the homogeneity of r groups may be expressed as a sum of individual scores which are shown to be closely related to the logrank scores when follow up intervals are made arbitrarily small

a new approach to the fuzzification of matroids in this paper the concept of closed fuzzy pre matroids is generalized to l fuzzy set theory when l is a complete lattice it is also called an l fuzzifying matroid in the definition of l fuzzifying matroids each subset can be regarded as an independent set to some degree when l is completely distributive an l fuzzifying matroid can be characterized by means of its l fuzzifying rank function an l fuzzifying matroid and its l fuzzifying rank function are one to one corresponding

additive hazards model with multivariate failure time data summary marginal additive hazards models are considered for multivariate survival data in which individuals may experience events of several types and there may also be correlation between individuals estimators are proposed for the parameters of such models and for the baseline hazard functions the estimators of the regression coefficients are shown asymptotically to follow a multivariate normal distribution with a sandwich type covariance matrix that can be consistently estimated the estimated baseline and subject specific cumulative hazard processes are shown to converge weakly to a zero mean gaussian random field the weak convergence properties for the corresponding survival processes are established a resampling technique is proposed for constructing simultaneous confidence bands for the survival curve of a specific subject the method ology is extended to a multivariate version of a class of partly parametric additive hazards model simulation studies are conducted to assess finite sample properties and the method is illustrated with an application to development of coronary heart diseases and cardiovascular accidents in the framingham heart study

connectedness of refined goetschel voxman fuzzy matroids this paper studies connectedness of goetschel voxman fuzzy matroids briefly g v fuzzy matroids an analog of connectedness of crisp finite matroids based on the results of fuzzy circuits given by goetschel and voxman the transitivity theorem concerning fuzzy circuits of g v fuzzy matroids is established and thus the useful notion of refined g v fuzzy matroid is introduced the connectedness of refined g v fuzzy matroids is then defined by using an equivalence relation on the set of all fuzzy points on the ground set and some expected properties of these g v fuzzy matroids are presented additionally five kinds of fuzzy matroids are compared

on goetschel and voxman fuzzy matroids abstract the concepts of fuzzy pre matroid and hereditary fuzzy pre matroid are introduced and investigated the property to be perfect for hereditary fuzzy pre matroids is also considered it is shown that goetschel and voxman fuzzy matroids coincide with perfect hereditary fuzzy pre matroids it is also shown that goetschel and voxman fuzzy matroids can be described via three fuzzy axioms two of which are direct fuzzy counter parts of the crisp matroid axioms in terms of elementary fuzzy sets and the third one is a decomposition axiom also in terms of elementary fuzzy sets

l m fuzzy matroids in this paper an extension of matroids is introduced in lattice valued fuzzy set theory such a generalized matroid is a pair made of a finite set and a fuzzy subfamily of its lattice valued fuzzy subsets satisfying three axioms it uses two lattices one for membership grades of elements to fuzzy sets and another for membership degrees of fuzzy sets in a fuzzy family of fuzzy sets it is a logical generalization of the notions of matroids and fuzzifying matroids in our definition of generalized fuzzy matroids each l fuzzy subset can be regarded to be independent of other ones to some degree the relevance of generalized fuzzy matroids is shown in the setting of fuzzy vector spaces and fuzzy graphs

fourth order superintegrable systems separating in cartesian coordinates i exotic quantum potentials a study is presented of two dimensional superintegrable systems separating in cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the momenta all quantum mechanical potentials that do not satisfy any linear differential equation are found they do however satisfy nonlinear odes we show that these equations always have the painleve property and integrate them in terms of known painleve transcendents or elliptic functions

asymptotic theory for the cox model with missing time dependent covariate the relationship between a time dependent covariate and survival times is usually evaluated via the cox model time dependent covariates are generally available as longitudinal data collected regularly during the course of the study a frequent problem however is the occurence of missing covariate data a recent approach to estimation in the cox model in this case jointly models survival and the longitudinal covariate however theoretical justification of this approach is still lacking in this paper we prove existence and consistency of the maximum likelihood estimators in a joint model the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance

projected partial likelihood and its application to longitudinal data summary an estimating equation which we call the projected partial score is introduced for longitudinal data analysis the estimating equation is obtained by projecting the partial likelihood score function onto the vector space spanned by a class of conditionally linear estimating equations we demonstrate that removing certain terms from the projection of the full likelihood score does not alter important inferential properties of the estimating equation and doing so is advantageous in handling missing data and time varying covariates within a prequential frame of reference it is shown that the estimating equation is optimal among the largest collection of estimating equations determined by the conditional moments furthermore the method possesses similar properties to generalised estimating equations in particular the correct conditional variance specification is necessary for efficiency but not for asymptotic consistency and distribution theory

age dependent u shaped risk functions and aalen s additive risk model epidemiologic studies of time to some failure often show a quadratic relation between the risk of failure and covariate s we study the nadir for a given covariate i e the value of the covariate associated with the lowest risk supposing a u shape within aalen s additive risk model this model was applied since the effect of the covariate s is allowed to vary over time and as a consequence a given nadir can vary over time we propose a test for the null hypothesis that the nadir is time independent and if this is the case an estimate of the nadir large sample properties of the test statistic and estimator are derived the methods are illustrated with data where time to death is related to body mass index

a nonparametric dynamic additive regression model for longitudinal data in this work we study additive dynamic regression models for longitudinal data these models provide a flexible and nonparametric method for investigating the time dynamics of longitudinal data the methodology is aimed at data where measurements are recorded at random time points we model the conditional mean of responses given the full internal history and possibly time varying covariates we derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time varying regression functions based on the asymptotic results confidence bands may be computed and inference about time varying coefficients may be drawn we propose two estimators of the cumulative regression function one estimator that involves smoothing and one that does not the latter however has twice the variance as the smoothing based estimator goodness of fit of the model is considered using martingale residuals finally we also discuss how partly conditional mean models in which the mean of the response is regressed onto selected time varying covariates may be analysed in the same framework we apply the methods to longitudinal data on height development for cystic fibrosis patients

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

an infinite family of solvable and integrable quantum systems on a plane an infinite family of exactly solvable and integrable potentials on a plane is introduced it is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family the underlying algebraic structure of the new potentials is revealed as well as its hidden algebra we conjecture that all members of the family are also superintegrable and demonstrate this for the first few cases a quasi exactly solvable and integrable generalization of the family is found

a partly parametric additive risk model summary aalen s additive risk model allows the influence of each covariate to vary separately over time although allowing greater flexibility of temporal structure than a cox model aalen s model is more limited in the number of covariates it can handle we introduce a partly parametric version of aalen s model in which the influence of only a few covariates varies nonparametrically over time and that of the remaining covariates is constant efficient procedures for fitting this new model are developed and studied the approach is applied to data from the medical research council s myelomatosis trials it is the first step of a taylor series expansion of a general hazard function about the zero of the covariate vector however in estimating the unknown functions in such a general model there is a variance bias trade off that may be critical in small and medium samples also after fitting the model one does not have parameters or formulae that are easily reported we propose a model that takes the additive structure of aalen s model and imposes parametric constraints to obtain a semiparametric submodel which may be more appropriate in some applications the model will be illustrated with data from clinical trials on myelomatosis covariates include treatment sex and four age strata which will be treated parametrically together with serum levels of haemoglobin and f32 microglobulin whose effects will be investigated nonparametrically the additive form can be interpreted loosely in terms of unobserved competing risks since the hazard function for the minimum of independent random vari ables is the sum of the hazard functions for the individual variables microglobulin levels are related to kidney function and tumour mass whereas haemoglobin is unaffected by kidney function hence one might anticipate that the hazard function associated with each covariate represents a different cause of death

inference for stochastic neuronal models stochastic models of some aspects of the electrical activity in the nervous system at the cellular level are developed in particular models of the subthreshold behavior of the membrane potential of neurons are considered along with the problem of estimation of physiologically meaningful parameters of the developed models both ordinary and partial stochastic differential equation models are treated

additive hazards markov regression models illustrated with bone marrow transplant data summary when there are covariate effects to be considered multi state survival analysis is dominated either by parametric markov regression models or by semiparametric markov regression models using cox s 1972 proportional hazards models for transition intensities between the states the purpose of this research work is to study alternatives to cox s model in a general finite state markov process setting we shall look at two alternative models aalen s 1989 nonparametric additive hazards model and lin ying s 1994 semiparametric additive hazards model the former allows the effects of covariates to vary freely over time while the latter assumes that the regression coefficients are constant over time with the basic tools of the product integral and the functional delta method we present an estimator of the transition probability matrix and develop the large sample theory for the estimator under each of these two models data on 1459 hla identical sibling transplants for acute leukaemia from the international bone marrow transplant registry serve as illustration

stochastic calculus as a tool in survival analysis a review this paper gives a brief survey of the uses of stochastic calculus in survival analysis the role played by martingale central limit theory in deriving asymptotic distributions of estimators and test statistics is described the nelson aalen estimator the kaplan meier estimator cox s proportional hazards model aalen s additive risk model and a goodness of fit test for cox s model are discussed sketches of the proofs of the main results are included

weighted least squares estimation for aalen s additive risk model abstract cox s proportional hazards model has so far been the most popular model for the regression analysis of censored survival data however the additive risk model of aalen can provide a useful and biologically more plausible alternative aalen s model stipulates that the conditional hazard function for a subject whose covariates are y y 1 yp has the form h t y y t where 1 p is an unknown vector of hazard functions this article discusses inference for based on a weighted least squares wls estimator of the vector of cumulative hazard functions the asymptotic distribution of the wls estimator is derived and used to obtain confidence intervals and bands for the cumulative hazard functions both a grouped data and a continuous data version of the estimator are examined an extensive simulation study is carried out the method is applied to grouped data on the incidence of cancer mortality among japanese atomic bomb survivors