regression models for relative survival four approaches to estimating a regression model for relative survival using the method of maximum likelihood are described and compared the underlying model is an additive hazards model where the total hazard is written as the sum of the known baseline hazard and the excess hazard associated with a diagnosis of cancer the excess hazards are assumed to be constant within pre specified bands of follow up the likelihood can be maximized directly or in the framework of generalized linear models minor differences exist due to for example the way the data are presented individual aggregated or grouped and in some assumptions e g distributional assumptions the four approaches are applied to two real data sets and produce very similar estimates even when the assumption of proportional excess hazards is violated the choice of approach to use in practice can therefore be guided by ease of use and availability of software we recommend using a generalized linear model with a poisson error structure based on collapsed data using exact survival times the model can be estimated in any software package that estimates glms with user defined link functions including sas stata s plus and r and utilizes the theory of generalized linear models for assessing goodness of fit and studying regression diagnostics

splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

assessing time by covariate interactions in proportional hazards regression models using cubic spline functions proportional hazards or cox regression is a popular method for modelling the effects of prognostic factors on survival use of cubic spline functions to model time by covariate interactions in cox regression allows investigation of the shape of a possible covariate time dependence without having to specify a specific functional form cubic spline functions allow one to graph such time by covariate interactions to test formally for the proportional hazards assumption and also to test for non linearity of the time by covariate interaction the functions can be fitted with existing software using relatively few parameters the regression coefficients are estimated using standard maximum likelihood methods

an overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death we propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors the baseline hazard was modelled until 10 years follow up using parametric continuous functions six models including cubic regression splines were considered and the akaike information criterion was used to select the final model this approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information splines were also used to model simultaneously non linear effects of continuous covariates and time dependent hazard ratios this led to a graphical representation of the hazard ratio that can be useful for clinical interpretation estimates of these models were obtained by likelihood maximization we showed that these estimates could be also obtained using standard algorithms for poisson regression

purely infinite partial crossed products let a g be a partial dynamical system we show that there is a bijective correspondence between g invariant ideals of a and ideals in the partial crossed product a rg provided the action is exact and residually topologically free assuming in addition a technical condition automatic when a is abelian we show that a rg is purely infinite if and only if the positive nonzero elements in a are properly infinite in a rg as an application we verify pure infiniteness of various partial crossed products including realisations of the cuntz algebras on oa on and oz as partial crossed products

a relative survival regression model using b spline functions to model non proportional hazards relative survival a method for assessing prognostic factors for disease specific mortality in unselected populations is frequently used in population based studies however most relative survival models assume that the effects of covariates on disease specific mortality conform with the proportional hazards hypothesis which may not hold in some long term studies to accommodate variation over time of a predictor s effect on disease specific mortality we developed a new relative survival regression model using b splines to model the hazard ratio as a flexible function of time without having to specify a particular functional form our method also allows for testing the hypotheses of hazards proportionality and no association on disease specific hazard accuracy of estimation and inference were evaluated in simulations the method is illustrated by an analysis of a population based study of colon cancer

nica toeplitz algebras associated with product systems over right lcm semigroups abstract we prove uniqueness of representations of nica toeplitz algebras associated to product systems of c correspondences over right lcm semigroups by applying our previous abstract uniqueness results developed for c precategories our results provide an interpretation of conditions identified in work of fowler and fowler raeburn and apply also to their crossed product twisted by a product system in the new context of right lcm semigroups as well as to a new doplicher roberts type c algebra associated to the nica toeplitz algebra as a derived construction we develop nica toeplitz crossed products by actions with completely positive maps this provides a unified framework for nica toeplitz semigroup crossed products by endomorphisms and by transfer operators we illustrate these two classes of examples with semigroup c algebras of right and left semidirect products

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

solving large scale minimax problems with the primal dual steepest descent algorithm this paper shows that the primal dual steepest descent algorithm developed by zhu and rockafellar for large scale extended linear quadratic programming can be used in solving constrained minimax problems related to a generalc2 saddle function it is proved that the algorithm converges linearly from the very beginning of the iteration if the related saddle function is strongly convex concave uniformly and the cross elements between the convex part and the concave part of the variables in its hessian are bounded on the feasible region better bounds for the asymptotic rates of convergence are also obtained the minimax problems where the saddle function has linear cross terms between the convex part and the concave part of the variables are discussed specifically as a generalization of the extended linear quadratic programming some fundamental features of these problems are laid out and analyzed

amenability for fell bundles given a fell bundle b over a discrete group we construct its reduced cross sectional algebra c r b in analogy with the reduced crossed products defined for c dynamical systems when the reduced and full cross sectional algebras of b are isomorphic we say that the bundle is amenable we then formulate an approximation property which we prove to be a sufficient condition for amenability a theory of graded c algebras possessing a conditional expectation is developed with an eye on the fell bundle that one naturally associates to the grading we show for instance that all such algebras are isomorphic to c r b when the bundle is amenable we also study induced ideals in graded c algebras and obtain a generalization of results of str til and voiculescu on af algebras and of nica on quasi lattice ordered groups a brief comment is made on the relevance to our theory of a certain open problem in the theory of exact c algebras an application is given to the case of an fn grading of the cuntz krieger algebras oa recently discovered by quigg and raeburn specifically we show that the cuntz krieger bundle satisfies the approximation property and hence is amenable for all matrices a with entries in 0 1 even if a does not satisfy the well known property i studied by cuntz and krieger in their paper

goodness of fit of relative survival models additive regression models are preferred over multiplicative models in the analysis of relative survival data such preferences are mainly grounded in practical experience with mostly cancer registries data where the basic assumption of the additivity of hazards is more likely to be met also the interpretation of coefficients is more meaningful in additive than in multiplicative models nonetheless the question of goodness of fit of the assumed model must still be addressed and while there is an abundance of methods to check the goodness of fit of multiplicative models the respective arsenal for additive models is almost empty we propose here a variety of procedures for testing the null hypothesis of a good fit these are based on partial residuals defined similarly to schoenfeld residuals familiar for cox model diagnostics the tests have appropriate sizes under the null hypothesis and good power under different alternatives we investigate their performance through simulations and apply the methods to data from a study into survival of colon cancer patients

flexible modeling of the effects of continuous prognostic factors in relative survival relative survival methods permit separating the effects of prognostic factors on disease related excess mortality from their effects on other causes natural mortality even when individual causes of death are unknown as in conventional crude survival accurate assessment of prognostic factors requires testing and possibly modeling of non proportional effects and for continuous covariates of non linear relationships with the hazard we propose a flexible extension of the additive hazards relative survival model in which the observed all causes mortality hazard is represented by a sum of disease related excess and natural mortality hazards in our flexible model the three functions representing i the baseline hazard for excess mortality ii the time dependent effects and iii for continuous covariates non linear effects on the logarithm of this hazard are all modeled by low dimension cubic regression splines non parametric likelihood ratio tests are proposed to test the time dependent and non linear effects the accuracy of the estimated functions is evaluated in multivariable simulations to illustrate the new insights offered by the proposed model we apply it to re assess the effects of patient age and of secular trends on disease related mortality in colon cancer

on the primal dual steepest descent algorithm for extended linear quadratic programming the aim of this paper is two fold first new variants are proposed for the primal dual steepest descent algorithm as one in the family of primal dual projected gradient algorithms developed by zhu and rockafellar siam j optim 3 1993 pp 751 783 for large scale extended linear quadratic programming the variants include a second update scheme for the iterates where the primal dual feedback is arranged in a new pattern as well as alternatives for the perfect line search in the original version of the reference second new linear convergence results are proved for all these variants of the algorithm including the original version as a special case without the additional assumptions used by zhu and rockafellar for the variants with the second update scheme a much sharper estimation for the rate of convergence is obtained due to the new primal dual feedback pattern

proportional excess hazards assume that the excess risk of an individual over a known background rate can be well approximated by the proportional hazards model such might be the case for a cohort at risk of dying from causes that are independent of those that affect the general population we propose estimators for both the regression parameters and the nonparametric baseline hazard function the estimators are shown to be consistent asymptotically normal and efficient analogues of the wald score and likelihood ratio test are provided the relevance of the asymptotic results to samples of sizes 500 and 100 is illustrated by simulation the model is used to estimate the prognostic significance of stage and histology in adults with non hodgkin s lymphoma

binomial regression with monotone splines a psychometric application abstract a binomial regression function p x models the probability of rj successes in nj trials as a function of the values of an observed covariate xj and or a latent variable j j 1 j this article explores the use of monotone regression splines to define p and applies them to the representation of test items as functions of examinee ability some illustrative data suggest that the flexibility of monotone splines permits the detection of item characteristics not observable using logistic based or log linear approaches a simulation study indicates that estimates of both item characteristic curves and ability are reasonably precise for numbers of items and examinees typical of large university lectures given a set of such binomial regression functions it can be useful to study the principal components of functional variation the extension of multivariate principal components analysis to permit the analysis of many item characteristic curves is described

purely infinite crossed products by endomorphisms 2013 elsevier inc all rights reserved this is the authors accepted and refereed manuscript to the article author s post print must be released with a creative commons attribution non commercial no derivatives license

pure infiniteness and ideal structure of c algebras associated to fell bundles abstract we investigate structural properties of the reduced cross sectional algebra c r b of a fell bundle b over a discrete group g conditions allowing one to determine the ideal structure of c r b are studied notions of aperiodicity paradoxicality and b infiniteness for the fell bundle b are introduced and investigated by themselves and in relation to the partial dynamical system dual to b several criteria of pure infiniteness of c r b are given it is shown that they generalize and unify corresponding results obtained in the context of crossed products by the following duos laca spielberg 34 jolissaint robertson 21 sierakowski rordam 47 giordano sierakowski 18 and ortega pardo 39 for exact separable fell bundles satisfying the residual intersection property primitive ideal space of c r b is determined the results of the paper are shown to be optimal when applied to graph c algebras applications to a class of exel larsen crossed products are presented

simple purely infinite c algebras and n filling actions let n be a positive integer we introduce a concept which we call the n filling property for an action of a group on a separable unital c algebra a if a c is a commutative unital c algebra and the action is induced by a group of homeomorphisms of then the n filling property reduces to a weak version of hyperbolicity the n filling property is used to prove that certain crossed product c algebras are purely infinite and simple a variety of group actions on boundaries of symmetric spaces and buildings have the n filling property an explicit example is the action of sln z on the projective n space

flexible estimation of survival curves conditional on non linear and time dependent predictor effects prognostic studies often estimate survival curves for patients with different covariate vectors but the validity of their results depends largely on the accuracy of the estimated covariate effects to avoid conventional proportional hazards and linearity assumptions flexible extensions of cox s proportional hazards model incorporate non linear nl and or time dependent td covariate effects however their impact on survival curves estimation is unclear our primary goal is to develop and validate a flexible method for estimating individual patients survival curves conditional on multiple predictors with possibly nl and or td effects we first obtain maximum partial likelihood estimates of nl and td effects and use backward elimination to select statistically significant effects into a final multivariable model we then plug the selected nl and td estimates in the full likelihood function and estimate the baseline hazard function and the resulting survival curves conditional on individual covariate vectors the td and nl functions and the log hazard are modeled with unpenalized regression b splines in simulations our flexible survival curve estimates were unbiased and had much lower mean square errors than the conventional estimates in real life analyses of mortality after a septic shock our model improved significantly the deviance likelihood ratio test 84 8 df 20 p 0 0001 and changed substantially the predicted survival for several subjects

outer automorphisms and reduced crossed products of simple c algebras every outer automorphism of a separable simplec algebra is shown to have a pure state which is mapped into an inequivalent state under this automorphism the reduced crossed product of a simplec algebra by a discrete group of outer automorphisms is shown to be simple

a general primal dual envelope method for convex programming problems a general decomposition framework for solving large scale convex programming problems is described new algorithms are obtained and several known techniques are recovered as special cases including dantzig wolfe column generation the finite envelope method of rockafellar and zhu s primal dual steepest descent method

co universal algebras associated to product systems and gauge invariant uniqueness theorems let x be a product system over a quasi lattice ordered group under mild hypotheses we associate to x a c algebra which is co universal for injective nica covariant toeplitz representations of x which preserve the gauge coaction under appropriate amenability criteria this co universalc algebra coincides with the cuntz nica pimsner algebra introduced by sims and yeend we prove two key uniqueness theorems and indicate how to use our theorems to realise a number of reduced crossed products as instances of our co universal algebras in each case it is an easy corollary that the cuntz nica pimsner algebra is isomorphic to the corresponding full crossed product

joint estimation of time dependent and non linear effects of continuous covariates on survival in order to yield more flexible models the cox regression model lambda t x lambda 0 t exp betax has been generalized using different non parametric model estimation techniques one generalization is the relaxation of log linearity in x lambda t x lambda 0 t exp r x another is the relaxation of the proportional hazards assumption lambda t x lambda 0 t exp beta t x these generalizations are typically considered independently of each other we propose the product model lambda t x lambda 0 t exp beta t r x which allows for joint estimation of both effects and investigate its properties the functions describing the time dependent beta t and non linear r x effects are modelled simultaneously using regression splines and estimated by maximum partial likelihood likelihood ratio tests are proposed to compare alternative models simulations indicate that both the recovery of the shapes of the two functions and the size of the tests are reasonably accurate provided they are based on the correct model by contrast type i error rates may be highly inflated and the estimates considerably biased if the model is misspecified applications in cancer epidemiology illustrate how the product model may yield new insights about the role of prognostic factors

dynamic regression hazards models for relative survival a natural way of modelling relative survival through regression analysis is to assume an additive form between the expected population hazard and the excess hazard due to the presence of an additional cause of mortality within this context the existing approaches in the parametric semiparametric and non parametric setting are compared and discussed we study the additive excess hazards models where the excess hazard is on additive form this makes it possible to assess the importance of time varying effects for regression models in the relative survival framework we show how recent developments can be used to make inferential statements about the non parametric version of the model this makes it possible to test the key hypothesis that an excess risk effect is time varying in contrast to being constant over time in case some covariate effects are constant we show how the semiparametric additive risk model can be considered in the excess risk setting providing a better and more useful summary of the data estimators have explicit form and inference based on a resampling scheme is presented for both the non parametric and semiparametric models we also describe a new suggestion for goodness of fit of relative survival models which consists on statistical and graphical tests based on cumulative martingale residuals this is illustrated on the semiparametric model with proportional excess hazards we analyze data from the trace study using different approaches and show the need for more flexible models in relative survival

a model combining excess and relative mortality for population based studies considering expected mortality provides an attractive approach to analyse mortality of population based cohorts of patients presenting with a chronic disease two classes of methods are available either modelling the excess mortality using an additive hazard model or modelling the relative mortality using a multiplicative hazard model because these two models are informative to look for factors associated with mortality related to a chronic disease we developed an alternative model modelling both the excess and the relative mortality we generalised andersen and vaeth s model to fit covariates and obtain directly an estimation of the excess mortality ratio and relative mortality ratio for each covariate we assessed the performances of the combined model by using simulations and it appeared satisfactorily we illustrate the combined model by data collected in patients presenting with end stage renal disease and treated by dialysis the combined model offers the possibility of performing pure additive and multiplicative models and thus to compare their log likelihoods the combined model appears useful to select one of these pure models or to conclude to the need of modelling both excess and relative mortality in this latter case our model enabled better describing the effect of covariates on the excess and relative mortality

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

a new proof of kirchberg s 2 stable classification i present a new proof of kirchbergs q2 stable classification theorem two separable nuclear stable unital q2 stable c algebras are isomorphic if and only if their ideal lattices are order isomorphic or equivalently their primitive ideal spaces are homeomorphic many intermediate results do not depend on pure infiniteness of any sort

multicategorical spline model for item response theory additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data a nonparametric divided by total model for joint maximum likelihood estimation of probability of choice functions for particular responses and of latent ability is proposed the model approximates probability functions by rational splines some illustrative examples of real test data analysis and the results of a monte carlo study are presented

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

crossed products by spectrally free actions abstract we define spectral freeness for actions of discrete groups on c algebras we relate spectral freeness to other freeness conditions an example result is that for an action of a finite group g spectral freeness is equivalent to strong pointwise outerness and also to the condition that g 1 for every g g 1 we then prove permanence results for reduced crossed products by exact spectrally free actions for crossed products by arbitrary actions of z 2 z and for extensions direct limits stable isomorphism and several related constructions for the following properties the combination of pure infiniteness and the ideal property residual hereditary infiniteness closely related to pure infiniteness residual sp a strengthening of property sp suitable for nonsimple c algebras the weak ideal property closely related to the ideal property for the weak ideal property we can allow arbitrary crossed products by any finite abelian group these properties of c algebras are shown to have formulations of the same general type allowing them all to be handled using a common set of theorems