stable cohomology of spaces of non singular hypersurfaces abstract we prove that the rational cohomology of the space x d n of non singular complex homogeneous polynomials of degree d in n variables stabilizes to the cohomology of gl n c for d sufficiently large

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

representations of kac moody and virasoro algebras on modules of greenberg mohapatra algebras the theory of greenberg mohapatra algebras is developed in continuation to a previous paper standard cyclic modules are constructed for the algebras and on them kac moody and virasoro algebras are represented through a basic procedure the representations of kac moody and virasoro algebras help to understand the structure of greenberg mohapatra algebras and the question of possible violation of the pauli exclusion principle

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

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

exponential decay for binary time varying covariates in cox models cox models are commonly used in the analysis of time to event data one advantage of cox models is the ability to include time varying covariates often a binary covariate that codes for the occurrence of an event that affects an individual subject a common assumption in this case is that the effect of the event on the outcome of interest is constant and permanent for each subject in this paper we propose a modification to the cox model to allow the influence of an event to exponentially decay over time methods for generating data using the inverse cumulative density function for the proposed model are developed likelihood ratio tests and aic are investigated as methods for comparing the proposed model to the commonly used permanent exposure model a simulation study is performed and 3 different data sets are presented as examples

accelerated hazards regression model and its adequacy for censored survival data summary the accelerated hazards regression model is introduced to study the relationship between survival times and covariates through a scale change between hazard functions the model is also compared with several other popular classes of regression models for censored survival data in statistical literature test statistics are proposed and studied to assess the model s adequacy actual data from a randomized clinical trial of biodegradable carmustine polymer for treatment of brain cancer are analyzed to demonstrate the potential application of the regression model and the proposed test statistics

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

kernel estimation in a nonparametric marker dependent hazard model we introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker we establish the pointwise and global convergence of our estimator

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

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

statistical analysis of repeated events forming renewal processes for each of several individuals a sequence of repeated events forming a renewal process is observed up to some censoring time the object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals medical motivation comes from gastroenterology and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state two statistical models are considered one is the standard variance component model adapted to censored data and the other is a recent intensity based model with a random proportionality factor representing interindividual variation these models are applied to the motility data and their advantages are discussed the intensity based model allows simple empirical bayes estimation of the expected interevent times for an individual in the presence of censoring

nonsmooth backfitting for the excess risk additive regression model with two survival time scales we consider an extension of aalen s additive regression model allowing covariates to have effects that vary on two different time scales the two time scales considered are equal up to a constant that varies for each individual such as for example follow up time and age in medical studies or calendar time and age in longitudinal studies the model has been introduced in scheike 2001 where it was solved via smoothing techniques we present a new backfitting 20 algorithm estimating the structured model without having to use smoothing estimators of the cumulative regression functions on the two time scales are suggested by solving local estimating equations jointly on the two time scales we provide large sample properties and simultaneous confidence bands the model is applied to data on myocardial infarction providing a separation of the two effects stemming from time since diagnosis and age

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

marginal analyses of longitudinal data with an informative pattern of observations we consider solutions to generalized estimating equations with singular working correlation matrices of which the estimator of diggle et al 2007 is a special case we give explicit conditions for consistent estimation when the pattern of observations may be informative in such cases simulations reveal reduced bias and reduced mean squared error compared with existing alternatives a study of peritoneal dialysis is used to illustrate the methodology

survival models for cost data the forgotten additive approach the usage of the aalen additive approach is proposed to model cost data using a monte carlo simulation in a wide set of scenarios we showed that the aalen model is performing well and can be a reasonable alternative to the standard gamma regression models in addition with reference to the costami trial data we highlighted the ability of the aalen model to offer additional information about the relationships between costs and specific covariates as compared with standard regression techniques

weight calibration to improve efficiency for estimating pure risks from the additive hazards model with the nested case control design we study the efficiency of covariate specific estimates of pure risk one minus the survival function when some covariates are only available for case control samples nested in a cohort we focus on the semiparametric additive hazards model in which the hazard function equals a baseline hazard plus a linear combination of covariates with either time varying or time invariant coefficients a published approach uses the design based inclusion probabilities to reweight the nested case control data we obtain more efficient estimates of pure risks by calibrating the design weights to data available in the entire cohort for both time varying and time invariant covariate coefficients we develop explicit variance formulas for the weight calibrated estimates based on influence functions simulations show the improvement in precision by using weight calibration and confirm the consistency of variance estimators and the validity of inference based on asymptotic normality examples are provided using data from the prostate lung colorectal and ovarian cancer screening trial study plco

a psudolikelihood approach to analysis of nested case control studies in nested case control studies the controls are sampled from the risk set at the failure times of the cases the analytical basis for such studies has been limited to semiparametric estimators under proportional hazard models in this paper it is observed that conditional inclusion probabilities of ever being included in the nested case control study can be obtained where conditioning is on the information needed to carry out a nested case control study the inclusion probabilities are used in pseudolikelihoods by weighting the individual log likelihood contributions by their inverse this makes it possible to fit parametric regression models also a new semiparametric estimator is obtained under the proportional hazard model the methods are illustrated by simulation experiments and by application to a dataset

young diagrammatic methods for the representation theory of the classical groups of type bn cn dn since the appearance of the celebrated article the classical groups of weyl 7 numerous influences have occurred in the representation theory of the classical groups especially it has become folklore that the facts in this field should be expressed only in terms of young diagrams the aim of this paper is one of the realizations of this principle a classical model of our approach is the results for gl n which are known as littlewood richardson coefficients and the kostka coefficients these two coefficients can be stated in the combinatorial manner using only young diagrams independently of the rank n of gl n we generalize these results to the other classical groups over c namely we give explicit formulas to decompose the tensor product of two irreducible representations into irreducible constituents also we have obtained an interesting relationship linking the irreducible characters of sp and so which we call duality relation between the representations of sp and so as for explicit formulas for the multiplicities of weights in the form of polynomials in the rank n we refer to 3

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

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

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

global tests in the additive hazards regression model in this article we discuss testing for the effect of several covariates in the additive hazards regression model bhattacharyya and klein statist med 2005 24 14 2235 2240 note that an ad hoc weight function suggested by aalen statist med 1989 8 907 925 is inconsistent when used as a global test for comparing groups since the test statistic depends on which group is used as the baseline group we will suggest a simple alternative test that does not exhibit this problem this test is a natural extension of the logrank test we shall also discuss an alternative covariance estimator the tests are applied to a data set and a simulation study is performed

a k nearest neighbors survival probability prediction method we introduce a nonparametric survival prediction method for right censored data the method generates a survival curve prediction by constructing a weighted kaplan meier estimator using the outcomes of the k most similar training observations each observation has an associated set of covariates and a metric on the covariate space is used to measure similarity between observations we apply our method to a kidney transplantation data set to generate patient specific distributions of graft survival and to a simulated data set in which the proportional hazards assumption is explicitly violated we compare the performance of our method with the standard cox model and the random survival forests method copyright 2012 john wiley sons ltd

representation theory and homological stability abstract we introduce the idea of representation stability and several variations for a sequence of representations v n of groups g n a central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability this makes it possible to extend classical theorems of homological stability to a much broader variety of examples representation stability also provides a framework in which to find and to predict patterns from classical representation theory littlewood richardson and murnaghan rules stability of schur functors to cohomology of groups pure braid torelli and congruence groups to lie algebras and their homology to the equivariant cohomology of flag and schubert varieties to combinatorics the n 1 n 1 conjecture the majority of this paper is devoted to exposing this phenomenon through examples in doing this we obtain applications theorems and conjectures beyond the discovery of new phenomena the viewpoint of representation stability can be useful in solving problems outside the theory in addition to the applications given in this paper it is applied by church ellenberg farb in preparation 20 to counting problems in number theory and finite group theory representation stability is also used by church 2012 19 to give broad generalizations and new proofs of classical homological stability theorems for configuration spaces on oriented manifolds

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

homological stability for hurwitz spaces and the cohen lenstra conjecture over function fields we prove a homological stabilization theorem for hurwitz spaces moduli spaces of branched covers of the complex projective line this has the following arithmetic consequence let 2 be prime and a a nite abelian group then there exists q q a such that for q greater than q a positive fraction of quadratic extensions of fq t have the part of their class group isomorphic to a

a note on testing in aalen s additive hazards regression models aalen s additive hazards regression model is a useful alternative to the proportional hazards model for censored data regression when used to compare treatments this approach leads to weighted comparisons of the crude estimate of the hazard rate of each group as compared to a baseline group this is contrasted to the weighted log rank test from the proportional hazards model which compares each treatment s rate to the pooled rate we show in this brief note that aalen s suggestion for weights in this test leads to inconsistent tests in the sense that the test statistic depends on which group we pick for a baseline group we show that consistent tests are obtained by using common weight functions for all comparisons and we make some suggestions

bertini theorems over finite fields let x be a smooth quasiprojective subscheme of pn of dimension m i 0 over fq then there exist homogeneous polynomials f over fq for which the intersection of x and the hypersurface f 0 is smooth in fact the set of such f has a positive density equal to aex m 1 1 where aex s zx q s is the zeta function of x an analogue for regular quasiprojective schemes over z is proved assuming the abc conjecture and another conjecture

residuals for relative risk regression summary several possible definitions of residuals are given for relative risk regression with time varying covariates each such residual has a representation as an estimator of a stochastic integral with respect to the martingale arising from a subject s failure time counting process previously proposed residuals for individual study subjects and for specific time points are shown to be special cases of this definition as are previously derived regression diagnostics an illustration and various generalizations are also given able methods are required to detect various departures from modelling assumptions suitably defined residuals may play an important role in such identification however the nonparametric aspect of the model the possibility that modelled regression variables may be varying with follow up time and most importantly the usual presence of right censorship implies that specialized residual definitions are required the class of residuals considered here is most easily formulated using counting process notation for the failure time data let ni t yi t and zi t represent respectively for the ith subject the values of counting censoring and covariate processes at follow up time t i 1 n while ni u yi u zi u 0c u t specifies the corresponding histories for the ith subject prior to time t thus in a typical univariate failure time application ni with right continuous sample paths will take value zero prior to the time of failure on the ith subject and value one thereafter while yi with left continuous sample paths will take value one at times at which the ith subject is at risk for an observed failure and value zero otherwise the counting process ni can be uniquely decomposed so that for all t i

the hazard potential introduction and overview this is an expository article directed at reliability theorists survival analysts and others interested in looking at life history and event data here we introduce the notion of a hazard potential as an unknown resource that an item is endowed with at inception the item fails when this resource becomes depleted the cumulative hazard is a proxy for the amount of resource consumed and the hazard function is a proxy for the rate at which this resource is consumed with this conceptualization of the failure process we are able to characterize accelerated decelerated and normal tests and are also able to provide a perspective on the cause of interdependent lifetimes specifically we show that dependent life lengths are the result of dependent hazard potentials consequently we are able to generate new families of multivariate life distributions using dependent hazard potentials as a seed for an item that operates in a dynamic environment we argue that its lifetime is the killing time of a continuo

motivic random variables and representation stability ii hypersurface sections abstract we prove geometric and cohomological stabilization results for the universal smooth degree d hypersurface section of a fixed smooth projective variety as d goes to infinity we show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed grothendieck ring of varieties and deduce from this the stabilization of the hodge euler characteristic of natural families of local systems constructed from the vanishing cohomology we prove explicit formulas for the stable values using a probabilistic interpretation along with the natural analogs in point counting over finite fields we explain how these results provide new geometric examples of a weak version of representation stability for symmetric symplectic and orthogonal groups this interpretation of representation stability was studied in the prequel 20 for configuration spaces

the partly aalen s model for recurrent event data with a dependent terminal event recurrent event data are commonly observed in biomedical longitudinal studies in many instances there exists a terminal event which precludes the occurrence of additional repeated events and usually there is also a nonignorable correlation between the terminal event and recurrent events in this article we propose a partly aalen s additive model with a multiplicative frailty for the rate function of recurrent event process and assume a cox frailty model for terminal event time a shared gamma frailty is used to describe the correlation between the two types of events consequently this joint model can provide the information of temporal influence of absolute covariate effects on the rate of recurrent event process which is usually helpful in the decision making process for physicians an estimating equation approach is developed to estimate marginal and association parameters in the joint model the consistency of the proposed estimator is established simulation studies demonstrate that the proposed approach is appropriate for practical use we apply the proposed method to a peritonitis cohort data set for illustration

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

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

instrumental variable estimation in semi parametric additive hazards models instrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available two stage least squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data the semi parametric additive hazard model which can include time independent and time dependent covariate effects is particularly suited for the two stage residual inclusion method since it allows direct estimation of time independent covariate effects without restricting the effect of the residual on the hazard in this article we prove asymptotic normality of two stage residual inclusion estimators of regression coefficients in a semi parametric additive hazard model with time independent and time dependent covariate effects we consider the cases of continuous and binary exposure estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands the new methods are compared to existing ones in a simulation study and are applied to a real data set the proposed methods perform favourably especially in cases with exposure dependent censoring

two stage residual inclusion for survival data and competing risks an instrumental variable approach with application to seer medicare linked data instrumental variable is an essential tool for addressing unmeasured confounding in observational studies two stage predictor substitution 2sps estimator and two stage residual inclusion 2sri are two commonly used approaches in applying instrumental variables recently 2sps was studied under the additive hazards model in the presence of competing risks of time to events data where linearity was assumed for the relationship between the treatment and the instrument variable this assumption may not be the most appropriate when we have binary treatments in this paper we consider the 2sri estimator under the additive hazards model for general survival data and in the presence of competing risks which allows generalized linear models for the relation between the treatment and the instrumental variable we derive the asymptotic properties including a closed form asymptotic variance estimate for the 2sri estimator we carry out numerical studies in finite samples and apply our methodology to the linked surveillance epidemiology and end results seer medicare database comparing radical prostatectomy versus conservative treatment in early stage prostate cancer patients

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

further results on the non parametric linear regression model in survival analysis this paper gives further developments of a non parametric linear regression model in survival analysis three subjects are studied first martingale residuals originally developed for the cox model are introduced for our linear model their theory is developed and they are shown to be useful for judging goodness of fit the second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation in particular this is applied to judging whether the effect of a covariate disappears over time a problem for which no formal test exists the third subject is density type or kernel estimation of the regression functions themselves this might give more direct information than the cumulative plots the approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx and by survival times of grafts in renal patients

estimation of integrated transition hazards and stage occupation probabilities for non markov systems under dependent censoring we propose nonparametric estimators of the stage occupation probabilities and transition hazards for a multistage system that is not necessarily markovian using data that are subject to dependent right censoring we assume that the hazard of being censored at a given instant depends on a possibly time dependent covariate process as opposed to assuming a fixed censoring hazard independent censoring the estimator of the integrated transition hazard matrix has a nelson aalen form where each of the counting processes counting the number of transitions between states and the risk sets for leaving each stage have an ipcw inverse probability of censoring weighted form we estimate these weights using aalen s linear hazard model finally the stage occupation probabilities are obtained from the estimated integrated transition hazard matrix via product integration consistency of these estimators under the general paradigm of non markov models is established and asymptotic variance formulas are provided simulation results show satisfactory performance of these estimators an analysis of data on graft versus host disease for bone marrow transplant patients is used as an illustration

on adjustment for auxiliary covariates in additive hazard models for the analysis of randomized experiments we consider additive hazard models aalen 1989 for the effect of a randomized treatment on a survival outcome adjusting for auxiliary baseline covariates we demonstrate that the aalen least squares estimator of the treatment effect parameter is asymptotically unbiased even when the hazard s dependence on time or on the auxiliary covariates is misspecified and even away from the null hypothesis of no treatment effect we moreover show that adjustment for auxiliary baseline covariates does not change the asymptotic variance of the aalen least squares estimator of the effect of a randomized treatment we conclude that in view of its robustness against model misspecification aalen least squares estimation is attractive for evaluating treatment effects on a survival outcome in randomized experiments and that the primary reasons to consider baseline covariate adjustment in such settings may be the interest in subgroup effects or the need to adjust for informative censoring or for baseline imbalances our results also shed light on the robustness of aalen least squares estimators against model misspecification in observational studies

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

a graphical method for assessing goodness of fit in cox s proportional hazards model abstract suggested here is a simple graphical method for studying the goodness of fit in cox s regression model for survival data the method is easy to use as it does not require the estimation of alternative models and only involves quantities similar to those already appearing in the partial likelihood expression that is needed in the parameter estimation the rationale behind the graphs is very intuitive they make a direct comparison between observed and expected failure frequencies as estimated from the model in a correctly specified model one anticipates an approximate balance between such frequencies otherwise there will typically be groups of individuals for which the expected frequencies are systematically too high or too low to match with the data and this shows in the graphs introduced here in the concrete applications of the method the individuals are stratified in a way that depends on what aspect of the model is being checked against data there is always one graph for each stratum s

homological stability for configuration spaces of manifolds let cn m be the configuration space of n distinct ordered points in m we prove that if m is any connected orientable manifold closed or open the homology groups hi cn m are representation stable in the sense of church and farb arxiv 1008 1368 applying this to the trivial representation we obtain as a corollary that the unordered configuration space bn m satisfies classical homological stability for each i hi bn m hi bn 1 m for n i this improves on results of mcduff segal and others for open manifolds applied to closed manifolds this provides natural examples where rational homological stability holds even though integral homological stability fails

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

a nonparametric multiplicative hazard model for event history analysis a major issue in exploring and analyzing life history data with multiple states and events is the development and availability of flexible methods that allow simultaneous incorporation and estimation of baseline hazards detection and modelling of nonlinear functional forms of covariates and time varying effects and the possibility to include time dependent covariates in this paper we consider a nonparametric multiplicative hazard model that takes into account these aspects embedded in the counting process approach estimation is based on penalized likelihoods and splines the methods are illustrated by two real data applications one to a more conventional survival data set with two absorbing states and one to more complex sleep electroencephalography data with multiple recurrent states of sleep

marginal estimation for multi stage models waiting time distributions and competing risks analyses we provide non parametric estimates of the marginal cumulative distribution of stage occupation times waiting times and non parametric estimates of marginal cumulative incidence function proportion of persons who leave stage j for stage j within time t of entering stage j using right censored data from a multi stage model we allow for stage and path dependent censoring where the censoring hazard for an individual may depend on his or her natural covariate history such as the collection of stages visited before the current stage and their occupation times additional external time dependent covariates that may induce dependent censoring can also be incorporated into our estimates if available our approach requires modelling the censoring hazard so that an estimate of the integrated censoring hazard can be used in constructing the estimates of the waiting times distributions for this purpose we propose the use of an additive hazard model which results in very flexible robust estimates examples based on data from burn patients and simulated data with tracking are also provided to demonstrate the performance of our estimators

empirical bayes estimation for additive hazards regression models we develop a novel empirical bayesian framework for the semiparametric additive hazards regression model the integrated likelihood obtained by integration over the unknown prior of the nonparametric baseline cumulative hazard can be maximized using standard statistical software unlike the corresponding full bayes method our empirical bayes estimators of regression parameters survival curves and their corresponding standard errors have easily computed closed form expressions and require no elicitation of hyperparameters of the prior the method guarantees a monotone estimator of the survival function and accommodates time varying regression coefficients and covariates to facilitate frequentist type inference based on large sample approximation we present the asymptotic properties of the semiparametric empirical bayes estimates we illustrate the implementation and advantages of our methodology with a reanalysis of a survival dataset and a simulation study

log linear models for event histories jeroen k vermunt sage publications london 1997 no of pages xi 348 price 37 isbn 0 7619 0937 0