semiparametric transformation models for semicompeting survival data semicompeting risk outcome data e g time to disease progression and time to death are commonly collected in clinical trials however analysis of these data is often hampered by a scarcity of available statistical tools as such we propose a novel semiparametric transformation model that improves the existing models in the following two ways first it estimates regression coefficients and association parameters simultaneously second the measure of surrogacy for example the proportion of the treatment effect that is mediated by the surrogate and the ratio of the overall treatment effect on the true endpoint over that on the surrogate endpoint can be directly obtained we propose an estimation procedure for inference and show that the proposed estimator is consistent and asymptotically normal extensive simulations demonstrate the valid usage of our method we apply the method to a multiple myeloma trial to study the impact of several biomarkers on patients semicompeting outcomes namely time to progression and time to death

nonparametric estimation of the sojourn time distributions for a multipath model summary we use a multipath multistate model to describe data with multiple end points statistical inference based on the intermediate end point is challenging because of the problems of nonidentifiability and dependent censoring we study nonparametric estimation for the path probability and the sojourn time distributions between the states the methodology proposed can be applied to analyse cure models which account for the competing risk of death asymptotic properties of the estimators proposed are derived simulation shows that the methods proposed have good finite sample performance the methodology is applied to two data sets

rank tests for association with right censored data summary rank tests for association between a time variable and a continuous covariate and between two time variables are given in the presence of censoring in the first case these tests are related to the semiparametric tests of cox 1972 and prentice 1978 but differ in that the covariate is replaced by a score computed from its rank in the second case the test statistic is again a simple inner product which in the proportional hazards model reduces to the correlation between the two vectors of log rank scores the loss of efficiency arising from incorrect score functions is also explored when there is no censoring in this paper we consider a general model for association between pairs of observations in which either variable or both variables may be right censored the aim is to develop tests based on the generalized ranks of both variables which have maximal power at alternatives which are near to the null hypothesis of independence attention will be concentrated on two special cases of interest in survival analysis tests for association between a censored survival time and a possibly censored continuous covariate and tests for association between the times to different events beginning with cox 1972 the first situation has been studied extensively in a semiparametric set up in which information based on ranks is used for the time variable but exact values are used for the covariate procedures which use only the ranks of both variables have been developed by brown hollander korwar 1974 and more recently by o brien 1978 however neither of these procedures have been developed with a particular model in mind and one of the achievements of the present paper is to derive rank tests with good local power when a particular model such as the proportional hazards model holds in the case of a proportional hazards model with a continuous covariate the present development may be preferable to the semiparametric methods when the functional form of the relation ship between the hazard and the covariate is not known in advance or when errors or outliers may exist in the observed covariate values thus significance levels may be obtained which are not inflated by multiple regroupings or transformations of the covariate data although it would be expected that parametric model building with variables found to be associated with survival would often be carried out in further analyses

adaptation of bivariate frailty models for prediction with application to biological markers as prognostic indicators serial biological markers are often used in medicine as prognostic indicators for example elevated tumour antigen tests presage tumour recurrence rapid decrease in the cd4 cell counts of hiv individuals indicate high risk for developing aids methods for evaluating the usefulness of markers should address how the prediction of future risk is revised in a way that assists the making of decisions at the time such an indicator is observed proportional hazards modelling with time varying covariates a common approach seems unnatural for this purpose because its orientation is explanatory it addresses the question is the individual suffering a failure more likely to have had the marker and allows use of all information prior to the failure rather than the more relevant predictive question does the appearance of the marker alter the individual s subsequent risk enough to warrant intervention today frailty models do address this question but available methods for their analysis make censoring assumptions which are inappropriate in the predictive setting we adapt frailty models to relevant censoring processes and propose a predictively oriented test statistic and a related estimation procedure based on summing concurrent martingales each representing a landmark analysis

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

numerical computation of the moments of a probability distribution from its transform we present a simple fast and robust algorithm for numerically computing the first n moments arbitrary n of a nonnegative probability distribution from its laplace stieltjes transform continuous mixed case or z transform discrete case the algorithm is based on numerically inverting an adaptively modified moment generating function it only requires computation of the transform at several complex values of its argument we also show that the high order moments may be used in detecting the presence of exponential or geometric tails in distributions and in case they are present the two parameters characterizing such a tail may be accurately computed several numerical examples of interest in the queueing literature illustrate the use of the algorithm they include commonly used distributions as well as the waiting time queue length and busy period in queues with poisson or more general markovian arrival processes priority queues are also considered

estimating survival and association in a semicompeting risks model in many follow up studies patients are subject to concurrent events in this article we consider semicompeting risks data as defined by fine jiang and chappell 2001 biometrika 88 907 919 where one event is censored by the other but not vice versa the proposed model involves marginal survival functions for the two events and a parametric family of copulas for their dependency this article suggests a general method for estimating the dependence parameter when the dependency is modeled with an archimedean copula it uses the copula graphic estimator of zheng and klein 1995 biometrika 82 127 138 for estimating the survival function of the nonterminal event subject to dependent censoring asymptotic properties of these estimators are derived simulations show that the new methods work well with finite samples the copula graphic estimator is shown to be more accurate than the estimator proposed by fine et al 2001 its performances are similar to those of the self consistent estimator of jiang fine kosorok and chappell 2005 scandinavian journal of statistics 33 1 20 the analysis of a data set emphasizing the estimation of characteristics of the observable region is presented as an illustration

statistical analysis of illness death processes and semicompeting risks data in many instances a subject can experience both a nonterminal and terminal event where the terminal event e g death censors the nonterminal event e g relapse but not vice versa typically the two events are correlated this situation has been termed semicompeting risks e g fine jiang and chappell 2001 biometrika 88 907 939 wang 2003 journal of the royal statistical society series b 65 257 273 and analysis has been based on a joint survival function of two event times over the positive quadrant but with observation restricted to the upper wedge implicitly this approach entertains the idea of latent failure times and leads to discussion of a marginal distribution of the nonterminal event that is not grounded in reality we argue that similar to models for competing risks latent failure times should generally be avoided in modeling such data we note that semicompeting risks have more classically been described as an illness death model and this formulation avoids any reference to latent times we consider an illness death model with shared frailty which in its most restrictive form is identical to the semicompeting risks model that has been proposed and analyzed but that allows for many generalizations and the simple incorporation of covariates nonparametric maximum likelihood estimation is used for inference and resulting estimates for the correlation parameter are compared with other proposed approaches asymptotic properties simulations studies and application to a randomized clinical trial in nasopharyngeal cancer evaluate and illustrate the methods a simple and fast algorithm is developed for its numerical implementation

on semi competing risks data summary we consider a variation of the competing risks problem in which a terminal event censors a non terminal event but not vice versa the joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable day et al 1997 with the marginal distributions unspecified an estimator for the association parameter is obtained from a concordance estimating function a novel plug in estimator for the marginal distribution of the non terminal event is shown to be uniformly consistent and to converge weakly to a gaussian process the assumptions on the joint distribution outside the upper wedge are weaker than those usually made in competing risks analyses simulations demonstrate that the methods work well with practical sample sizes the proposals are illustrated with data on morbidity and mortality in leukaemia patients

regression modeling of semicompeting risks data semicompeting risks data are often encountered in clinical trials with intermediate endpoints subject to dependent censoring from informative dropout unlike with competing risks data dropout may not be dependently censored by the intermediate event there has recently been increased attention to these data in particular inferences about the marginal distribution of the intermediate event without covariates in this article we incorporate covariates and formulate their effects on the survival function of the intermediate event via a functional regression model to accommodate informative censoring a time dependent copula model is proposed in the observable region of the data which is more flexible than standard parametric copula models for the dependence between the events the model permits estimation of the marginal distribution under weaker assumptions than in previous work on competing risks data new nonparametric estimators for the marginal and dependence models are derived from nonlinear estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes graphical model checking techniques are presented for the assumed models nonparametric tests are developed accordingly as are inferences for parametric submodels for the time varying covariate effects and copula parameters a novel time varying sensitivity analysis is developed using the estimation procedures simulations and an aids data analysis demonstrate the practical utility of the methodology

regression analysis based on semicompeting risks data summary semicompeting risks data are commonly seen in biomedical applications in which a terminal event censors a non terminal event possible dependent censoring complicates statistical analysis we consider regression analysis based on a non terminal event say disease progression which is subject to censoring by death the methodology proposed is developed for discrete covariates under two types of assumption first separate copula models are assumed for each covariate group and then a flexible regression model is imposed on the progression time which is of major interest model checking procedures are also proposed to help to choose a best fitted model under a two sample setting lin and co workers proposed a competing method which requires an additional marginal assumption on the terminal event and implicitly assumes that the dependence structures in the two groups are the same using simulations we compare the two approaches on the basis of their finite sample performances and robustness properties under model misspecification the method proposed is applied to a bone marrow transplant data set

semiparametric analysis of survival data with left truncation and dependent right censoring summary studies of chronic life threatening diseases often involve both mortality and morbidity in observational studies the data may also be subject to administrative left truncation and right censoring because mortality and morbidity may be correlated and mortality may censor morbidity the lynden bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the nonterminal event we propose a semiparametric estimator for this survival function based on a joint model for the two time to event variables which utilizes the gamma frailty specification in the region of the observable data first we develop a novel estimator for the gamma frailty parameter under left truncation using this estimator we then derive a closed form estimator for the marginal distribution of the nonterminal event the large sample properties of the estimators are established via asymptotic theory the methodology performs well with moderate sample sizes both in simulations and in an analysis of data from a diabetes registry

semiparametric inferences for association with semi competing risks data in many biomedical studies it is of interest to assess dependence between bivariate failure time data we focus here on a special type of such data referred to as semi competing risks data in this article we develop methods for making inferences regarding dependence of semi competing risks data across strata of a discrete covariate z a class of rank statistics for testing constancy of association across strata are proposed its asymptotic properties are also derived we develop a novel resampling based technique for calculating the variances of the proposed test statistics in addition we develop methods for combining test statistics for assessing marginal effects of z on the dependent censoring variable as well as its effects on association the finite sample properties of the proposed methodology are assessed using simulation studies and they are applied to data from a leukaemia transplantation study copyright 2005 john wiley sons ltd

estimating survival under a dependent truncation summary the product limit estimator calculated from data subject to random left truncation relies on the testable assumption of quasi independence between the failure time and the truncation time in this paper we propose a model for a truncated sample of pairs xi y satisfying 1 xi a possible dependency between the truncation time and the variable of interest is modelled with a parametric family of copulas the model also features a distribution function fx and a survival distribution sy associated with the marginal behaviours of x and y in the observable region y x semiparametric estimators for these two functions are proposed they do not make any parametric assumption about either fx or sy we derive an estimator for the copula parameter cx based on the conditional kendall s tau we generalise the copula graphic estimators of zheng klein 1995 to truncated variables the asymptotic distributions of all these estimators are then investigated the methods are illustrated with a real dataset on hiv infection by transfusion and by simulations

a shape distance based on the fisher rao metric and its application for shapes clustering abstract in the clustering of shapes which is a longstanding challenge in the framework of geometric morphometrics and shape analysis is crucial the selection and application of a suitable and appropriate measurement of distance among observations i e individuals the aim of this study is to model shapes from complex systems using information geometry tools it is well known that the fisher information endows the statistical manifold defined by a family of probability distributions with a riemannian metric called the fisher rao metric with respect to this geodesic paths are determined minimizing information in fisher sense the geodesic distance induced by the fisher rao metric can be used to define a shape metric which enables us to quantify differences between shapes the discriminative power of the proposed fisher rao distance is tested in the context of shapes clustering on both simulated and real data sets results show a better ability in recovering the true cluster structure with respect to the standard kendall s shape metric

variability functions for parametric decomposition approximations of queueing networks we propose an enhancement to the parametric decomposition method for calculating approximate steady state performance measures of open queueing networks with non poisson arrival processes and nonexponential service time distributions instead of using a variability parameter ca2 for each arrival process we suggest using a variability function ca2 0 1 for each arrival process i e the variability parameter should be regarded as a function of the traffic intensity of a queue to which the arrival process might go variability functions provide a convenient representation of different levels of variability in different time scales for arrival processes that are not nearly renewal processes variability functions enable the approximations to account for long range effects in queueing networks that cannot be addressed by variability parameters for example the variability functions provide a way to address the heavy traffic bottleneck phenomenon in which exceptional variability either high or low

approximating a point process by a renewal process ii superposition arrival processes to queues we develop an approximation for a queue having an arrival process that is the superposition of independent renewal processes i e gi1 g 1 this model is useful for example in analyzing networks of queues where the arrival process to an individual queue is the superposition of departure processes from other queues if component arrival processes are approximated by renewal processes the gi1 g 1 model applies the approximation proposed is a hybrid that combines two basic methods described by whitt all these methods approximate the complex superposition process by a renewal process and yield a gi g 1 queue that can be solved analytically or approximately in the hybrid method the moments of the intervals in the approximating renewal process are a convex combination of the moments determined by the basic methods the weight in the convex combination is identified using the asymptotic properties of the basic methods together with simulation when compared to simulation estimates the error in hybrid

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

choice of conditional models in bivariate survival we consider bivariate survival problems in which interest is in the conditional distribution of one survival variable given an uncensored observation of the other the work is motivated by an analysis of time to cancer diagnosis then subsequent survival amongst a group of organ transplant recipients the effect of conditioning is illustrated for five standard bivariate models the consequences of adopting a misspecified marginal approach in which the conditioning variable is considered to be a fixed covariate are investigated

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

approximating nonrenewal processes by markov chains use of super erlang se chains we study a class of point processes generated by transitions in markov chains we are primarily concerned with approximating superposed phase renewal processes by these point processes we identify a subclass of markov chains that we call super erlang chains these chains have special properties that facilitate the development of approximations we outline an approximation procedure and provide computational results that demonstrate the potential of the approach the primary motivation for this study is the analysis of open queueing networks

a missing data approach to semi competing risks problems for event time data involving multiple mutually exclusive competing causes of failure classic competing risks results show that marginal survival distributions are not identifiable in a related instance one or more failure modes may be observed provided that the failure events occur in a specific order in such situations sometimes referred to as semi competing risks problems the observations may under realistic assumptions lend information about parameters of interest that would be nonidentifiable in the strict competing risks case here we present an approach that makes use of partially observable multiple modes of failures to obtain an estimate of the marginal distribution of one event type that may occur prior to the occurrence of another event type or be precluded by it we apply the proposed method to the problem of estimating the distribution of time to tumour recurrence at specific sites among breast cancer patients participating in randomized clinical trials

class dependent departure process from multiclass phase queues exact and approximate analyses in this paper we study class dependent departure processes from phase type queues when the arrival process for a subset of the classes is a poisson process we determine the laplace stieltjes transform of the stationary inter departure times of the combined output of all the other classes we also propose and test approximations for the squared coefficient of variation of the stationary inter departure times of each customer class the approximations are based on the detailed structure of the second order measures of the aggregate departure process finally we propose renewal approximations for the class dependent departure process that take into account the utilization of the queue that customers next visit