semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

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

model inconsistency illustrated by the cox proportional hazards model we consider problems involving the comparison of two or more treatments where we have the opportunity to adjust for relevant covariates either conditionally in a regression model or implicitly in repeated measures data for example in crossover trials it is seen that for data arising from non normal distributions there is the possibility that models adjusting for covariates and those not adjusting for covariates will be inconsistent that is at most one of the models can be valid alternatively even if conditional and unconditional models are valid parameters in each model may have different interpretations we note that this presents difficulties for the specification and interpretation of the analysis it is also clear that model validation is critical specific attention is paid to survival data analysed by the cox proportional hazards model

a latent variable model for discrete multivariate psychometric waiting times a version of the discrete proportional hazards model is developed for psychometrical applications in such applications a primary covariate that influences failure times is a latent variable representing a psychological construct the metropolis hastings algorithm is studied as a method for performing marginal likelihood inference on the item parameters the model is illustrated with a real data example that relates the age at which teenagers first experience various substances to the latent ability to avoid the onset of such behaviors

bounds and expansions for fisher information when the moments are known summary an expansion of the score statistic as a polynomial in the random variable can be used to provide a nondecreasing sequence of lower bounds for the fisher information when the moments are known as functions of the parameter if the random variable is asymptotically normal the first three bounds provide the first three terms in the asymptotic expansion for the fisher information this leads to a definition of efficiency which may be used to advantage with small sample sizes providing lower bounds for the efficiency of any statistic whose moments are known but whose exact distribution is intractable fisher 1925 suggested that the efficiency of a statistic be measured by its squared correlation with the maximum likelihood estimate this idea was extended by rao 1962 who defined first and second order efficiency by considering how well a linear or quadratic function of the statistic correlated with the derivative of the log likelihood in 2 of the present paper we develop this further by looking at polynomial expansions of the score statistic to obtain a nondecreasing sequence of lower bounds for the fisher information 4y 0 of a statistic y y x which is some function of the data x these bounds may be expressed in terms of the moments of the statistic and their first derivatives with respect to the unknown parameter 0 if we return to fisher s 1925 definition of efficiency as the ratio of fy 0 ox 0 whre ox 0 is the fisher information in the whole sample we can use this to obtain an efficiency for y which is invariant under one one transformations and which does not need to appeal to asymptotic arguments the results are particularly useful for random variables whose moments are known but whose exact sampling distribution is either unknown or intractable in 3 we consider other implications such as the possibility of using different sequences of functions and the question of convergence a recent application of these results by brockwell brown 1981 is given as an example rao 1962 pointed out that the limit of the ratio fy 0 fx o in large samples was the asymptotic squared correlation between the statistic y and the derivative of the log likelihood function lx o alx 0 ao for the full data set when this ratio tends to one both fisher and rao suggested using lim fx 0 fy 0 as n oo as a means of discriminating between alternative statistics this asymptotic concept of second order

nonparametric estimation of cause specific cross hazard ratio with bivariate competing risks data we propose an alternative representation of the cause specific cross hazard ratio for bivariate competing risks data the representation leads to a simple plug in estimator unlike an existing ad hoc procedure the large sample properties of the resulting inferences are established simulations and a real data example demonstrate that the proposed methodology may substantially reduce the computational burden of the existing procedure while maintaining similar efficiency properties

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

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

semiparametric inference for surrogate endpoints with bivariate censored data considerable attention has been recently paid to the use of surrogate endpoints in clinical research we deal with the situation where the two endpoints are both right censored while proportional hazards analyses are typically used for this setting their use leads to several complications in this article we propose the use of the accelerated failure time model for analysis of surrogate endpoints based on the model we then describe estimation and inference procedures for several measures of surrogacy a complication is that potentially both the independent and dependent variable are subject to censoring we adapt the theil sen estimator to this problem develop the associated asymptotic results and propose a novel resampling based technique for calculating the variances of the proposed estimators the finite sample properties of the estimation methodology are assessed using simulation studies and the proposed procedures are applied to data from an acute myelogenous leukemia clinical trial

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

higher dimensional clayton oakes models for multivariate failure time data the clayton oakes bivariate failure time model is extended to dimensions m 2 in a manner that allows unspecified marginal survivor functions for all dimensions less than m special cases that allow unspecified marginal survivor functions of dimension q with q m while making some provisions for dependencies of dimension greater than q are also described

a goodness of fit test for association in a bivariate survival model summary we propose a simple test of constant conditional hazard ratio in the clayton model 1978 by comparing the unweighted and weighted concordance estimators of the association parameter if the clayton model holds the difference of these two estimates converges to zero the proposed test is consistent against alternatives under which the two concordance estimators converge to different values we derive an explicit formula for the asymptotic variance and derive the asymptotic distribution of the test statistic under the clayton model then we extend the test statistic to incorporate censoring the proposed test is expected to perform well for a general class of alternatives with monotone conditional hazard ratio we examine the finite sample properties of the test statistic through simulations

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

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

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

transmission of packets on a hierarchical network statistics and explosive percolation we analyze an idealized model for the transmission or flow of particles or discrete packets of information in a weight bearing branching hierarchical two dimensional network and its variants the capacities add hierarchically down the clusters each node can accommodate a limited number of packets depending on its capacity and the packets hop from node to node following the links between the nodes the statistical properties of this system are given by the maxwell boltzmann distribution we obtain analytical expressions for the mean occupation numbers as functions of capacity for different network topologies the analytical results are shown to be in agreement with the numerical simulations the traffic flow in these models can be represented by the site percolation problem it is seen that the percolation transitions in the 2d model and in its variant lattices are continuous transitions whereas the transition is found to be explosive discontinuous for the v lattice the critical case of the 2d lattice the scaling behavior of the second order percolation case is studied in detail we discuss the implications of our analysis

time dependent cross ratio estimation for bivariate failure times in the analysis of bivariate correlated failure time data it is important to measure the strength of association among the correlated failure times one commonly used measure is the cross ratio motivated by cox s partial likelihood idea we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is examined using simulation studies and it is applied to the australian twin data

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

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

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

nonparametric estimation of bivariate failure time associations in the presence of a competing risk most research on the study of associations among paired failure times has either assumed time invariance or been based on complex measures or estimators little has accommodated competing risks this paper targets the conditional cause specific hazard ratio henceforth called the cause specific cross ratio a recent modification of the conditional hazard ratio designed to accommodate competing risks data estimation is accomplished by an intuitive non parametric method that localizes kendall s tau time variance is accommodated through a partitioning of space into bins between which the strength of association may differ inferential procedures are developed small sample performance is evaluated and the methods are applied to the investigation of familial association in dementia onset

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

regression models and multivariate life tables semiparametric multiplicative form regression models are specified for marginal single and double failure hazard rates for the regression analysis of multivariate failure time data cox type estim

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

an extension of kendall s coefficient of concordance to bivariate interval censored data non parametric tests of independence as well as accompanying measures of association are essential tools for the analysis of bivariate data such tests and measures have been developed for uncensored and right censored failure time data but have not been developed for interval censored failure time data bivariate interval censored data arise in aids studies in which screening tests for early signs of viral and bacterial infection are done at clinic visits because of missed clinic visits the actual times of first positive screening tests are interval censored to handle such data we propose an extension of kendall s coefficient of concordance we apply it to data from an aids study that recorded times of shedding of cytomegalovirus cmv and times of colonization of mycobacterium avium complex mac we examine the performance of our proposed measure through a simulation study

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

fock model and segal bargmann transform for minimal representations of hermitian lie groups abstract for any hermitian lie group g of tube type we construct a fock model of its minimal representation the fock space is defined on the minimal nilpotent k c orbit x in p c and the l 2 inner product involves a k bessel function as density here k g is a maximal compact subgroup and g c k c p c is a complexified cartan decomposition in this realization the space of k finite vectors consists of holomorphic polynomials on x the reproducing kernel of the fock space is calculated explicitly in terms of an i bessel function we further find an explicit formula of a generalized segal bargmann transform which intertwines the schrodinger and fock model its kernel involves the same i bessel function using the segal bargmann transform we also determine the integral kernel of the unitary inversion operator in the schrodinger model which is given by a j bessel function

efficient estimation of semiparametric multivariate copula models we propose a sieve maximum likelihood estimation procedure for a broad class of semiparametric multivariate distributions a joint distribution in this class is characterized by a parametric copula function evaluated at nonparametric marginal distributions this class of distributions has gained popularity in diverse fields due to its flexibility in separately modeling the dependence structure and the marginal behaviors of a multivariate random variable and its circumvention of the curse of dimensionality associated with purely nonparametric multivariate distributions we show that the plug in sieve maximum likelihood estimators mles of all smooth functionals including the finite dimensional copula parameters and the unknown marginal distributions are semiparametrically efficient and that their asymptotic variances can be estimated consistently moreover prior restrictions on the marginal distributions can be easily incorporated into the sieve maximum likelihood estimation procedure to achieve fu

checking the adequacy of the gamma frailty model for multivariate failure times summary multivariate failure time data arise when the sample consists of clusters and each cluster contains several dependent failure times the semiparametric gamma frailty model vaupel manton stallard 1979 clayton 1978 oakes 1982 for multivariate failure times characterises the intracluster dependence by the gamma frailty distribution while allowing the marginal distributions to be unspecified this paper develops both graphical and numerical techniques for checking the adequacy of this model the proposed techniques are based on the posterior expectation of the frailty given the observable data two examples from genetics are provided