analysis of clustered failure time data with cure fraction using copula clustered survival data in the presence of cure has received increasing attention in this paper we consider a semiparametric mixture cure model which incorporates a logistic regression model for the cure fraction and a semiparametric regression model for the failure time we utilize archimedean copula ac models to assess the strength of association for both susceptibility and failure times between susceptible individuals in the same cluster instead of using the full likelihood approach we consider a composite likelihood function and a two stage estimation procedure for both marginal and association parameters a jackknife procedure that takes out one cluster at a time is proposed for the variance estimation of the estimators akaike information criterion is applied to select the best model among acs simulation studies are performed to validate our estimating procedures and two real data sets are analyzed to demonstrate the practical use of our proposed method

a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

extending the archimedean copula methodology to model multivariate survival data grouped in clusters of variable size summary for the analysis of clustered survival data two different types of model that take the association into account are commonly used frailty models and copula models frailty models assume that conditionally on a frailty term for each cluster the hazard functions of individuals within that cluster are independent these unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster copula models in contrast assume that the joint survival function of the individuals within a cluster is given by a copula function evaluated in the marginal survival function of each individual it is the copula function which describes the association between the lifetimes within a cluster a major disadvantage of the present copula models over the frailty models is that the size of the different clusters must be small and equal to set up manageable estimation procedures for the different model parameters we describe a copula model for clustered survival data where the clusters are allowed to be moderate to large and varying in size by considering the class of archimedean copulas with completely monotone generator we develop both one and two stage estimators for the copula parameters furthermore we show the consistency and asymptotic normality of these estimators finally we perform a simulation study to investigate the finite sample properties of the estimators we illustrate the method on a data set containing the time to first insemination in cows with cows clustered in herds

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

a practical algorithm for making filled graphs minimal for an arbitrary filled graph g of a given original graph g we consider the problem of removing fill edges from g in order to obtain a graph m that is both a minimal filled graph of g and a subgraph of g for g with f fill edges and e original edges we give a simple o f e f algorithm which solves the problem and computes a corresponding minimal elimination ordering of g we report on experiments with an implementation of our algorithm where we test graphs g corresponding to some real sparse matrix applications and apply well known and widely used ordering heuristics to find g our findings show the amount of fill that is commonly removed by a minimalization for each of these heuristics and also indicate that the runtime of our algorithm on these practical graphs is better than the presented worst case bound

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

a mixture model combining logistic regression with proportional hazards regression summary a model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event the proposed model is a semiparametric generalization of a parametric model due to farewell 1982 estimates of the regression parameters are obtained by maximizing a monte carlo approximation of a marginal likelihood and the em algorithm is used to estimate the baseline survivor function we present some simulation results to verify the validity of the suggested estimation procedure it appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

nonparametric transition based tests for jump diffusions we develop a specification test for the transition density of a discretely sampled continuous time jump diffusion process based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis as a special case our method applies to pure diffusions we provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions we establish the asymptotic null distributions of proposed test statistics and compute their power functions we investigate the finite sample properties through simulations and compare them with those of other tests this article has supplementary material online

generalised likelihood ratio tests for spectral density there are few techniques available for testing whether or not a family of parametric times series models fits a set of data reasonably well without serious restrictions on the forms of alternative models in this paper we consider generalised likelihood ratio tests of whether or not the spectral density function of a stationary time series admits certain parametric forms we propose a bias correction method for the generalised likelihood ratio test of fan et al 2001 in particular our methods can be applied to test whether or not a residual series is white noise sampling properties of the proposed tests are established a bootstrap approach is proposed for estimating the null distribution of the test statistics simulation studies investigate the accuracy of the proposed bootstrap estimate and compare the power of the various ways of constructing the generalised likelihood ratio tests as well as some classic methods like the cramer von mises and ljung box tests our results favour the newly proposed bias reduction method using the local likelihood estimator

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

parametric spatial cure rate models for interval censored time to relapse data summary several recent papers e g chen ibrahim and sinha 1999 journal of the american statistical association94 909 919 ibrahim chen and sinha 2001a biometrics57 383 388 have described statistical methods for use with time to event data featuring a surviving fraction i e a proportion of the population that never experiences the event such cure rate models and their multivariate generalizations are quite useful in studies of multiple diseases to which an individual may never succumb or from which an individual may reasonably be expected to recover following treatment e g various types of cancer in this article we extend these models to allow for spatial correlation estimable via zip code identifiers for the subjects as well as interval censoring our approach is bayesian where posterior summaries are obtained via a hybrid markov chain monte carlo algorithm we compare across a broad collection of rather high dimensional hierarchical models using the deviance information criterion a tool recently developed for just this purpose we apply our approach to the analysis of a smoking cessation study where the subjects reside in 53 southeastern minnesota zip codes in addition to the usual posterior estimates our approach yields smoothed zip code level maps of model parameters related to the relapse rates over time and the ultimate proportion of quitters the cure rates

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

a generalized f mixture model for cure rate estimation cure rate estimation is an important issue in clinical trials for diseases such as lymphoma and breast cancer and mixture models are the main statistical methods in the last decade mixture models under different distributions such as exponential weibull log normal and gompertz have been discussed and used however these models involve stronger distributional assumptions than is desirable and inferences may not be robust to departures from these assumptions in this paper a mixture model is proposed using the generalized f distribution family although this family is seldom used because of computational difficulties it has the advantage of being very flexible and including many commonly used distributions as special cases the generalised f mixture model can relax the usual stronger distributional assumptions and allow the analyst to uncover structure in the data that might otherwise have been missed this is illustrated by fitting the model to data from large scale clinical trials with long follow up of lymphoma patients computational problems with the model and model selection methods are discussed comparison of maximum likelihood estimates with those obtained from mixture models under other distributions are included

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

fully dynamic algorithm for chordal graphs with o 1 query time and o n 2 update time we propose dynamic algorithms and data structures for chordal graphs supporting the following operation determine if an edge can be added or removed from the graph while preserving the chordality in o 1 time we show that the complexity of the algorithms for updating the data structures when an edge is actually inserted or deleted is o n 2 where n is the number of vertices of the graph

fast minimal triangulation algorithm using minimum degree criterion we propose an algorithm for minimal triangulation which using simple and efficient strategy subdivides the input graph in different almost non overlapping subgraphs using the technique of matrix multiplication for saturating the minimal separators we show that the partition of the graph can be computed in time o n a where n a is the time required by the binary matrix multiplication after saturating the minimal separators the same procedure is recursively applied on each subgraphs we also present a variant of the algorithm in which the minimum degree criterion is used in this way we obtain an algorithm that uses minimum degree criterion and at the same time produces a minimal triangulation thus shedding new light on the effectiveness of the minimum degree heuristics

on the desirability of acyclic database schemes a class of database schemes called acychc was recently introduced it is shown that this class has a number of desirable properties in particular several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity in addition several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given and a smaple algorithm for determining acychclty is presented also given are several eqmvalent characterizations of those sets m of multivalued dependencies such that m is the set of murlvalued dependencies that are the consequences of a given join dependency several characterizations for a conflict free in the sense of lien set of muluvalued dependencies are provided

simple algorithms for minimal triangulation of a graph and backward selection of a decomposable markov network in this paper we propose a simple algorithm called cliquemintriang for computing a minimal triangulation of a graph if f is the set of edges that is added to g to make it a complete graph k n then the asymptotic complexity of cliquemintriang is o f d 2 f where d is the degree of the subgraph of k n induced by f therefore our algorithm performs well when g is a dense graph we also show how to exploit the existing minimal triangulation techniques in conjunction with cliquemintriang to efficiently find a minimal triangulation of nondense graphs finally we show how the algorithm can be adapted to perform a backward stepwise selection of decomposable markov networks the resulting procedure has the same time complexity as that of existing similar algorithms

mixture cure model with random effects for clustered interval censored survival data the mixture cure model is an effective tool for analysis of survival data with a cure fraction this approach integrates the logistic regression model for the proportion of cured subjects and the survival model either the cox proportional hazards or accelerated failure time model for uncured subjects methods based on the mixture cure model have been extensively investigated in the literature for data with exact failure censoring times in this paper we propose a mixture cure modeling procedure for analyzing clustered and interval censored survival time data by incorporating random effects in both the logistic regression and ph regression components under the generalized linear mixed model framework we develop the reml estimation for the parameters as well as an iterative algorithm for estimation of the survival function for interval censored data the estimation procedure is implemented via an em algorithm a simulation study is conducted to evaluate the performance of the proposed method in various practical situations to demonstrate its usefulness we apply the proposed method to analyze the interval censored relapse time data from a smoking cessation study whose subjects were recruited from 51 zip code regions in the southeastern corner of minnesota