how community structure influences epidemic spread in social networks abstract two key features of social networks are the community structure and the high clustering coefficient for understanding their influences on dynamical processes we present a model with both an adjustable clustering coefficient and an adjustable degree of community this model has an invariant degree distribution when its clustering coefficient is being adjusted we find that the efficiency of epidemic spreading in this model depends mainly on the degree of community and decreases with increase of the degree of community for a fixed degree of community the efficiency will decrease with increase of the clustering coefficient numerical simulations have confirmed the theoretic analysis

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

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

critical probabilities for diversity and number of clusters in randomly occupied square lattices we report the occurrence of critical probabilities associated with the maximum of diversity and the maximum number of fragments clusters on a two dimensional square lattice some scaling relations of these two variables are observed in accordance with work on fragmentation processes

growing scale free networks with tunable clustering we extend the standard scale free network model to include a triad formation step we analyze the geometric properties of networks generated by this algorithm both analytically and by numerical c

partially linear hazard regression with varying coefficients for multivariate survival data summary the paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data a profile pseudo partial likelihood estimation method is proposed the estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo partial likelihood whereas the varying coefficient functions are considered as nuisance parameters that are profiled out of the likelihood it is shown that the estimators of the parameters are root n consistent and the estimators of the non parametric coefficient func tions achieve optimal convergence rates asymptotic normality is obtained for the estimators of the finite parameters and varying coefficient functions consistent estimators of the asymptotic variances are derived and empirically tested which facilitate inference for the model we prove that the varying coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent simulations are con ducted to demonstrate the performance of the estimators proposed a real data set is analysed to illustrate the methodology proposed

testing equality of survival functions based on both paired and unpaired censored data summary we introduce two test procedures for comparing two survival distributions on the basis of randomly right censored data consisting of both paired and unpaired observations our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data one generalization adapts the prentice wilcoxon score while the other adapts the akritas score the use of these particular scoring systems in pooled rank tests with randomly right censored paired data has been advocated by several researchers our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores permutation versions of tests for right censored paired data and for two independent right censored samples that use the proposed scoring systems are obtained as special cases of our test procedures simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log logistic distributions for the survival times we also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data the tests are applied to skin graft data previously reported elsewhere

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

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

fisher information for a bivariate extreme value distribution summary a representation of lee 1979 is used to give an explicit algebraic formula for the 5 x 5dimensional fisher information matrix for gumbel s 1960 bivariate type ii distribution of extreme values with weibull marginals numerical evaluations show that our parameterization makes the dependence parameter almost exactly orthogonal to the two marginal scale parameters

scale free networks from self organization we show how scale free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment this result holds for several variants of the walk algorithm and for a wide range of parameters the growth mechanism is based on using local graph information only so this is a process of self organisation the standard mean field equations are an excellent approximation for network growth using these rules we discuss the effects of finite size on the degree distribution and compare analytical results to simulated networks finally we generalise the random walk algorithm to produce weighted networks with power law distributions of both weight and degree

finiteness and fluctuations in growing networks we study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks we first determine the exact degree distribution of finite networks by generating function approaches the resulting distributions exhibit an unusual finite size scaling behaviour and they are also sensitive to the initial conditions we argue that fluctuations in the number of nodes of degree k become gaussian for fixed degree as the size of the network diverges we also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution

pairwise dependence diagnostics for clustered failure time data frailty and copula models specify a parametric dependence structure for multivariate failure time data estimation of some joint quantities can be highly sensitive to the assumed parametric form and hence model fit is an important issue this paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models the approach is based on the cumulative sum of residuals that are calculated in bivariate time the residuals reflect the difference between the observed and expected bivariate association structures the proposed model checking process is interpretable with a limiting distribution which can be approximated using the bootstrap simulations and a data example illustrate the practical application of the method

incorporating correlation for multivariate failure time data when cluster size is large we propose a new estimation method for multivariate failure time data using the quadratic inference function qif approach the proposed method efficiently incorporates within cluster correlations therefore it is more efficient than those that ignore within cluster correlation furthermore the proposed method is easy to implement unlike the weighted estimating equations in cai and prentice 1995 biometrika 82 151 164 it is not necessary to explicitly estimate the correlation parameters this simplification is particularly useful in analyzing data with large cluster size where it is difficult to estimate intracluster correlation under certain regularity conditions we show the consistency and asymptotic normality of the proposed qif estimators a chi squared test is also developed for hypothesis testing we conduct extensive monte carlo simulation studies to assess the finite sample performance of the proposed methods we also illustrate the proposed methods by analyzing primary biliary cirrhosis pbc data

cluster size entropy in the axelrod model of social influence small world networks and mass media we study the axelrod s cultural adaptation model using the concept of cluster size entropy s c which gives information on the variability of the cultural cluster size present in the system using networks of different topologies from regular to random we find that the critical point of the well known nonequilibrium monocultural multicultural order disorder transition of the axelrod model is given by the maximum of the s c q distributions the width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order by scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q c and the number f of cultural features in two dimensional regular networks we also analyze the effect of the mass media external field on social systems within the axelrod model in a square network we find a partially ordered phase whose largest cultural cluster is not aligned with the external field in contrast with a recent suggestion that this type of phase cannot be formed in regular networks we draw a q b phase diagram for the axelrod model in regular networks

estimation of copula based semiparametric time series models this paper studies the estimation of a class of copula based semiparametric stationary markov models these models are characterized by nonparametric marginal distributions and parametric copula functions while the copulas capture all the scale free temporal dependence of the processes simple estimators of the marginal distribution and the copula parameter are provided and their asymptotic properties are established under easily verifiable conditions these results are used to obtain root n consistent and asymptotically normal estimators of important features of the transition distribution such as the nonlinear conditional moments and conditional quantiles the semiparametric conditional quantile estimators are automatically monotonic across quantiles which is attractive for portfolio conditional value at risk calculations

dynamics of directed graphs the world wide web we introduce and simulate a growth model of the world wide web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real web to update outgoing links re directing them towards constantly changing selected nodes emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the web the growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links we obtain quantitative agreement with the recent empirical data in the real web for the distributions of in and out links and for the size of the connected component in a fully grown network of n nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node the distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior by decreasing the control parameter average fraction of updated and added links per time step towards c n 10 the web can resume a critical structure with no giant component in it we find a different universality class when the updates of links are not allowed i e for 0 corresponding to the network of science citations

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

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

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 concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

scale free networks generated by random walkers we present a simple mechanism for generating undirected scale free networks using random walkers where the network growth is determined by choosing parent vertices by sequential random walks we show that this mechanism produces scale free networks with degree exponent 3 and clustering coefficients depending on random walk length the mechanism can be interpreted in terms of preferential attachment without explicit knowledge of node degrees

complex scale free networks with tunable power law exponent and clustering abstract we introduce a network evolution process motivated by the network of citations in the scientific literature in each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network this set includes m ambassador nodes and l of each ambassador s descendants where m and l are random variables selected from any choice of distributions p l and q m the process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite we show that the degree distributions of the networks generated after a large number of iterations are scale free and derive an expression for the power law exponent in a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l the power law exponent is 2 l 1 l for this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m we conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale free distributions that have been studied empirically

modelling failure time associations in data with multiple levels of clustering summary in recent years substantial research has been devoted to developing failure time methodology which accounts for possible dependency between observations an example is the univariate frailty model vaupel manton stallard 1979 which incorporates an exchangeable dependence structure by the inclusion of cluster specific random effects in some studies it may be reasonable to expect more than one level of within cluster association for instance association between a parent and child versus that between two siblings in studies of familial disease aggregation or association between two village residents who live in different households versus that between residents of the same household in intervention studies we propose a family of distributional models for failure time data that accounts for multiple levels of clustering and reduces in the case of a single clustering level to a univariate frailty model the resulting survival functions are constructed by a recursive nesting of univariate frailty type distributions through which archimedean copula forms are determined for all bivariate margins properties of the proposed model are developed illustrated and briefly contrasted with multivariate frailty model properties in conclusion we outline the application of our model to marginal risk regression problems

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

permutation tests for comparing marginal survival functions with clustered failure time data we propose a class of two sample non parametric permutation tests to compare the marginal survival distributions of two groups when the failure times are correlated within cluster with clusters nested within each group the permutation distribution effectively takes into account the correlation between failure times within a cluster the method is able to handle data with clusters of either fixed or variable sizes moreover this class of test statistics is sensitive to various alternatives the size and power of the proposed tests are assessed by a series of simulation studies the method is illustrated by application to data from the hypertension detection and follow up program trial

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

spatially self organized resilient networks by a distributed cooperative mechanism abstract the robustness of connectivity and the efficiency of paths are incompatible in many real networks we propose a self organization mechanism for incrementally generating onion like networks with positive degree degree correlations whose robustness is nearly optimal as a spatial extension of the generation model based on cooperative copying and adding shortcut we show that the growing networks become more robust and efficient through enhancing the onion like topological structure on a space the reasonable constraint for locating nodes on the perimeter in typical surface growth as a self propagation does not affect these properties of the tolerance and the path length moreover the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures

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

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

combining stratified and unstratified log rank tests in paired survival data the log rank test is the most widely used nonparametric method for testing treatment differences in survival between two treatment groups due to its efficiency under the proportional hazards model most previous work on the log rank test has assumed that the samples from the two treatment groups are independent this assumption is not always true in multi center clinical trials survival times of patients in the same medical center may be correlated due to factors specific to each center for such data we can construct both stratified and unstratified log rank tests these two tests turn out to have very different powers for correlated samples an appropriate linear combination of these two tests may give a more powerful test than either of the individual test under a bivariate frailty model we obtain closed form asymptotic local alternative distributions and the correlation coefficient between these two tests based on these results we construct an optimal linear combination of the two test statistics to maximize the local power simulation studies with hougaard s model confirm our construction we also study the robustness of the combined test by simulations

distribution characteristics of weighted bipartite evolving networks abstract motivated by an evolving model of online bipartite networks we introduce a model of weighted bipartite evolving networks in this model there are two disjoint sets of nodes called user node set and object node set edges only exist between two disjoint sets edge weights represent the usage amount between a couple of user node and object node this model not only clinches the bipartite networks internal mechanism of network growth but also takes into account the object strength deterioration over time step user strength and object strength follow power law distributions respectively the weighted bipartite evolving networks have scare free property in certain situations numerical simulations results agree with the theoretical analyses

proportional hazards model with a change point for clustered event data in many epidemiology studies family data with survival endpoints are collected to investigate the association between risk factors and disease incidence sometimes the risk of the disease may change when a certain risk factor exceeds a certain threshold finding this threshold value could be important for disease risk prediction and diseases prevention in this work we propose a change point proportional hazards model for clustered event data the model incorporates the unknown threshold of a continuous variable as a change point in the regression the marginal pseudo partial likelihood functions are maximized for estimating the regression coefficients and the unknown change point we develop a supremum test based on robust score statistics to test the existence of the change point the inference for the change point is based on the m out of n bootstrap we establish the consistency and asymptotic distributions of the proposed estimators the finite sample performance of the proposed method is demonstrated via extensive simulation studies finally the strong heart family study dataset is analyzed to illustrate the methods

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

scaling and critical probabilities for cluster size and la diversity on randomly occupied square lattices using monte carlo simulations we report the behaviour of the total number of clusters the cluster size diversity and the lattice animals la diversity on randomly occupied square lattices the critical probability associated with the maximum of these variables is determined in comparison with the percolation probability pc our simulations indicate that pc and the critical probability of the maximum cluster size diversity pc d s max occur at the same point as indicated in a previous paper tsang i r and tsang i j 1997 j phys a math gen 30 l239 the probability for the maximum number of clusters is obtained at a lower value pc n max 0 27 0 01 we describe the cluster identification algorithm used to count the different la and determined the critical probability for the maximum la diversity pc d f max 0 45 0 02 we derive the exponents characterizing the relation between d s max d f max and n max and several scaling relations between the variables measured the lattice size and the probability of occupation p in addition we show the scaling behaviour of la diversity versus cluster size diversity for each value of p

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

nonparametric inference on bivariate survival data with interval sampling association estimation and testing in many biomedical applications interest focuses on the occurrence of two or more consecutive failure events and the relationship between event times such as age of disease onset and residual lifetime bivariate survival data with interval sampling arise frequently when disease registries or surveillance systems collect data based on disease incidence occurring within a specific calendar time interval the initial event is then retrospectively confirmed and the subsequent failure event may be observed during follow up in life history studies the initial and two consecutive failure events could correspond to birth disease onset and death the statistical features and bias of observed data in relation to interval sampling were discussed by zhu wang 2012 here we propose nonparametric estimation of the association between bivariate failure times based on kendall s tau for data collected with interval sampling a nonparametric estimator is given where the contribution of each comparable and orderable pair is weighted by the inverse of the associated selection probability analysis methods for bivariate survival data with interval sampling rely on the assumption of quasi independence i e that bivariate failure times and the time of the initial event are independent in the observable region this paper develops a nonparametric test of quasi independence based on a bivariate conditional kendall s tau for such data simulation studies demonstrate that the association estimator and testing procedure perform well with moderate sample sizes illustrations with two real datasets are provided

supremum versions of the log rank and generalized wilcoxon statistics abstract considerable progress has been made in generalizing to censored data hypothesis tests based on rank statistics the most commonly used generalizations are the log rank test statistic which extends the savage exponential scores statistic cox 1972 mantel 1966 and the generalized wilcoxon statistics gehan 1965 peto and peto 1972 gill 1980 showed that in the two sample problem the asymptotic efficiency properties of the savage and wilcoxon statistics are maintained in censored data by the log rank and peto and peto wilcoxon statistics respectively when censoring is the same in both samples heuristics and simulations have implied that some recently proposed supremum statistics closely related to these two popular linear rank statistics can be used to construct tests that provide good power against a much wider range of nonlocal alternatives see e g fleming and harrington 1981 fleming o brien o fallon and harrington 1980 gill 1980 schumacher 1984 in this article we consider n

permutational distribution of the log rank statistic under random censorship with applications to carcinogenicity assays in the random censorship model the log rank test is often used for comparing a control group with different dose groups if the number of tumors is small so called exact methods are often applied for computing critical values from a permutational distribution two of these exact methods are discussed and shown to be incorrect the correct permutational distribution is derived and studied with respect to its behavior under unequal censoring in the light of recent results proving that the permutational version and the unconditional version of the log rank test are asymptotically equivalent even under unequal censoring the log rank test is studied by simulations of a realistic scenario from a bioassay with small numbers of tumors

formation and maintenance of complex systems a complex system is often identified by the absence of a characteristic length e g as in a fractal a very large system subject to a fragmentation and or aggregation dynamics passes through such complex configurations we study statistically creation and maintenance of such configurations in space dimensions d 1 to 5 and find that they are easily created maintained for small large d an intermediate d such as d 3 seems to be ideal for the creation and maintenance of complex systems this has consequences in a statistical description of the universe

analysing bivariate survival data with interval sampling and application to cancer epidemiology in biomedical studies ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease in cancer studies interest could be focused on bivariate failure times for example time from birth to cancer onset and time from cancer onset to death this paper considers a sampling scheme termed interval sampling in which the first failure event is identified within a calendar time interval the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring in a cancer data application the initiating first and second events could correspond to birth cancer onset and death the fact that the data are collected conditional on the first failure event occurring within a time interval induces bias interval sampling is widely used for collection of disease registry data by governments and medical institutions though the interval sampling bias is frequently overlooked by researchers this paper develops statistical methods for analysing such data semiparametric methods are proposed under semi stationarity and stationarity numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes we apply the proposed methods to ovarian cancer registry data

kaplan meier estimate on the plane estimation of the bivariate survival function from censored data is considered the product integral representation of univariate survival functions is generalized to the bivariate case and used to determine identifiability of the survival function of the partially observed data a bivariate analogue of the kaplan meier estimate is introduced and its almost sure consistency is studied extensions to the general multivariate case are sketched

hazard models with varying coefficients for multivariate failure time data statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis a local pseudo partial likelihood procedure is proposed for estimating the unknown coefficient functions a weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator the consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested to reduce the computational burden of the maximum local pseudo partial likelihood estimator a simple and useful one step estimator is proposed statistical properties of the one step estimator are established and simulation studies are conducted to compare the performance of the one step estimator to that of the maximum local pseudo partial likelihood estimator the results show that the one step estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudo partial likelihood estimator a data set from the busselton population health surveys is analyzed to illustrate our proposed methodology

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

model selection and semiparametric inference for bivariate failure time data abstract we propose model selection procedures for bivariate survival models for censored data generated by the archimedean copula family in route to constructing the selection methodology we develop estimates of some time dependent association measures including estimates of the local and global kendall s tau local odds ratio and other measures defined throughout the literature we propose a goodness of fit based model selection methodology as well as a graphical approach we show that the proposed methods have desirable asymptotic properties and perform well in finite samples

cumulative incidence association models for bivariate competing risks data association models like frailty and copula models are frequently used to analyze clustered survival data and evaluate within cluster associations the assumption of noninformative censoring is commonly applied to these models though it may not be true in many situations in this paper we consider bivariate competing risk data and focus on association models specified for the bivariate cumulative incidence function cif a nonparametrically identifiable quantity copula models are proposed which relate the bivariate cif to its corresponding univariate cifs similarly to independently right censored data and accommodate frailty models for the bivariate cif two estimating equations are developed to estimate the association parameter permitting the univariate cifs to be estimated either parametrically or nonparametrically goodness of fit tests are presented for formally evaluating the parametric models both estimators perform well with moderate sample sizes in simulation studies the practical use of the methodology is illustrated in an analysis of dementia associations

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

on the game of life population and its diversity abstract one of the most important features of biological life in all levels is its astounding diversity in this work we study the well known game life due to conway analysing the statistics of cluster population n t and cluster diversity d t we have performed simulations on life for dimensions d 1 and 2 starting with an uncorrelated distribution of live and dead sites at t 0 for d 2 we study the effect of different neighbourhood relations in identifying and counting clusters an interesting scaling relation connecting the maxima of n t and d t is found

numerical simulations for fragmentation dynamics a geometrical model for the study of fragmentation dynamics is introduced detailed statistical analysis of the fragment distribution for percolation clusters sierpinski carpets and menger sponges on square and cubic lattices is given and static and dynamic critical exponents are calculated

partially linear hazard regression for multivariate survival data this article studies estimation of partially linear hazard regression models for multivariate survival data a profile pseudo partial likelihood estimation method is proposed under the marginal hazard model framework the estimation on the parameters for the linear part is accomplished by maximization of a pseudo partial likelihood profiled over the nonparametric part this enables us to obtain consistent estimators of the parametric component asymptotic normality is obtained for the estimates of both the linear and nonlinear parts the new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit an algorithm of fast implementation of our proposed method is presented consistent standard error estimates using sandwich type ideas are also developed which facilitates inferences for the model it is shown that the nonparametric component can be estimated as well as if the parametric components were known and the

measuring the preferential attachment mechanism in citation networks abstract in this paper we investigated the preferential attachment mechanism pam by considering the dynamic property in papers in degree k for three citation networks we found that the past citations obtained in different years will have different influences on papers attachment rate k t we proposed two methods to consider these different influences one is the gradually vanishing memory preferential attachment mechanism gmpam based on weighted past citations the other is the short term memory preferential attachment mechanism smpam based on citations obtained in the recent one year period experiments showed that smpam is simpler and more universal in practice we can just calculate the citations to papers in the recent one year period to study the papers attachment property

some permutation tests for survival data summary we introduce two new classes of tests for censored data the first tests for association between survival and a covariate and the second tests for equality of survival distributions between k groups both tests are permutation tests based on nonparametric test statistics and unlike the wald test in the proportional hazards model or the log rank test can detect alternatives of the crossed hazards type the tests are simple to implement and require no theoretical analysis by the user nor an appeal to asymptotic distribution theory simulation results show that the tests are competitive with their classical counterparts under proportional hazards and superior under certain nonproportional hazards alternatives in both the continuous and k sample cases the tests are applied to data from the british medical research council s fourth myelomatosis trial and from a danish study of malignant melanoma

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

emergence of the small world architecture in neural networks by activity dependent growth abstract in this paper we propose a model describing the growth and development of neural networks based on the latest achievements of experimental neuroscience the model is based on two evolutionary equations the first equation is for the evolution of the neurons state and the second is for the growth of axon tips by using the model we demonstrated the neuronal growth process from disconnected neurons to fully connected three dimensional networks for the analysis of the network s connections structure we used the random graphs theory methods it is shown that the growth in neural networks results in the formation of a well known small world network model the analysis of the connectivity distribution shows the presence of a strictly non gaussian but no scale free degree distribution for the in degree node distribution in terms of the graphs theory this study developed a new model of dynamic graph

time dependent tree structured survival analysis with unbiased variable selection through permutation tests incorporating time dependent covariates into tree structured survival analysis tssa may result in more accurate prognostic models than if only baseline values are used available time dependent tssa methods exhaustively test every binary split on every covariate however this approach may result in selection bias towards covariates with more observed values we present a method that uses unbiased significance levels from newly proposed permutation tests to select the time dependent or baseline covariate with the strongest relationship with the survival outcome the specific splitting value is identified using only the selected covariate simulation results show that the proposed time dependent tssa method produces tree models of equal or greater accuracy as compared to baseline tssa models even with high censoring rates and large within subject variability in the time dependent covariate to illustrate the proposed method is applied to data from a cohort of bipolar youth to identify subgroups at risk for self injurious behavior

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

inference for events with dependent risks in multiple endpoint studies abstract kaplan meier and cumulative incidence functions are not sufficient descriptive devices for studies that have multiple time to event endpoints for example in cancer treatment research the probability of tumor recurrence conditional on not having died from treatment related toxicities and the prevalence of graft versus host disease among leukemia free patients surviving a bone marrow transplant are of interest these quantities can be estimated nonparametrically using simple functions of several kaplan meier and cumulative incidence estimates for events with possibly dependent risks we derive asymptotic distribution theory for such functions by representing kaplan meier cumulative incidence and cumulative hazard estimators as sums of iid random variables variance estimation also follows directly from this representation two sample test statistics with asymptotic null distribution theory are presented several examples illustrate the utility of these results

efficient two step estimation via targeting abstract the standard description of two step extremum estimation amounts to plugging in a first step estimator of nuisance parameters to simplify the optimization problem and then deducing a user friendly but potentially inefficient estimator for the parameters of interest in this paper we consider a more general setting of two step estimation where we do not necessarily have nuisance parameters but rather awkward occurrences of the parameters of interest the efficiency problem associated with two step estimators in this context is more difficult than with standard nuisance parameters as even if the true unknown value of the parameters were plugged in to alleviate the awkward occurrences of the parameters the resulting second step estimator may not be efficient in addition standard approaches to restore efficiency for two step procedures may not work due to a consistency issue to alleviate this potential issue we propose a new computationally simple two step estimation procedure that relies on targeting and penalization to enforce consistency with the second step estimators maintaining asymptotic efficiency we compare this new method with existing iterative methods in the framework of copula models and asset pricing models simulation results illustrate that this new method performs better than existing iterative procedures and is nearly computationally equivalent

flexible maximum likelihood methods for bivariate proportional hazards models this article presents methodology for multivariate proportional hazards ph regression models the methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional ph models along with assumptions about the association among lifetimes because the models are parametric ordinary maximum likelihood can be applied it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes unlike existing semiparametric methods a bivariate clayton model 1978 biometrika 65 141 151 is used to illustrate the approach taken because a parametric assumption about association is made efficiency and robustness comparisons are made between estimation based on the bivariate clayton model and working independence methods that specify only marginal distributions for each lifetime variable

on dependence estimation using correlated failure time data from case control family studies correlated failure time data arise routinely in case control family studies to measure the dependence between bivariate failure times a cross ratio i e conditional hazard ratio function has been used many approaches ranging from estimating equations to likelihood score equations have been proposed for the estimation of parameters in the cross ratio function from prospective family data however the adaptation of these approaches to case control family data appears too complicated and computationally intensive to be practical in this paper a connection is established between the cross ratio function and the relative risk function in a stratified proportional hazards model leading to the development of a set of partial likelihood based estimating equations a simulation study is conducted to evaluate the performance of this estimation procedure and two datasets are analysed to illustrate this method

a family of distributions for modelling non elliptically symmetric multivariate data summary the paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation we present a relatively simple family of distributions for use in describing data which are not elliptically symmetric properties of the family are discussed and it is shown that multivariate pareto burr and logistic distributions are special cases in addition simulation methods for applications in monte carlo robustness studies are outlined and finally the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution

modeling the association of bivariate interval censored data using the copula approach in a survival study it may not be possible to record the exact event time but only that the event has occurred between two time points or still has to occur leading to interval censored survival times recently sun et al scand j stat 2006 33 4 637 649 suggested to fit a clayton copula with nonparametric marginal distributions to estimate the association for bivariate interval censored failure data we propose here to model the marginal distributions with an accelerated failure time model with a flexible error term as suggested by komarek et al j comput graph stat 2005 14 3 726 745 in combination with a one parameter copula in addition we allow the association parameter of the copula to depend on covariates the performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from a longitudinal dental study

scale free characteristics of random networks the topology of the world wide web the world wide web forms a large directed graph whose vertices are documents and edges are links pointing from one document to another here we demonstrate that despite its apparent random character the topology of this graph has a number of universal scale free characteristics we introduce a model that leads to a scale free network capturing in a minimal fashion the self organization processes governing the world wide web c 2000 elsevier science b v all rights reserved pacs 84 35 i 64 60 fr 87 23 ge

analysis of failure time data with multilevel clustering with application to the child vitamin a intervention trial in nepal we consider the problem of estimating covariate effects in the marginal cox proportional hazard model and multilevel associations for child mortality data collected from a vitamin a supplementation trial in nepal where the data are clustered within households and villages for this purpose a class of multivariate survival models that can be represented by a functional of marginal survival functions and accounts for hierarchical structure of clustering is exploited based on this class of models an estimation strategy involving a within cluster resampling procedure is proposed and a model assessment approach is presented the asymptotic theory for the proposed estimators and lack of fit test is established the simulation study shows that the estimates are approximately unbiased and the proposed test statistic is conservative under extremely heavy censoring but approaches the size otherwise the analysis of the nepal study data shows that the association of mortality is much greater within households than within villages

quantifying the association between progression free survival and overall survival in oncology trials using kendall s τ this paper considers methods for estimating the association between progression free and overall survival in oncology trials copula based nonparametric and illness death model based methods are reviewed in addition the approach based on an underlying illness death model is generalized to allow general parametric models the performance of these methods in terms of bias and efficiency is investigated through simulation and also illustrated using data from a clinical trial of treatments for colon cancer the simulations suggest that the illness death model based method provides good estimates of kendall s across several scenarios in some situations copula based methods perform well but their performance is sensitive to the choice of copula the clayton copula is most appropriate in scenarios which might realistically reflect an oncology trial but the use of copula models in practice is questionable

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

identifying nonlinear covariate effects in semimartingale regression models letxt be a semimartingale which is either continuous or of counting process type and which satisfies the stochastic differential equationdxt yt t zt dt dmt wherey andz are predictable covariate processes m is a martingale and is an unknown nonrandom function we study inference for by introducing an estimator for a t z int limits 0 z int limits 0 t alpha s x dsdx and deriving a functional central limit theorem for the estimator the asymptotic distribution turns out to be given by a gaussian random field that admits a representation as a stochastic integral with respect to a multiparameter wiener process this result is used to develop a test for independence ofx from the covariatez a test for time homogeneity of and a goodness of fit test for the proportional hazards model t z 1 t a2 z used in survival analysis