a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

assessment of stratum covariate interactions in cox s proportional hazards regression model we assess stratum e g treatment interactions with covariates and with the baseline hazard function in the proportional hazards ph regression model for lifetime data we consider models incorporating stratum interactions both with and without stratification of the risk sets in the likelihood function and describe likelihood ratio statistics for tests of the presence of these interactions we also present step down methods for building reduced models which include stratum specific parameters corresponding to covariates which interact with treatment we apply ph models with such interactions to a clinical trial of des in the treatment of prostate cancer to determine optimal treatment conditional on each patient s covariates

proportional hazards estimate of the conditional survival function summary we introduce a new estimator of the conditional survival function given some subset of the covariate values under a proportional hazards regression the new estimate does not require estimating the base line cumulative hazard function an estimate of the variance is given and is easy to compute involving only those quantities that are routinely calculated in a cox model analysis the asymptotic normality of the new estimate is shown by using a central limit theorem for kaplan meier integrals we indicate the straightforward extension of the estimation procedure under models with multiplicative relative risks including non proportional hazards and to stratified and frailty models the estimator is applied to a gastric cancer study where it is of interest to predict patients survival based only on measurements obtained before surgery the time at which the most important prognostic variable stage becomes known

robust tests for treatment effects based on censored recurrent event data observed over multiple periods summary we derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods these methods are based on estimating functions motivated by a working mixed poisson assumption under which conditioning can eliminate subject specific random effects robust pseudoscore test statistics are obtained via sandwich variance estimation the relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time homogeneous poisson model the robustness and empirical power of the semiparametric approach are assessed through simulation adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two period crossover trial of patients with bronchial asthma

the steiner tree problem i formulations compositions and extension of facets in this paper we give some integer programming formulations for the steiner tree problem on undirected and directed graphs and study the associated polyhedra we give some families of facets for the undirected case along with some compositions and extensions we also give a projection that relates the steiner tree polyhedron on an undirected graph to the polyhedron for the corresponding directed graph this is used to show that the lp relaxation of the directed formulation is superior to the lp relaxation of the undirected one

a modification of the redistribution to the right algorithm using disease markers summary disease markers are time dependent covariates which describe progression towards development of disease traditional methods in survival analysis do not make use of available data on these markers to recover additional information from censored individuals using a heuristic modification of the redistribution to the right algorithm efron 1967 a new approach for recovering information for censored individuals using disease markers is proposed additionally the statistical properties of the proposed method are examined there are two possible advantages to this modification i bias reduction when censoring is informative and ii an increase in efficiency in the case of truly noninformative censoring

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

point process modelling for directed interaction networks abstract network data often take the form of repeated interactions between senders and receivers tabulated over time a primary question to ask of such data is which traits and behaviors are predictive of interaction to answer this question a model is introduced for treating directed interactions as a multivariate point process a cox multiplicative intensity model using covariates that depend on the history of the process consistency and asymptotic normality are proved for the resulting partial likelihood based estimators under suitable regularity conditions and an efficient fitting procedure is described multicast interactions those involving a single sender but multiple receivers are treated explicitly the resulting inferential framework is then employed to model message sending behavior in a corporate e mail network the analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection

a comparison of two simple hazard ratio estimators based on the logrank test two hazard ratio estimators based on the logrank test are investigated using a simulation study the pike estimator ratio of relative death rates was shown to be consistently less biased than the peto 1 step estimator the latter has recently been advocated as the method of choice for point and interval estimation both estimators exhibited bias with increasing hazard ratios although the bias was minimal for effects less than 3 the confidence intervals also did not achieve the nominal coverage with increasing hazard ratios but again the pike estimator was superior the coverage could be improved by recalculation of the variance incorporating the point estimate for a hazard ratio of less than 3 we recommend the use of the pike estimator otherwise it is necessary to use a more complex method of estimation

a meta heuristic approach for solving the urban network design problem abstract this paper proposes an optimisation model and a meta heuristic algorithm for solving the urban network design problem the problem consists in optimising the layout of an urban road network by designing directions of existing roads and signal settings at intersections a non linear constrained optimisation model for solving this problem is formulated adopting a bi level approach in order to reduce the complexity of solution methods and the computation times a scatter search algorithm based on a random descent method is proposed and tested on a real dimension network initial results show that the proposed approach allows local optimal solutions to be obtained in reasonable computation times

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

information bounds for cox regression models with missing data we derive information bounds for the regression parameters in cox models when data are missing at random these calculations are of interest for understanding the behavior of efficient estimation in case cohort designs a type of two phase design often used in cohort studies the derivations make use of key lemmas appearing in robins rotnitzky and zhao j amer statist assoc 89 1994 846 866 and robins hsieh and newey j roy statist soc ser b 57 1995 409 424 but in a form suited for our purposes here we begin by summarizing the results of robins rotnitzky and zhao in a form that leads directly to the projection method which will be of use for our model of interest we then proceed to derive new information bounds for the regression parameters of the cox model with data missing at random mar in the final section we exemplify our calculations with several models of interest in cohort studies including an i i d version of the classical case cohort design of prentice biometrika 73 1986 1 11 and self and prentice ann statist 16 1988 64 81

stratified partial likelihood estimation when multiple durations are generated by a single unit they may be related in a way that is not fully captured by the regressors the omitted unit specific variables might vary over the durations they might also be correlated with the variables in the regression component we propose an estimator that responds to these concerns and develop a specification test for detecting unobserved unit specific effects data from malaysia reveal that concentration of child mortality in some families is imperfectly explained by observed explanatory variables and that failure to control for unobserved heterogeneity seriously biases the parameter estimates

benders and cut algorithm for fixed charge capacitated network design problem abstract we develop a benders and cut algorithm for fixed charge capacitated network design problem which incorporates both benders cuts and polyhedral cuts into an implicit branch and bound algorithm the algorithm is tested over a wide range of problem instances with varying sizes and traffic conditions it is shown that this new algorithm s performance is competitive compared with existing algorithms and that benders cuts are more effective under heavy traffic load while cut set inequalities are more effective under light traffic load

flood frequency analysis using the cox regression model procedures for incorporating time varying exogenous information into flood frequency analyses are developed using the cox regression model for counting processes in this statistical model the probability of occurrence of a flood peak in a short interval t t dt depends in an explicit manner on the values at t of k covariate processes z1 zk specifically letting dn t be 1 if a flood peak occurs in t t dt and 0 otherwise dn t a t exp j 1kbjzj t dm t where a the baseline intensity is an unknown function b is a vector of unknown regression parameters and the error dm t is conditionally orthogonal to the past history two applications assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time varying flood frequency estimates are considered

a capacity scaling heuristic for the multicommodity capacitated network design problem in this paper we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem the capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities which depend on flow volumes on the arcs by combining a column and row generation technique and a strong formulation including forcing constraints this heuristic derives high quality results and computational effort can be reduced considerably the capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem

reweighting estimators for cox regression with missing covariates missingness in covariates is a common problem in survival data in this article we propose a reweighting method for estimating the regression parameters in the cox model with missing covariates we also consider the augmented reweighting method by subtracting the projection term onto the nuisance tangent space the proposed method provides consistent and asymptotically normally distributed estimators when the missing data mechanism depends on the outcome variables as well as on the observed covariates with either monotone or arbitrary nonmonotone missingness patterns simulation results indicate that in most situations the proposed reweighting estimators are more efficient than the inverse probability weighting estimators for the regression coefficients of the missing covariates and are as efficient as or more efficient than the inverse probability weighting estimators for the regression coefficients of the completely observed covariates the simple reweighting estimators can be easily implemented in st

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

inference on the rate ratio of recurrent events for the matched pairs design as statistical methods for testing the null hypothesis of no difference between two groups for the matched pairs design the paired t test wilcoxon signed rank sum test and mcnemar test are well known however there is no simple test for the comparison of incidence rate of recurrent events this paper proposes a simple statistical method and a sample size formula for the comparison of counts of recurrent events over a specified period of observation under the matched pairs design where the subject specific incidence of recurrent events is assumed to follow a time homogeneous poisson process as a special case the proposed method is found to be virtually equivalent in form to mantel haenszel method for a common rate ratio among the set of stratified tables based on person time data the proposed methods are illustrated with the within arm comparison of data from a clinical trial of 59 epileptics with baseline count data

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

an approach to nonparametric regression for life history data using local linear fitting most hazard regression models in survival analysis specify a given functional form to describe the influence of the covariates on the hazard rate for instance cox s model assumes that the covariates act multiplicatively on the hazard rate and aalen s additive risk model stipulates that the covariates have a linear additive effect on the hazard rate in this paper we study a fully nonparametric model which makes no assumption on the association between the hazard rate and the covariates we propose a class of estimators for the conditional hazard function the conditional cumulative hazard function and the conditional survival function and study their large sample properties when the size of a data set is relatively large this fully nonparametric approach may provide more accurate information than that acquired from more restrictive models it may also be used to test whether a particular submodel gives a good fit to a given data set because our results are obtained under the multivariate counting process setting of aalen they apply to a number of models arising in survival analysis including various censoring and random truncation models our estimators are related to the conditional nelson aalen estimators proposed by beran for the random censorship model

accelerated failure time models for counting processes summary we present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events a class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model in addition a nelson aalen type estimator for the mean function of the counting process is constructed which is consistent and properly normalised converges weakly to a zeromean gaussian process we assess the finite sample properties of the proposed estimators and the associated inference procedures through monte carlo simulation and provide an application to a well known bladder cancer study

the l 1 method for robust nonparametric regression abstract consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy tailed error distribution the two standard approaches to such a problem are each flawed robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods which are not resistant against outliers existing algorithms for robustifying nonparametric regression procedures use either nonlinear optimization of an influence function or iterative solution of local polynomial fitting using reweighted least squares neither of these two approaches combines computational ease with asymptotic theoretical results furthermore application of the robust procedure has been limited almost exclusively to the case of a single explanatory variable with the response variable in this article a new hybrid method is propose

maximum weighted partial likelihood estimators for the cox model new estimators for cox regression that maximize a weighted version of the partial likelihood are considered their asymptotic properties on the model are sketched estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency the results of a small simulation study are included the estimators are applied to a well known data set the possible influence of an outlying observation on the cox estimator can be of any magnitude individuals who survive longest have a high potential of being influential in analogy with weighted linear rank tests we introduce estimators of the regression coefficients that maximize a weighted partial likelihood for instance by using weights proportional to the number at risk one obtains a wilcoxon type estimator this estimator has bounded influence provided the covariate space is compact and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the wilcoxon test asymptotic prop

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

a dual ascent procedure for large scale uncapacitated network design the fixed charge network design problem arises in a variety of problem contexts including transportation communication and production scheduling we develop a family of dual ascent algorithms for this problem this approach generalizes known ascent procedures for solving shortest path plant location steiner network and directed spanning tree problems our computational results for several classes of test problems with up to 500 integer and 1 98 million continuous variables and constraints show that the dual ascent procedure and an associated drop add heuristic generate solutions that in almost all cases are guaranteed to be within 1 to 4 of optimality moreover the procedure requires no more than 150 seconds on an ibm 3083 computer the test problems correspond to dense and sparse networks including some models that arise in freight transport

a dual ascent approach to the fixed charge capacitated network design problem abstract in this paper we consider the problem of constructing a network over which a number of commodities are to be transported fixed costs are associated to the construction of network arcs and variable costs are associated to routing of commodities in addition one capacity constraint is related to each arc the problem is to determine a network design that minimizes the total cost i e it balances the construction and operating costs a dual ascent procedure for finding improved lower bounds and near optimal solutions for the fixed charge capacitated network design problem is proposed the method is shown to generate tighter lower bounds than the linear programming relaxation of the problem

the packing property a clutter v e packs if the smallest number of vertices needed to intersect all the edges i e a minimum transversal is equal to the maximum number of pairwise disjoint edges i e a maximum matching this terminology is due to seymour 1977 a clutter is minimally nonpacking if it does not pack but all its minors pack an m n 0 1 matrix is minimally nonpacking if it is the edge vertex incidence matrix of a minimally nonpacking clutter minimally nonpacking matrices can be viewed as the counterpart for the set covering problem of minimally imperfect matrices for the set packing problem this paper proves several properties of minimally nonpacking clutters and matrices

a pairwise likelihood augmented cox estimator for left truncated data survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging conditional approaches for left truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times length biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform otherwise they may generate biased estimates we propose a semiparametric method for left truncated data under the cox model with no parametric distributional assumption about the truncation times our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood which eliminates the truncation distribution yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood an iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously by empirical process and u process theories it has been shown that the proposed estimator is consistent and asymptotically normal with a closed form consistent variance estimator simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator when the uniform truncation assumption holds our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator an application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method

ideal clutters that do not pack for a clutter x1d49e over ground set e a pair of distinct elements e f e are coexclusive if every minimal cover contains at most one of them an identification of x1d49e is another clutter obtained after identifying coexclusive elements of x1d49e if a clutter is nonpacking then so is any identification of it inspired by this observation and impelled by the lack of a qualitative characterization for ideal minimally nonpacking mnp clutters we reduce ideal mnp clutters even further by taking their identifications in doing so we reveal chains of ideal mnp clutters demonstrate the centrality of mnp clutters with covering number two as well as provide a qualitative characterization of irreducible ideal mnp clutters with covering number two at the core of this characterization lies a class of objects called marginal cuboids that naturally give rise to ideal nonpacking clutters with covering number two we present an explicit class of marginal cuboids and show that the corresponding clutters have one of q6 q

simultaneous inference on treatment effects in survival studies with factorial designs a clinical trial with a 2 2 factorial design involves randomization of subjects to treatment a or a and within each group further randomization to treatment b or b under this design one can assess the effects of treatments a and b on a clinical endpoint using all patients one may additionally compare treatment a treatment b or combination therapy ab to a b with multiple comparisons however it may be desirable to control the overall type i error especially for regulatory purposes because the subjects overlap in the comparisons the test statistics are generally correlated by accounting for the correlations one can achieve higher statistical power compared to the conventional bonferroni correction herein we derive the correlation between any two stratified or unstratified log rank statistics for a 2 2 factorial design with a survival time endpoint such that the overall type i error for multiple treatment comparisons can be properly controlled in addition we allow for adjustment of prognostic factors in the treatment comparisons and conduct simultaneous inference on the effect sizes we use simulation studies to show that the proposed methods perform well in realistic situations we then provide an application to a recently completed randomized controlled clinical trial on alcohol dependence finally we discuss extensions of our approach to other factorial designs and multiple endpoints

pseudomartingale estimating equations for modulated renewal process models summary we adapt martingale estimating equations based on gap time information to a gen eral intensity model for a single realization of a modulated renewal process the consistency and asymptotic normality of the estimators is proved under ergodicity conditions previous work has considered either parametric likelihood analysis or semiparametric multiplicative models using partial likelihood the framework is generally applicable to semiparametric and paramet ric models including additive and multiplicative specifications and periodic models it facilitates a semiparametric extension of a popular parametric earthquake model simulations and empir ical analyses of taiwanese earthquake sequences illustrate the methodology s practical utility

a semiparametric model for the analysis of recurrent event panel data summary in many longitudinal studies interest focuses on the occurrence rate of some phenomenon for the subjects in the study when the phenomenon is nonterminating and possibly recurring the result is a recurrent event data set examples include epileptic seizures and recurrent cancers when the recurring event is detectable only by an expensive or invasive examination only the number of events occurring between follow up times may be available this article presents a semiparametric model for such data based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function a random subject specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data estimators are determined from quasi likelihood estimating functions because only first and second moment assumptions are required for quasi likelihood the method is more robust than those based on the specification of a full parametric likelihood consistency of the estimators depends only on the assumption of the proportional intensity model the semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators as with semiparametric methods in survival analysis the method provides useful diagnostics for specific parametric models including a quasi score statistic for testing specific baseline intensity functions the techniques are used to analyze cancer recurrences and a pheromone based mating disruption experiment in moths a simulation study confirms that for many practical situations the estimators possess appropriate small sample characteristics

sparse estimation of cox proportional hazards models via approximated information criteria we propose a new sparse estimation method for cox 1972 proportional hazards models by optimizing an approximated information criterion the main idea involves approximation of the l0 norm with a continuous or smooth unit dent function the proposed method bridges the best subset selection and regularization by borrowing strength from both it mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter we further reformulate the problem with a reparameterization step so that it reduces to one unconstrained nonconvex yet smooth programming problem which can be solved efficiently as in computing the maximum partial likelihood estimator mple furthermore the reparameterization tactic yields an additional advantage in terms of circumventing postselection inference the oracle property of the proposed method is established both simulated experiments and empirical examples are provided for assessment and illustration

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

opposite elements in clutters let e be a finite set of elements and let l be a clutter over ground set e we say distinct elements e f are opposite if every member and every minimal cover of l contains at most one of e f in this paper we investigate opposite elements and reveal a rich theory underlying such a seemingly simple restriction the clutter c obtained from l after identifying some opposite elements is called an identification of l inversely l is called a split of c we will show that splitting preserves three clutter properties i e idealness the max flow min cut property and the packing property we will also display several natural examples in which a clutter does not have these properties but a split of them does we will develop tools for recognizing when splitting is not a useful operation and as well we will characterize when identification preserves the three mentioned properties we will also make connections to spanning arborescences steiner trees comparability graphs degenerate projective planes bi

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

aalen additive hazards change point model we study a test comparing the full aalen additive hazards model and the change point model and suggest how to estimate the parameters of the change point model we also study a test for no change point effect both tests are provided with large sample properties and a resampling method is applied to obtain p values the finite sample properties of the proposed inference procedures and estimators are assessed through a simulation study the methods are further applied to a dataset concerning myocardial infarction

score tests for homogeneity of regression effect in the proportional hazards model a simple model containing the proportional hazards regression model as a special case is presented the purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested rank invariant score tests for linear quadratic or exponential trends can for instance all be undertaken within this framework in the case of the two sample problem the required calculations are shown to take a particularly simple form special consideration is given to the two sample case in which there is an inversion of the regression effect i e where the hazard functions cross at some given point both of the motivating examples are concerned with this problem computational aspects are relatively straightforward and some discussion on this is provided

weighted breslow type and maximum likelihood estimation in semiparametric transformation models a semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard intensity the breslow type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures we show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation with the weights depending on the martingale residuals the weighted breslow type estimator suggests an iterative reweighting algorithm for nonparametric maximum likelihood estimation which can be implemented by a weighted variant of the existing algorithms for inefficient estimation and can be computationally more efficient than an em type algorithm the weighting idea is further extended to semiparametric transformation models with mismeasured covariates

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

correcting for selective compliance in a re employment bonus experiment we propose a two stage instrumental variable estimator that is consistent if there is selective compliance in the treatment group of a randomized experiment and the outcome variable is a censored duration the estimator assumes full compliance in the control group we use the estimator to re analyze data from the illinois re employment bonus experiment

cox regression with survival time dependent missing covariate values analysis with time to event data in clinical and epidemiological studies often encounters missing covariate values and the missing at random assumption is commonly adopted which assumes that missingness depends on the observed data including the observed outcome which is the minimum of survival and censoring time however it is conceivable that in certain settings missingness of covariate values is related to the survival time but not to the censoring time this is especially so when covariate missingness is related to an unmeasured variable affected by the patient s illness and prognosis factors at baseline if this is the case then the covariate missingness is not at random as the survival time is censored and it creates a challenge in data analysis in this article we propose an approach to deal with such survival time dependent covariate missingness based on the well known cox proportional hazard model our method is based on inverse propensity weighting with the propensity estimated by nonparametric kernel regression our estimators are consistent and asymptotically normal and their finite sample performance is examined through simulation an application to a real data example is included for illustration

survival analysis with error prone time varying covariates a risk set calibration approach occupational environmental and nutritional epidemiologists are often interested in estimating the prospective effect of time varying exposure variables such as cumulative exposure or cumulative updated average exposure in relation to chronic disease endpoints such as cancer incidence and mortality from exposure validation studies it is apparent that many of the variables of interest are measured with moderate to substantial error although the ordinary regression calibration approach is approximately valid and efficient for measurement error correction of relative risk estimates from the cox model with time independent point exposures when the disease is rare it is not adaptable for use with time varying exposures by re calibrating the measurement error model within each risk set a risk set regression calibration method is proposed for this setting an algorithm for a bias corrected point estimate of the relative risk using an rrc approach is presented followed by the derivation of an estimate of its variance resulting in a sandwich estimator emphasis is on methods applicable to the main study external validation study design which arises in important applications simulation studies under several assumptions about the error model were carried out which demonstrated the validity and efficiency of the method in finite samples the method was applied to a study of diet and cancer from harvard s health professionals follow up study hpfs

the asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time the log rank test derived by mantel 1966 and peto 1972 is a special case of the efficient scores test for the proportional hazards model it is used frequently in the analysis of survival duration in clinical trials where patients entering the study are assigned at random to different treatments and are followed until they either fail or the study is terminated most survival studies are designed so that the log rank test is calculated at the termination of the study however it is not unusual for the investigator to monitor the experiment periodically it would be very useful to know the joint distribution of the test statistic at different points in time in order to adjust for the effect of repeated significance testing although the joint distribution has not been derived previously sequential procedures for the analysis of survival data in clinical trials have been given by several authors including armitage 1975 pp 140 6 jones whitehead 1979 and nagelkerke hart 1980 in this paper we establish the asymptotic joint distribution of the more general efficient scores test for the proportional hazards model calculated at different points in time and indicate how this can be used for repeated significance testing

competing risks regression for stratified data for competing risks data the fine gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function however in many important applications proportional hazards may not be satisfied including multicenter clinical trials where the baseline subdistribution hazards may not be common due to varying patient populations in this article we consider a stratified competing risks regression to allow the baseline hazard to vary across levels of the stratification covariate according to the relative size of the number of strata and strata sizes two stratification regimes are considered using partial likelihood and weighting techniques we obtain consistent estimators of regression parameters the corresponding asymptotic properties and resulting inferences are provided for the two regimes separately data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified fine gray model

a general framework for random effects survival analysis in the cox proportional hazards setting summary the use of random effects modeling in statistics has increased greatly in recent years the introduction of such modeling into event time analysis has proceeded more slowly however previously random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit in this paper we develop a method of random effect analysis of survival data the hierarchical cox model that is an extension of cox s original formulation in that the baseline hazard function remains unspecified this method also allows an arbitrary distribution for the random effects we accomplish this using markov chain monte carlo methods in a bayesian setting the method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control this analysis is more satisfying than standard approaches such as studying the first event for each subject which does not fully use the data or assuming independence which in this case would overestimate the precision

quasi maximum likelihood estimation of volatility with high frequency data this paper investigates the properties of the well known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise by extending the classic asymptotic results of quasi maximum likelihood estimation when trying to estimate the integrated volatility and the variance of noise this parametric approach remains consistent efficient and robust as a quasi estimator under misspecified assumptions moreover it shares the model free feature with nonparametric alternatives for instance realized kernels while being advantageous over them in terms of finite sample performance in light of quadratic representation this estimator behaves like an iterative exponential realized kernel asymptotically comparisons with a variety of implementations of the tukey hanning2 kernel are provided using monte carlo simulations and an empirical study with the euro us dollar future illustrates its application in practice

models and algorithms for network reduction abstract we study models and algorithms for a network reduction nr problem that entails constructing a reduced network in place of an existing large network so that the shortest path lengths between specified node pairs in this network are equal to or only slightly longer than the corresponding shortest path lengths in the original network solving this problem can be very useful both to accelerate shortest path calculations in many practical contexts and to reduce the size of optimization models that contain embedded shortest path problems this work was motivated by a real problem of scheduling and routing resources to perform spatially dispersed jobs but also has other applications we consider two variants of the nr problem a min size nr problem that minimizes the number of arcs in the reduced network while ensuring that the shortest path lengths in this network are close to the original lengths and a min length nr problem that minimizes a weighted sum of shortest path lengths over all the specified node pairs while limiting the number of arcs in the reduced network we model both problems as integer programs with multi commodity flows and propose optimization based heuristic algorithms to solve them these methods include preprocessing a shortest path based procedure with local improvement and a dual ascent algorithm we report on the successful applications to reduce the network for practical infrastructure project planning and to condense a transportation network for distribution planning we also compare these solutions with those obtained using algorithms for minimum length trees

generalized martingale residual processes for goodness of fit inference in cox s type regression models in the paper a general class of stochastic processes based on the sums of weighted martingale transform residuals for goodness of fit inference in general cox s type regression models is studied their form makes the inference robust to covariate outliers a weak convergence result for such processes is obtained giving the possibility of establishing the randomness of their graphs together with the construction of the formal x 2 type goodness of fit tests by using the khmaladze innovation approach a modified version of the initial class of processes is also defined weak convergence results for the processes are derived this leads to the main application which concerns the formal construction of the kolmogorov smirnov and cramer von mises type goodness of fit tests this is done within the general situation considered

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

nested frailty models using maximum penalized likelihood estimation the frailty model is a random effect survival model which allows for unobserved heterogeneity or for statistical dependence between observed survival data the nested frailty model accounts for the hierarchical clustering of the data by including two nested random effects nested frailty models are particularly appropriate when data are clustered at several hierarchical levels naturally or by design in such cases it is important to estimate the parameters of interest as accurately as possible by taking into account the hierarchical structure of the data we present a maximum penalized likelihood estimation mpnle to estimate non parametrically a continuous hazard function in a nested gamma frailty model with right censored and left truncated data the estimators for the regression coefficients and the variance components of the random effects are obtained simultaneously the simulation study demonstrates that this semi parametric approach yields satisfactory results in this complex setting in order to illustrate the mpnle method and the nested frailty model we present two applications one is for modelling the effect of particulate air pollution on mortality in different areas with two levels of geographical regrouping the other application is based on recurrent infection times of patients from different hospitals we illustrate that using a shared frailty model instead of a nested frailty model with two levels of regrouping leads to inaccurate estimates with an overestimation of the variance of the random effects we show that even when the frailty effects are fairly small in magnitude they are important since they alter the results in a systematic pattern

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

on confidence intervals for the hazard ratio in randomized clinical trials the log rank test is widely used to compare two survival distributions in a randomized clinical trial while partial likelihood cox 1975 is the method of choice for making inference about the hazard ratio under the cox 1972 proportional hazards model the wald 95 confidence interval of the hazard ratio may include the null value of 1 when the p value of the log rank test is less than 0 05 peto et al 1977 provided an estimator for the hazard ratio based on the log rank statistic the corresponding 95 confidence interval excludes the null value of 1 if and only if the p value of the log rank test is less than 0 05 however peto s estimator is not consistent and the corresponding confidence interval does not have correct coverage probability in this article we construct the confidence interval by inverting the score test under the possibly stratified cox model and we modify the variance estimator such that the resulting score test for the null hypothesis of no treatment difference is identical to the log rank test in the possible presence of ties like peto s method the proposed confidence interval excludes the null value if and only if the log rank test is significant unlike peto s method however this interval has correct coverage probability an added benefit of the proposed confidence interval is that it tends to be more accurate and narrower than the wald confidence interval we demonstrate the advantages of the proposed method through extensive simulation studies and a colon cancer study

a simple test for goodness of fit of cox s proportional hazards model cox s proportional hazards model for survival analysis 1972 has gained widespread attention from both applied and theoretical statisticians and is central to most work on survival analysis to verify the assumption of proportional hazards underlying the model several methods have recently been put forward cox 1979 schoenfeld 1980 andersen 1982 kalbfleisch and prentice 1980 these methods consist either of graphical techniques designed so as to visualize departures from the proportional hazards ph assumption or of formal tests based on parameterizing the interaction between covariates and time in this paper a simple test statistic is proposed for detecting departures from the ph assumption the proposed test is computationally and conceptually straightforward expressions for the first two moments of the test statistic are presented

comparison of methods for the analysis of longitudinal interval count data longitudinal studies are often concerned with estimating the recurrence rate of a non fatal event in many cases only the total number of events occurring during successive time intervals is known we compared a mixed poisson gamma regression method proposed by thall and a quasi likelihood method proposed by zeger and liang for the analysis of such data in the case where the mean was correctly specified using simulation techniques with large samples both methods produced similar standard errors in most situations except in the case of time dependent covariates with non poisson gamma data where they were seriously underestimated by the thall method a simple method for discriminating between the variance forms of the two methods is described the findings are applied to the analyses of clinical trials of non melanoma skin cancer and familial polyposis this study extends the findings of breslow concerning variance misspecification in overdispersed poisson and quasi likelihood models to the longitudinal setting

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

a note on a dual ascent approach to the fixed charge capacitated network design problem abstract we show by a counterexample that the dual ascent procedure proposed by herrmann ioannou minis and proth in a 1996 issue of the european journal of operational research is incorrect in the sense that it does not generate a valid lower bound to the optimal value of fixed charge capacitated network design problems we provide a correct dual ascent procedure based on the same ideas and we give an interpretation of it in terms of a simple lagrangean relaxation although correct this procedure is not effective as in general it provides a less tighter bound than the linear programming relaxation

a dual approach to inference for partially identified econometric models abstract this paper considers inference for the set i of parameter values that minimize a criterion function chernozhukov et al 2007 cht develop a general theory of estimation and inference using the level set of a criterion function we establish a dual relationship between the level set estimator and its support function and show that the properly normalized support function provides alternative wald type inference methods these methods can be used to obtain confidence sets for i and points inside it for models with finitely many moment inequalities we show that our wald type statistic is asymptotically equivalent to cht s statistic under regularity conditions

efficiency lost by analyzing counts rather than event times in poisson and overdispersed poisson regression models abstract inference for point processes is most efficient if the event times for each individual are available sometimes the study design is such that only aggregated data are collected consisting of the number of events or recurrences for each individual over the observation period this article discusses the loss in efficiency of an analysis of the aggregated counts versus an analysis of the actual event times one particular case is exemplified that in which the purpose of the experiment or trial is to compare the effects of treatments and the loss in efficiency in the estimator of the treatment effect is computed the specific point process considered here is the nonhomogeneous poisson process with a proportional intensity model for the treatment effects random effects models are also considered with estimation via a quasi likelihood approach the quasi likelihood analysis proposed here is an extension of such techniques for the homogeneous poisson process the resulting estimating equations for

case cohort and case control analysis with cox s model prentice 1986 proposed the case cohort design and studied a pseudolikelihood estimator of regression parameters in cox s model we derive a class of estimating equations for case cohort sampling each depending on a different estimator of the population distribution which lead naturally to simple estimators that improve on prentice s pseudolikelihood estimator we also discuss an equivalence between case control and case cohort sampling in terms of the estimation of regression parameters in cox s model

demographic incidence rates and estimation of intensities with incomplete information many population processes in demography epidemiology and other fields can be represented by a time continuous markov chain model with a finite state space if we have complete information on the life history of a cohort the intensities of the markov model may be estimated by the occurrence exposure rates or by nonparametric techniques in many situations however we have only incomplete information in this paper we consider the special but important case where the occurrences and the total exposure are known but not the distribution of the latter over the various separate statuses methods for handling such data so called demographic incidence rates and methods for estimating the intensities from this kind of data are known in the literature however their statistical properties are only vaguely known the present paper gives a thorough presentation of the theory of these methods and provide rigorous proofs of their statistical properties using stochastic process theory 1 introduction in demography and fields with a similar methodology a population process on the individual level can frequently be represented by a time continuous markov chain with a finite state space the states of the markov chain represent the demographic statuses and the jumps between the states correspond to the demographic events the time parameter of the markov process may be the age of an individual the time since a specific event or some such quantity we will call it seniority given this general framework the population phenomena may be described by the transition intensities of the model consequently it is of great interest to estimate these functions in principle this is an easy task if the individuals studied are watched continuously over some period of time one may then use the classical methods based on occurrence exposure rates for a review see hoem 1976 or for small populations or samples nonparametric techniques developed by aalen 1978 and others quite often however one does not obtain the sufficiently detailed data required to use any of these methods this fact has inhibited the use of markov chain models in demography and related fields the development and study of statistical methods for situations with incomplete data is therefore of considerable interest there seems to be no general solution to the problem of estimating the intensities of partially observed markov chains in the present paper we consider a special but important type of incomplete observation namely that transitions within a subset of states k are observed in detail while counts of transitions out

adjusted score functions for monotone likelihood in the cox regression model standard inference procedures for the cox model involve maximizing the partial likelihood function monotone partial likelihood is an issue that frequently happens in the analysis of health science studies monotone likelihood mainly occurs in samples with substantial censoring of survival times and is associated with categorical covariates in particular and more frequently it usually happens when one level of a categorical covariate has just experienced censoring times in order to overcome this problem heinze and schemper proposed an adjusted partial likelihood score function obtained by suitably adapting the general approach of firth for mean bias reduction the procedure is effective in preventing infinite estimates as an alternative solution we propose an approach based on the adjusted score function recently suggested by kenne pagui et al for median bias reduction this procedure also solves the infinite estimate problem and has an additional advantage of being invariant under componentwise reparameterizations this latter fact is fundamental under cox model since hazards ratio interpretation is obtained by exponentiating parameter estimates numerical studies of the proposed method suggest better inference properties than those of the mean bias reduction a real data application related to a melanoma skin dataset is used as illustration for a comparison basis of the methods

on fitting cox s regression model with time dependent coefficients summary this paper examines goodness of fit testing in the cox regression model with timevarying regression coefficients arjas 1988 approach is used to define test statistics of the kolmogorov smirnov and cramer von mises types their asymptotic limits are shown to be well known functionals of standard brownian motion leading to the construction of formal goodness of fit tests some numerical studies are also included to illustrate the performance of the tests for moderate sample sizes

marginal regression models for multivariate failure time data abstract in this article we propose a general cox type regression model to formulate the marginal distributions of multivariate failure time data this model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type we prove that the maximum quasi partial likelihood estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided furthermore we establish the uniform consistency and joint weak convergence of the aalen breslow type estimators for the cumulative baseline hazard functions and develop a resampling technique to approximate the joint distribution of these processes which enables one to make simultaneous inference about the survival functions over the time axis and across failure types finally we assess the small sample pro

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

fixed charge multicommodity network design using p partition facets abstract we are given an undirected network g v e and a set of traffic demands to install a potential edge e e we incur a cost fe to provide a positive capacity ae the objective is to select edges at minimum cost so as to permit a feasible multicommodity flow of all traffic we study structure of the projection polytope of this problem in the space of binary variables associated with fixed charges by relating facets of a p node problem p 2 3 or 4 defined over a multi graph obtained by a p partition of v to the facets of the original problem inspired from the well known cover inequalities of the knapsack problem we develop the notion of p partition cover inequalities we present necessary and sufficient conditions for such inequalities to be facet defining for p 3 and 4 a simple heuristic approach for separating and adding such violated inequalities is presented and implemented for p values up to 10 we report optimal solutions for problems with 30 nodes 60 edges and fully dense demand matrices within a few minutes of cpu time for most instances some results for dense graph problems are also reported

penalized partial likelihood regression for right censored data with bootstrap selection of the penalty parameter le modele de cox a risque proportionnel est souvent utilise pour estimer l association entre des covariables et un delai de survenue d un evenement qui peut etre censure les estimateurs bases sur la vraisemblance partielle sont utilises pour l estimation et la prediction du risque relatif de l evenement cependant ces estimateurs sont instables et ont une grande variance en cas de colinearite entre les covariables ou quand le nombre d evenements n est pas nettement plus grand que le nombre de covariables une vraisemblance partielle penalisee est proposee pour donner des estimateurs du risque relatif plus precis nous montrons qu asymptotiquement il existe toujours un parametre de penalite pour la vraisemblance partielle penalisee qui reduit le carre moyen de l erreur d estimation du logarithme du risque relatif nous proposons une methode de reechantillonnage pour choisir le parametre de penalite des simulations et un exemple montrent que des estimateurs bases sur la vraisemblance partielle penalisee et la methode du bootstrap peuvent dans certaines circonstances avoir un biais plus petit que celui des estimateurs bases sur la vraisemblance partielle ainsi qu un carre moyeu plus petit de l erreur d estimation et de prediction du logarithme du risque relatif nous illustrons ces methodes avec des donnees d une etude sur le myelome multiple du eastern cooperative oncology group ecog

assessing cumulative incidence functions under the semiparametric additive risk model in analyzing competing risks data a quantity of considerable interest is the cumulative incidence function often the effect of covariates on the cumulative incidence function is modeled via the proportional hazards model for the cause specific hazard function as the proportionality assumption may be too restrictive in practice we consider an alternative more flexible semiparametric additive hazards model of biometrika 1994 81 501 514 for the cause specific hazard this model specifies the effect of covariates on the cause specific hazard to be additive as well as allows the effect of some covariates to be fixed and that of others to be time varying we present an approach for constructing confidence intervals as well as confidence bands for the cause specific cumulative incidence function of subjects with given values of the covariates furthermore we also present an approach for constructing confidence intervals and confidence bands for comparing two cumulative incidence functions given values of the covariates the finite sample property of the proposed estimators is investigated through simulations we conclude our paper with an analysis of the well known malignant melanoma data using our method