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

conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

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

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

on the removal of the non uniqueness in the solution of elastostatic problems by symmetric galerkin bem a study of the removal of the non uniqueness in the solution of elastostatic problems by means of the symmetric galerkin boundary element method is presented the paper focuses on elastic problems defined on domains with cavities where cavity boundaries are subjected to traction boundary conditions a simple method consisting in a direct application of support conditions and several methods based on the fredholm theory of linear operators are introduced implemented and analysed numerical examples demonstrate the performance of the proposed methods and accuracy of their results a comparative evaluation of the methods developed being finally presented copyright 2005 john wiley sons ltd

proportional hazards model with covariates subject to measurement error when covariates of a proportional hazards model are subject to measurement error the maximum likelihood estimates of regression coefficients based on the partial likelihood are asymptotically biased prentice 1982 biometrika 69 331 342 presents an example of such bias and suggests a modified partial likelihood this paper applies the corrected score function method nakamura 1990 biometrika 77 127 137 to the proportional hazards model when measurement errors are additive and normally distributed the result allows a simple correction to the ordinary partial likelihood that yields asymptotically unbiased estimates the validity of the correction is confirmed via a limited simulation study

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

continuous time penalty methods for nash equilibrium seeking of a nonsmooth generalized noncooperative game in this paper we propose centralized and distributed continuous time penalty methods to find a nash equilibrium for a generalized noncooperative game with shared inequality and equality constraints and private inequality constraints that depend on the player itself by using the l 1 penalty function we prove that the equilibrium of a differential inclusion is a normalized nash equilibrium of the original generalized noncooperative game and the centralized differential inclusion exponentially converges to the unique normalized nash equilibrium of a strongly monotone game suppose that the players can communicate with their neighboring players only and the communication topology can be represented by a connected undirected graph based on a leader following consensus scheme and singular perturbation techniques we propose distributed algorithms by using the exact l 1 penalty function and the continuously differentiable squared l 2 penalty function respectively the squared l 2 penalty function method works for games with smooth constraints and the exact l 2 penalty function works for certain scenarios the proposed two distributed algorithms converge to an neighborhood of the unique normalized nash equilibrium and an neighborhood of an approximated nash equilibrium respectively with being a positive constant for each 0 and each initial condition there exists an varepsilon such that for each 0 varepsilon varepsilon the convergence can be guaranteed where varepsilon is a parameter in the algorithm

distributed robust adaptive equilibrium computation for generalized convex games this paper considers a class of generalized convex games where each player is associated with a convex objective function a convex inequality constraint and a convex constraint set the players aim to compute a nash equilibrium through communicating with neighboring players the particular challenge we consider is that the component functions are unknown a priori to associated players we study two distributed computation algorithms and analyze their convergence properties in the presence of data transmission delays and dynamic changes of network topologies the algorithm performance is verified through demand response on the ieee 30 bus test system our technical tools integrate convex analysis variational inequalities and simultaneous perturbation stochastic approximation

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

parameterization and inference for nonparametric regression problems we consider local likelihood or local estimating equations in which a multivariate function is estimated but a derived function of is of interest in many applications when most naturally formulated the derived function is a non linear function of in trying to understand whether the derived non linear function is constant or linear a problem arises with this approach when the function is actually constant or linear the expectation of the function estimate need not be constant or linear at least to second order in such circumstances the simplest standard methods in nonparametric regression for testing whether a function is constant or linear cannot be applied we develop a simple general solution which is applicable to nonparametric regression varying coefficient models nonparametric generalized linear models etc we show that in local linear kernel regression inference about the derived function is facilitated without a loss of power by reparameterization so that is itself a component of our approach is in contrast with the standard practice of choosing for convenience and allowing to be a non linear function of the methods are applied to an important data set in nutritional epidemiology

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

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

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

the boundary node method for three dimensional linear elasticity the boundary node method bnm is developed in this paper for solving three dimensional problems in linear elasticity the bnm represents a coupling between boundary integral equations bie and moving least squares mls interpolants the main idea is to retain the dimensionality advantage of the former and the meshless attribute of the later this results in decoupling of the mesh and the interpolation procedure for problems in linear elasticity free rigid body modes in traction prescribed problems are typically eliminated by suitably restraining the body however an alternative approach developed recently for the boundary element method bem is extended in this work to the bnm this approach is based on ideas from linear algebra to complete the rank of the singular stiffness matrix also the bnm has been extended in the present work to solve problems with material discontinuities and a new procedure has been developed for obtaining displacements and stresses accurately at internal points close to the boundary of a body copyright 1999 john wiley sons ltd

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

a semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error summary a common objective in longitudinal studies is to characterise the relationship between a failure time process and time independent and time dependent covariates timedependent covariates are generally available as longitudinal data collected periodically during the course of the study we assume that these data follow a linear mixed effects model with normal measurement error and that the hazard of failure depends both on the underlying random effects describing the covariate process and other time independent covariates through a proportional hazards relationship a routine assumption is that the random effects are normally distributed however this need not hold in practice within this framework we develop a simple method for estimating the proportional hazards model parameters that requires no assumption on the distribution of the random effects large sample properties are discussed and finite sample performance is assessed and compared to competing methods via simulation

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

distributed nash equilibrium seeking in networked graphical games abstract this paper considers a gossip approach for finding a nash equilibrium in networked games on graphs where a player s cost function may be affected by the actions of any subset of players an interference graph illustrates the partially coupled cost functions i e the asymmetric strategic interaction and information requirements an algorithm is proposed whereby players make decisions based only on the estimates of their interfering players actions given the interference graph not necessarily complete a communication graph is designed so that players exchange only their required information when the interference graph is sparse the algorithm can offer substantial savings in communication and computation almost sure convergence to a nash equilibrium is proved for diminishing step sizes the effect of the second largest eigenvalue of the expected communication matrix on the convergence rate is quantified

hazard ratio estimation for biomarker calibrated dietary exposures uncertainty concerning the measurement error properties of self reported diet has important implications for the reliability of nutritional epidemiology reports biomarkers based on the urinary recovery of expended nutrients can provide an objective measure of short term nutrient consumption for certain nutrients and when applied to a subset of a study cohort can be used to calibrate corresponding self report nutrient consumption assessments a non standard measurement error model that makes provision for systematic error and subject specific error along with the usual independent random error is needed for the self report data three estimation procedures for hazard ratio cox model parameters are extended for application to this more complex measurement error structure these procedures are risk set regression calibration conditional score and nonparametric corrected score an estimator for the cumulative baseline hazard function is also provided the performance of each method is assessed in a simulation study the methods are then applied to an example from the women s health initiative dietary modification trial

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

an algebraic multigrid method with interpolation reproducing rigid body modes for semi definite problems in two dimensional linear elasticity based on the geometric grid information as geometric coordinates an algebraic multigrid amg method with the interpolation reproducing the rigid body modes namely the kernel elements of semi definite operator arising from linear elasticity is constructed and such method is applied to the linear elasticity problems with a traction free boundary condition and crystal problems with free boundary conditions as well the results of various numerical experiments in two dimensions are presented it is shown from the numerical results that the constructed amg method is robust and efficient for such semi definite problems and the convergence is uniformly bounded away from one independent of the problem size furthermore the amg method proposed in this paper has better convergence rate than the commonly used amg methods simultaneously an amg method that can preserve the quotient space which means that if the exact solution of original problem belongs to the quotient space of discrete operator considered then the numerical solution of amg method is convergent in the same quotient space is obtained using the technique of orthogonal decomposition

advanced 3d beam element of arbitrary composite cross section including generalized warping effects summary in this paper an advanced 20 20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed taking into account shear lag effects due to both flexure and torsion the case of the three dimensional beam element of arbitrary homogeneous cross section is treated as a special one the composite member consists of materials in contact each of which can surround a finite number of inclusions nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions ten boundary value problems with respect to the kinematical components are formulated and solved employing the analog equation method a bem based technique the aforementioned boundary value problems are formulated employing either an improved stress field arising from the correction of shear stress components or the stress field arising directly from displacement considerations the warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure bem approach that is only boundary discretization of the cross section is used numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy the deviations arising from the use of the advanced 20 20 stiffness matrix and the classical 12 12 or 14 14 ones employed in commercial software packages are illustrated through examples of great practical interest moreover the influence of nonuniform warping effects necessitating the use of the aforementioned advanced stiffness matrix is also demonstrated copyright 2015 john wiley sons ltd

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

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

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

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

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

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

logistic regression with exposure biomarkers and flexible measurement error regression calibration refined regression calibration and conditional scores estimation procedures are extended to a measurement model that is motivated by nutritional and physical activity epidemiology biomarker data available on a small subset of a study cohort for reasons of cost are assumed to adhere to a classical measurement error model while corresponding self report nutrient consumption or activity related energy expenditure data are available for the entire cohort the self report assessment measurement model includes a person specific random effect the mean and variance of which may depend on individual characteristics such as body mass index or ethnicity logistic regression is used to relate the disease odds ratio to the actual but unmeasured dietary or physical activity exposure simulation studies are presented to evaluate and contrast the three estimation procedures and to provide insight into preferred biomarker subsample size under selected cohort study configurations

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

regression calibration in failure time regression in this paper we study a regression calibration method for failure time regression analysis when data on some covariates are missing or mismeasured the method estimates the missing data based on the data structure estimated from a validation data set a random subsample of the study cohort in which covariates are always observed ordinary cox 1972 journal of the royal statistical society series b 34 187 220 regression is then applied to estimate the regression coefficients using the observed covariates in the validation data set and the estimated covariates in the nonvalidation data set the method can be easily implemented we present the asymptotic theory of the proposed estimator finite sample performance is examined and compared with an estimated partial likelihood estimator and other related methods via simulation studies where the proposed method performs well even though it is technically inconsistent finally we illustrate the method with a mouse leukemia data set

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

estimating the parameters in the cox model when covariate variables are measured with error the cox proportional hazards model is commonly used to model survival data as a function of covariates because of the measuring mechanism or the nature of the environment covariates are often measured with error and are not directly observable a naive approach is to use the observed values of the covariates in the cox model which usually produces biased estimates of the true association of interest an alternative strategy is to take into account the error in measurement which may be carried out for the cox model in a number of ways we examine several such approaches and compare and contrast them through several simulation studies we introduce a likelihood based approach which we refer to as the semiparametric method and show that this method is an appealing alternative the methods are applied to analyze the relationship between survival and cd4 count in patients with aids

multi agent discrete time graphical games and reinforcement learning solutions this paper introduces a new class of multi agent discrete time dynamic games known in the literature as dynamic graphical games for that reason a local performance index is defined for each agent that depends only on the local information available to each agent nash equilibrium policies and best response policies are given in terms of the solutions to the discrete time coupled hamilton jacobi equations since in these games the interactions between the agents are prescribed by a communication graph structure we have to introduce a new notion of nash equilibrium it is proved that this notion holds if all agents are in nash equilibrium and the graph is strongly connected a novel reinforcement learning value iteration algorithm is given to solve the dynamic graphical games in an online manner along with its proof of convergence the policies of the agents form a nash equilibrium when all the agents in the neighborhood update their policies and a best response outcome when the agents in the neighborhood are kept constant the paper brings together discrete hamiltonian mechanics distributed multi agent control optimal control theory and game theory to formulate and solve these multi agent dynamic graphical games a simulation example shows the effectiveness of the proposed approach in a leader synchronization case along with optimality guarantees

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

elimination of rigid body modes from discretized boundary integral equations abstract free rigid body modes in neumann problems are typically eliminated by suitably restraining the body an alternative approach here called regularization involves first computing the singular stiffness matrix and then suitably modifying it using ideas from linear algebra this idea has been suggested by verchery 1990 for symmetric matrices this paper is concerned with regularization of nonsymmetric stiffness matrices that arise from the boundary element method bem for linear elasticity existence and uniqueness issues as well as properties of the displacement field for elasticity problems with tractions prescribed at every point on the boundary are discussed in this paper

a risk set calibration method for failure time regression by using a covariate reliability sample regression parameter estimation in the cox failure time model is considered when regression variables are subject to measurement error assuming that repeat regression vector measurements adhere to a classical measurement model we can consider an ordinary regression calibration approach in which the unobserved covariates are replaced by an estimate of their conditional expectation given available covariate measurements however since the rate of withdrawal from the risk set across the time axis due to failure or censoring will typically depend on covariates we may improve the regression parameter estimator by recalibrating within each risk set the asymptotic and small sample properties of such a risk set regression calibration estimator are studied a simple estimator based on a least squares calibration in each risk set appears able to eliminate much of the bias that attends the ordinary regression calibration estimator under extreme measurement error circumstances corresponding asymptotic distribution theory is developed small sample properties are studied using computer simulations and an illustration is provided

distributed nash equilibrium seeking this paper presents an asynchronous gossip based algorithm for finding a nash equilibrium ne of a game in a distributed multi player network the algorithm is designed in such a way that players make decisions based on estimates of the other players actions obtained from local neighbors using a set of standard assumptions on the cost functions and communication graph the paper proves almost sure convergence to a ne for diminishing step sizes for constant step sizes an error bound on expected distance from a ne is established the effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes

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

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 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

semiparametric failure time regression with replicates of mismeasured covariates this article proposes a general strategy for the regression analysis of univariate and multivariate failure time data when a subset of covariates cannot be measured precisely but replicate measurements of their surrogates are available multivariate failure time data include recurrent events and clustered survival data the number of replicate measurements can vary from subject to subject and can even depend on the failure time no parametric assumption is imposed on the error or on any other random variable several semiparametric regression models are considered including the cox proportional hazards model for univariate failure time data multiplicative intensity rate models for recurrent events data and marginal cox proportional hazards models for general multivariate failure time data the existing estimating functions in the absence of measurement error are corrected to yield consistent and asymptotically normal estimators of the regression parameters the estimation of the underlying failure time

on corrected score approach for proportional hazards model with covariate measurement error in the presence of covariate measurement error with the proportional hazards model several functional modeling methods have been proposed these include the conditional score estimator tsiatis and davidian 2001 biometrika 88 447 458 the parametric correction estimator nakamura 1992 biometrics 48 829 838 and the nonparametric correction estimator huang and wang 2000 journal of the american statistical association 95 1209 1219 in the order of weaker assumptions on the error although they are all consistent each suffers from potential difficulties with small samples and substantial measurement error in this article upon noting that the conditional score and parametric correction estimators are asymptotically equivalent in the case of normal error we investigate their relative finite sample performance and discover that the former is superior this finding motivates a general refinement approach to parametric and nonparametric correction methods the refined correction estimators are asymptotically equivalent to their standard counterparts but have improved numerical properties and perform better when the standard estimates do not exist or are outliers simulation results and application to an hiv clinical trial are presented

cox regression with accurate covariates unascertainable a nonparametric correction approach abstract many survival studies involve covariates that are not accurately ascertainable cd4 lymphocyte count in hiv aids research is a typical example for which the gold standard of the measurement is not available this article proposes a consistent estimation procedure for cox regression under the additive measurement error model distinct from existing methods the proposed estimation for regression coefficients does not require any additional assumptions we establish the normalized partial score function as a functional of empirical processes which facilitates the construction of an estimating function with the same limit using replicated mismeasured covariates the resulting regression coefficient estimators are shown to be consistent and asymptotically normal a consistent sandwich variance estimate is presented we also suggest estimators for the baseline cumulative hazard function numerical studies demonstrate that the procedure performs well under practical sample sizes application to an aid

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

distributed seeking of nash equilibria with applications to mobile sensor networks we consider the problem of distributed convergence to a nash equilibrium in a noncooperative game where the players generate their actions based only on online measurements of their individual cost functions corrupted with additive measurement noise exact analytical forms and or parameters of the cost functions as well as the current actions of the players may be unknown additionally the players actions are subject to linear dynamic constraints we propose an algorithm based on discrete time stochastic extremum seeking using sinusoidal perturbations and prove its almost sure convergence to a nash equilibrium we show how the proposed algorithm can be applied to solving coordination problems in mobile sensor networks where motion dynamics of the players can be modeled as 1 single integrators velocity actuated vehicles 2 double integrators force actuated vehicles and 3 unicycles a kinematic model with nonholonomic constraints examples are given in which the cost functions are selected such that the problems of connectivity control formation control rendezvous and coverage control are solved in an adaptive and distributed way the methodology is illustrated through simulations

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