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

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

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

proportional hazards regression with missing covariates abstract nonparametric maximum likelihood npml is used to estimate regression parameters in a proportional hazards regression model with missing covariates the npml estimator is shown to be consistent and asymptotically normally distributed under some conditions em type algorithms are applied to solve the maximization problem variance estimates of the regression parameters are obtained by a profile likelihood approach that uses em aided numerical differentiation simulation results indicate that the npml estimates of the regression parameters are more efficient than the approximate partial likelihood estimates and estimates from complete case analysis when missing covariates are missing completely at random and that the proposed method corrects for bias when the missing covariates are missing at random

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

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

analysis of the proportional hazards model with sparse longitudinal covariates regression analysis of censored failure observations via the proportional hazards model permits time varying covariates that are observed at death times in practice such longitudinal covariates are typically sparse and only measured at infrequent and irregularly spaced follow up times full likelihood analyses of joint models for longitudinal and survival data impose stringent modeling assumptions that are difficult to verify in practice and that are complicated both inferentially and computationally in this article a simple kernel weighted score function is proposed with minimal assumptions two scenarios are considered half kernel estimation in which observation ceases at the time of the event and full kernel estimation for data where observation may continue after the event as with recurrent events data it is established that these estimators are consistent and asymptotically normal however they converge at rates that are slower than the parametric rates that may be achieved with fully observe

estimation for a semimartingale regression model using the method of sieves estimation by the method of sieves for a semimartingale regression model introduced by aalen 1980 is studied it is of interest to estimate functions which describe the influence of the covariates over time an estimator for these functions is introduced and conditions which ensure consistency of the estimator in l 2 norm are given applications to diffusion processes and point processes with censored data are also discussed

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

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

modeling left truncated and right censored survival data with longitudinal covariates there is a surge in medical follow up studies that include longitudinal covariates in the modeling of survival data so far the focus has been largely on right censored survival data we consider survival data that are subject to both left truncation and right censoring left truncation is well known to produce biased sample the sampling bias issue has been resolved in the literature for the case which involves baseline or time varying covariates that are observable the problem remains open however for the important case where longitudinal covariates are present in survival models a joint likelihood approach has been shown in the literature to provide an effective way to overcome those difficulties for right censored data but this approach faces substantial additional challenges in the presence of left truncation here we thus propose an alternative likelihood to overcome these difficulties and show that the regression coefficient in the survival component can be estimated unbiasedly and efficiently issues about the bias for the longitudinal component are discussed the new approach is illustrated numerically through simulations and data from a multi center aids cohort study

a computational methodology for shape optimization of structures in frictionless contact this paper presents a computational methodology for shape optimization of structures in frictionless contact which provides a basis for developing user friendly and efficient shape optimization software for evaluation it has been implemented as a subsystem of a general finite element software the overall design and main principles of operation of this software are outlined the parts connected to shape optimization are described in more detail the key building blocks are analytic sensitivity analysis an adaptive finite element method an accurate contact solver and a sequential convex programing optimization algorithm results for three model application examples are presented in which the contact pressure and the effective stress are optimized

covariate measurement errors in frailty models for clustered survival data summary we propose a new class of frailty measurement error models for clustered survival data when covariates are measured with error we show that the induced hazard function conditional on the observed covariates also follows a frailty model but of a more complicated form we study the asymptotic bias in regression coefficients and variance components when measurement error is ignored and the impact of censoring on this asymptotic bias we show that the naive estimator of the regression coefficient is attenuated and the naive estimator of the variance component is inflated when measurement error is ignored as the censoring proportion increases the asymptotic bias in the former becomes larger but the asymptotic bias in the latter interestingly becomes smaller we develop a structural approach for parameter estimation using the nonparametric maximum likelihood method where the baseline hazard is estimated nonparametrically we prove model identifiability and the existence of the nonparametric maximum likelihood estimators an em algorithm is developed for calculating the nonparametric maximum likelihood estimates the method is applied to the western kenya parasitaemia data and its performance is evaluated through simulations

asymptotic theory for the frailty model the frailty model is a generalization of cox s proportional hazards model which includes a random effect nielsen gill andersen and sorensen 1992 proposed an em algorithm to estimate the cumulative baseline hazard and the variance of the random effect here the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance

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

consistency in a proportional hazards model incorporating a random effect supported in part by the north atlantic treaty organization under a grant awarded in 1990 conducted at the mathematical institute of the university of utrecht the netherlands

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

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

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

on using the cox proportional hazards model with missing covariates summary we propose two methods for handling missing covariates in using the cox proportional hazards model the maximum partial likelihood estimator based only on study subjects having complete covariates does not utilise all available information also it is biased when the probability of missingness depends on the failure or censoring time our suggestion is to impute the conditional expectation of the statistic involving missing covariates given the available information the proposed method provides a consistent regression parameter estimator when the probability of missingness depends on the failure or censoring time as well as on the observed covariates also the proposed estimator is more efficient than the estimator suggested previously by lin ying 1993 when data are missing completely at random

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

explicit lower bounds for residues at s 1 of dedekind zeta functions and relative class numbers of cm fields let s be a given set of positive rational primes assume that the value of the dedekind zeta function k of a number field k is less than or equal to zero at some real point in the range 1 we give explicit lower bounds on the residue at s 1 of this dedekind zeta function which depend on the absolute value d k of the discriminant of k and the behavior in k of the rational primes p e s now let k be a real abelian number field and let be any real zero of the zeta function of k we give an upper bound on the residue at s 1 of which depends on d and the behavior in k of the rational primes p e s by combining these two results we obtain lower bounds for the relative class numbers of some normal cm fields k which depend on the behavior in k of the rational primes p e s we will then show that these new lower bounds for relative class numbers are of paramount importance for solving for example the exponent two class group problem for the non normal quartic cm fields finally we will prove brauer siegel like results about the asymptotic behavior of relative class numbers of cm fields

asymptotic theory for the cox model with missing time dependent covariate the relationship between a time dependent covariate and survival times is usually evaluated via the cox model time dependent covariates are generally available as longitudinal data collected regularly during the course of the study a frequent problem however is the occurence of missing covariate data a recent approach to estimation in the cox model in this case jointly models survival and the longitudinal covariate however theoretical justification of this approach is still lacking in this paper we prove existence and consistency of the maximum likelihood estimators in a joint model the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance

auxiliary covariate data in failure time regression summary we consider the problem of missing covariate data in the context of censored failure time relative risk regression auxiliary covariate data which are considered informative about the missing data but which are not explicitly part of the relative risk regression model may be available full covariate information is available for a validation set an estimated partial likelihood method is proposed for estimating relative risk parameters this method is an extension of the estimated likelihood regression analysis method for uncensored data pepe 1992 pepe fleming 1991 a key feature of the method is that it is nonparametric with respect to the association between the missing and observed including auxiliary covariate components asymptotic distribution theory is derived for the proposed estimated partial likelihood estimator in the case where the auxiliary or mismeasured covariates are categorical asymptotic efficiencies are calculated for exponential failure times using an exponential relative risk model the estimated partial likelihood estimator compares favourably with a fully parametric maximum likelihood analysis comparisons are also made with a standard partial likelihood analysis which ignores the incomplete observations important efficiency gains can be made with the estimated partial likelihood method small sample properties are investigated through simulation studies

the reciprocal variational approach to the signorini problem with friction approximation results in this paper a new variational formulation of the signorini problem with friction is given in terms of the contact stresses the method corresponds to the direct integral equation approach in classical elastostatic problems first the displacement and mixed problems are briefly described together with some numerical results next the displacements are eliminated by the use of green s function and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived then the resulting approximation procedure is studied and certain convergence results are proved finally some remarks on the signorini problem with coulomb friction are presented numerical results illustrate the theory

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