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

an analysis and comparison of conservative upwind difference schemes for ideal and non ideal gases in a recent paper p glaister conservative upwind difference schemes for the euler equations comput math appl 45 2003 1673 1682 a number of numerical schemes were presented for the euler equations governing compressible flows of an ideal gas the principal one of which is based on a conservative linearisation approach this scheme was subsequently extended to encompass compressible flows of real gases where the equation of state allows for non ideal gases p glaister conservative upwind difference schemes for compressible flows of a real gas comput math appl 48 2004 469 480 these schemes use different parameter vectors in their construction and consequently the scheme in p glaister conservative upwind difference schemes for compressible flows of a real gas comput math appl 48 2004 469 480 when applied to the special case of an ideal gas is not identical to the principal ideal gas scheme in p glaister conservative upwind difference schemes for the euler equations comput math appl 45 2003 1673 1682 in this paper it is shown how these schemes are related followed by a numerical comparison when each is applied to two standard test problems

inverse probability weighting in nested case control studies with additional matching a simulation study nested case control designs are inevitably less efficient than full cohort designs and it is important to use available information as efficiently as possible reuse of controls by inverse probability weighting may be one way to obtain efficiency improvements and it can be particularly advantageous when two or more endpoints are analyzed in the same cohort the controls in a nested case control design are often matched on additional factors than at risk status and this should be taken into account when reusing controls although some studies have suggested methods for handling additional matching a thorough investigation of how this affects parameter estimates and weights is lacking our aim is to provide such a discussion to help developing guidelines for practitioners we demonstrate that it is important to adjust for the matching variables in regression analyses when the matching is broken we present three types of estimators for the inverse sampling probabilities accounting for additional matching one of these estimators was somewhat biased when the cases and controls were matched very closely we investigated how additional matching affected estimates of interest with varying degree of association between the matching variables and exposure outcome strong associations introduced only a small bias when the matching variables were properly adjusted for sometimes exposure variables for example blood samples are analyzed in batches rather strong batch effects had to be present before this introduced much bias when the matching was broken all simulations are based on a study of prostate cancer and vitamin d copyright 2013 john wiley sons ltd

counter matching a stratified nested case control sampling method summary the counter matching design for sampling from risk sets is presented in which each sampled risk set includes the failure and a random sample of controls from sampling strata defined by exposure information available for all cohort subjects asymptotic relative efficiency comparisons indicate that this type of sampling has superior efficiency to simple nested case control sampling in situations of practical interest a simple extension of the method is given which allows for nonrepresentative sampling of failures analysis of data from counter matched studies may be performed using standard conditional logistic likelihood software which allows for an offset in the model

fitting prospective regression models to case control data summary we consider fitting prospective regression models to data obtained by case control or response selective sampling from a finite population with known population totals in each response category maximum likelihood estimation is developed and compared with two pseudo likelihood approaches the relative efficiencies of the methods are explored in the special case of estimating the parameters of the proportional odds model for ordinal responses for such applications the method hsieh manski mcfadden 1985 call conditional maximum likelihood is shown to be essentially as efficient as maximum likelihood the latter is considerably more difficult to implement in contrast the use of a weighted estimate of the prospective likelihood can lead to a substantial loss of efficiency

a psudolikelihood approach to analysis of nested case control studies in nested case control studies the controls are sampled from the risk set at the failure times of the cases the analytical basis for such studies has been limited to semiparametric estimators under proportional hazard models in this paper it is observed that conditional inclusion probabilities of ever being included in the nested case control study can be obtained where conditioning is on the information needed to carry out a nested case control study the inclusion probabilities are used in pseudolikelihoods by weighting the individual log likelihood contributions by their inverse this makes it possible to fit parametric regression models also a new semiparametric estimator is obtained under the proportional hazard model the methods are illustrated by simulation experiments and by application to a dataset

estimation of excess risk from case control data using aalen s linear regression model we introduce methods for statistical inference in aalen s non parametric linear regression model of disease incidence aalen 1989 statistics in medicine 8 907 925 from nested case control data these methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history the methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case control samples from the colorado plateau uranium miners cohort language en

noncommutative geometry for symmetric non self adjoint operators abstract we introduce the notion of a pre spectral triple which is a generalisation of a spectral triple a h d where d is no longer required to be self adjoint but closed and symmetric despite having weaker assumptions pre spectral triples allow us to introduce noncompact noncommutative geometry with boundary in particular we derive the hochschild character theorem in this setting we give a detailed study of dirac operators with dirichlet boundary conditions on domains in r d d 2

conservative upwind difference schemes for compressible flows of a real gas in a recent paper 1 numerical schemes based on a conservative linearisation arepresented for the euler equations governing compressible flows of an ideal gas and the subsequent study of these schemes establishes relationships between them through the use of a source term in this paper we seek to extend these ideas to encompass compressible flows of real gases where the equation of state allows for nonideal gases

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

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

fitting logistic models under case control or choice based sampling on compare deux approches dans le cas important de l ajustement des modeles de regression logistique

testing goodness of fit for the proportional hazards model based on nested case control data nested case control sampling is a popular design for large epidemiological cohort studies due to its cost effectiveness a number of methods have been developed for the estimation of the proportional hazards model with nested case control data however the evaluation of modeling assumption is less attended in this paper we propose a class of goodness of fit test statistics for testing the proportional hazards assumption based on nested case control data the test statistics are constructed based on asymptotically mean zero processes derived from samuelsen s maximum pseudo likelihood estimation method in addition we develop an innovative resampling scheme to approximate the asymptotic distribution of the test statistics while accounting for the dependent sampling scheme of nested case control design numerical studies are conducted to evaluate the performance of our proposed approach and an application to the wilms tumor study is given to illustrate the methodology

nonparametric estimation of relative mortality from nested case control studies andersen et al 1985 biometrics 41 921 932 gave an estimator of the cumulative relative mortality comparing rates of death in an epidemiologic cohort to an external population as a function of time when covariate information is available on all cohort members we present an analogous estimator when covariate information is known only on a nested case control sample counting process techniques are used to show that this estimator is almost unbiased and an estimator of its variance is derived estimators of the relative mortality function using kernel smoothing methods and the average relative mortality over grouped time intervals are also presented the methods are illustrated by comparing rates of lung cancer mortality in a cohort of montana smelter workers to that in the united states population

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

conservative upwind difference schemes for the euler equations abstract in a recent paper 1 a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed in particular it is established that the schemes are related through the use of a source term in this paper this technique is applied to the euler equations and further analysis suggests a new formulation of an existing scheme having the same key properties

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

fitting logistic regression models in stratified case control studies summary methods are developed for fitting logistic models to data in which cases and or controls are sampled from the available cases and controls within population strata particular attention is paid to models in which stratum differences are modelled as well as the effects of the different risk factors experienced by individuals within strata maximum likelihood estimation is developed for discrete explanatory variables and is compared with the method of fears and brown 1986 biometrics 42 955 960 and breslow and cain 1988 biometrika 75 11 20 in which the prospective logistic model is fitted with a fixed offset an example is explored in which maximum likelihood estimation proves to be substantially more efficient than the fears brown method and the modelling of the stratum effects leads to much more efficient estimates of regression coefficients for the remaining variables

weight calibration to improve the efficiency of pure risk estimates from case control samples nested in a cohort cohort studies provide information on relative hazards and pure risks of disease for rare outcomes large cohorts are needed to have sufficient numbers of events making it costly to obtain covariate information on all cohort members we focus on nested case control designs that are used to estimate relative hazard in the cox regression model in 1997 langholz and borgan showed that pure risk can also be estimated from nested case control data however these approaches do not take advantage of some covariates that may be available on all cohort members researchers have used weight calibration to increase the efficiency of relative hazard estimates from case cohort studies and nested cased control studies our objective is to extend weight calibration approaches to nested case control designs to improve precision of estimates of relative hazards and pure risks we show that calibrating sample weights additionally against follow up times multiplied by relative hazards during the risk projection period improves estimates of pure risk efficiency improvements for relative hazards for variables that are available on the entire cohort also contribute to improved efficiency for pure risks we develop explicit variance formulas for the weight calibrated estimates simulations show how much precision is improved by calibration and confirm the validity of inference based on asymptotic normality examples are provided using data from the american association of retired persons diet and health cohort study

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

cox regression in nested case control studies with auxiliary covariates nested case control ncc design is a popular sampling method in large epidemiological studies for its cost effectiveness to investigate the temporal relationship of diseases with environmental exposures or biological precursors thomas maximum partial likelihood estimator is commonly used to estimate the regression parameters in cox s model for ncc data in this article we consider a situation in which failure censoring information and some crude covariates are available for the entire cohort in addition to ncc data and propose an improved estimator that is asymptotically more efficient than thomas estimator we adopt a projection approach that heretofore has only been employed in situations of random validation sampling and show that it can be well adapted to ncc designs where the sampling scheme is a dynamic process and is not independent for controls under certain conditions consistency and asymptotic normality of the proposed estimator are established and a consistent variance estimator is also developed furthermore a simplified approximate estimator is proposed when the disease is rare extensive simulations are conducted to evaluate the finite sample performance of our proposed estimators and to compare the efficiency with thomas estimator and other competing estimators moreover sensitivity analyses are conducted to demonstrate the behavior of the proposed estimator when model assumptions are violated and we find that the biases are reasonably small in realistic situations we further demonstrate the proposed method with data from studies on wilms tumor

additive hazards regression for case cohort studies summary the case cohort design is a common means of reducing cost in large epidemiological cohort studies under this design covariates are measured only on the cases and a subcohort randomly selected from the entire cohort in this paper we demonstrate how to use the case cohort data to estimate the regression parameter of the additive hazards model which specifies that the conditional hazard function given a set of covariates is the sum of an arbitrary baseline hazard function and a regression function of the covariates the proposed estimator is shown to be consistent and asymptotically normal with an easily estimated variance the subcohort may be selected by independent bernoulli sampling with arbitrary selection probabilities or by stratified simple random sampling the efficiencies of various sampling schemes are investigated both analytically and by simulation a real example is provided