semiparametric mixed effects models for clustered failure time data the cox proportional hazards model with a random effect has been proposed for the analysis of data which consist of a large number of small clusters of correlated failure time observations the class of linear transformation models provides many useful alternatives to the cox model for analyzing univariate failure time data in this article we generalize these models by incorporating random effects which generate the dependence among the failure times within the cluster to handle correlated data inference and prediction procedures for such random effects models are proposed they are relatively simple compared with the methods based on the nonparametric maximum likelihood estimators for the cox frailty model in the literature our proposals are illustrated with a data set from a well known eye study extensive numerical studies are conducted to evaluate various robustness properties of the new procedures

symplectic integrators for index one constraints we show that symplectic runge kutta methods provide effective symplectic integrators for hamiltonian systems with index one constraints these include the hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities such as those arising in sub riemannian geometry and control theory

geometric description of vakonomic and nonholonomic dynamics comparison of solutions we treat the vakonomic dynamics with general constraints within a new geometric framework which can be useful in the study of optimal control problems we compare our formulation with the one of vershik and gershkovich in the case of linear constraints we show how nonholonomic mechanics also admits a new geometrical description which allows us to develop an algorithm of comparison between the solutions of both dynamics examples illustrating the theory are treated

random effects cox models a poisson modelling approach summary we propose a poisson modelling approach to nested random effects cox proportional hazards models an important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects the orthodox best linear unbiased predictor approach to random effects poisson modelling techniques enables us to justify appropriate consistency and optimality the explicit expressions for the random effects given by our approach facilitate incorporation of a relatively large number of random effects the use of the proposed methods is illustrated through the reanalysis of data from a large scale cohort study of particulate air pollution and mortality previously reported by pope et al 1995

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

discrete vakonomic mechanics discretizations of vakonomic mechanics are developed by using the methodology of variational integrators the resulting algorithms are symplectic in some sense that we will explain and preserve the momentum map associated with a lie group of symmetries a specific example illustrating the theory is tested numerically

a bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model when multicentre clinical trial data are analysed it has become more and more popular to look for possible heterogeneity in outcome between centres however beyond the investigation of such heterogeneity it is also interesting to consider heterogeneity in treatment effect over centres for time to event outcomes this may be investigated by including a random centre effect and a random treatment by centre interaction in a cox proportional hazards model assuming independence between the random effects we propose a bayesian approach to fit our proposed model the parameters of interest are the variance components sigma 0 2 and a of these random effects which can be interpreted as a measure of centre and treatment effect over centres heterogeneity of the hazard these variance components are estimated from their marginal posterior density after integrating out the fixed treatment effect and the random effects as this integration cannot be performed analytically the marginal posterior density is approximated using the laplace integration technique statistical inference is then based on the characteristics of the posterior marginal density such as the mode and the standard deviation we demonstrate the proposed technique using data from a pooled database of seven eortc bladder cancer clinical trials substantial centre and treatment effect over centres heterogeneity in disease free interval was found copyright c 2005 john wiley sons ltd

lyapunov functions for the global stability of competing predators in this paper we study the global stability of an exploitative competition system between two predator species and a single prey species a sufficient condition for the global stability is given which is applicable to most of three dimensional competing predators system then we restrict our attentions to the case in which the prey is of logistic growth and predators have holling s type ii functional responses

optimal control of underactuated mechanical systems a geometric approach in this paper we consider a geometric formalism for optimal control of underactuated mechanical systems our techniques are an adaptation of the classical skinner and rusk approach for the case of lagrangian dynamics with higher order constraints we study a regular case where it is possible to establish a symplectic framework and as a consequence to obtain a unique vector field determining the dynamics of the optimal control problem these developments will allow us to develop a new class of geometric integrators based on discrete variational calculus

reml estimation for survival models with frailty a method of estimation for generalised mixed models is applied to the estimation of regression parameters in proportional hazards models for failure times when there are repeated observations of failure on each subject the subject effect is incorporated into the model as a random frailty term best linear unbiased predictors are used as an initial step in the computation of maximum likelihood and residual maximum likelihood estimates

variance component models with binary response interviewer variability summary interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non normal family the maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire this raises some interesting questions about the use of unbalanced ano va methods with these data two interviewers asking the same question of the same respondent can obtain different responses such interviewer effects create problems in the design and analysis of survey questionnaires collins 1980 gives a review of these problems together with a variety of partial remedies these include pilot studies and careful design to eliminate difficulties with wording of questions and instructions on the questionnaires in spite of these precautions interviewer effects remain questionnaire items are usually categorical and occasionally binary but usually for analysis the questionnaire item is reduced to a binary response it is the variability of the population of interviewers that is of interest and not just the individual interviewers thus this variability is best modelled as a random effect rather than a fixed effect the number of interviews completed by each interviewer varies so that the design is unbalanced thus we have an unbalanced variance component model with a categorical or binary response the intraclass correlation the ratio of the interviewer variance to the sum of all variances in the model is of great interest as a measure of interviewer variability in estimating the variance components the categorical or binary nature of the response is usually ignored and the analysis carried out using analysis of variance this is not maximum likelihood but analysis of variance does have some desirable properties when the error variables are non normal the rule of thumb generally applied is that the analysis of variance is reasonably accurate as long as the proportions in each of the categories of the response are between 0 1 and 0 9 scheffe 1959 p 343 discusses the effects of non normality in a one way balanced model very little theoretical work has been

reml and ml estimation for clustered grouped survival data clustered grouped survival data arise naturally in clinical medicine and biological research for example in a randomized clinical trial the variable of interest is the time to occurrence of a certain event with or without a new treatment and the data are collected from possibly correlated subjects from independent clusters however it is sometimes impossible or too expensive to monitor the experimental subjects continuously the subjects are examined regularly and the continuous survival data are thus grouped into a discrete time scale with such a design researchers are mainly interested in the effectiveness of the new treatment as well as the correlation among subjects from the same cluster namely the intracluster correlation this paper suggests a random effects approach to the estimation of the regression parameter with various choices of regression model and also the dependence parameter which characterizes the intracluster correlation time dependent covariates can be accommodated in the proposed model and the estimation procedure will not be further complicated with large cluster sizes the proposed method is applied to the data from the diabetic retinopathy study the objective of which is to evaluate the effectiveness of laser photocoagulation in delaying or preventing the onset of blindness in the left and right eyes of individuals with diabetes associated retinopathy the intracluster correlation using a grouped proportional hazards regression model can be estimated and the relationship between the regression parameter estimates based on the random effects approach and the marginal approach using a dynamic logistic regression model are discussed results from a simulation study of the proposed method are also presented

generalized gamma frailty model in this article we present a frailty model using the generalized gamma distribution as the frailty distribution it is a power generalization of the popular gamma frailty model it also includes other frailty models such as the lognormal and weibull frailty models as special cases the flexibility of this frailty distribution makes it possible to detect a complex frailty distribution structure which may otherwise be missed due to the intractable integrals in the likelihood function and its derivatives we propose to approximate the integrals either by monte carlo simulation or by a quadrature method and then determine the maximum likelihood estimates of the parameters in the model we explore the properties of the proposed frailty model and the computation method through a simulation study the study shows that the proposed model can potentially reduce errors in the estimation and that it provides a viable alternative for correlated data the merits of proposed model are demonstrated in analysing the effects of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients based on the data set in danahy et al sustained hemodynamic and antianginal effect of high dose oral isosorbide dinitrate circulation 1977 55 381 387

posterior likelihood methods for multivariate survival data this article deals with the semiparametric analysis of multivariate survival data with random block group effects survival times within the same group are correlated as a consequence of a frailty random block effect the standard approaches assume either a parametric or a completely unknown baseline hazard function this paper considers an intermediate solution that is a nonparametric function that is reasonably smooth this is accomplished by a bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard the posterior likelihood based on data as well as the prior process is similar to the discretized penalized likelihood for the frailty model the methodology is exemplified with the recurrent kidney infections data of mcgilchrist and aisbett 1991 biometrics 47 461 466 in which the times to infections within the same patients are expected to be correlated the reanalysis of the data has shown that the estimates of the parameters of interest and the associated standard errors depend on the prior knowledge about the smoothness of the baseline hazard

robust estimation in generalized linear mixed models generalized linear mixed models glmms are widely used to analyse non normal response data with extra variation but non robust estimators are still routinely used we propose robust methods for maximum quasi likelihood and residual maximum quasi likelihood estimation to limit the influence of outlying observations in glmms the estimation procedure parallels the development of robust estimation methods in linear mixed models but with adjustments in the dependent variable and the variance component the methods proposed are applied to three data sets and a comparison is made with the nonparametric maximum likelihood approach when applied to a set of epileptic seizure data the methods proposed have the desired effect of limiting the influence of outlying observations on the parameter estimates simulation shows that one of the residual maximum quasi likelihood proposals has a smaller bias than those of the other estimation methods we further discuss the equivalence of two glmm formulations when the response variable follows an exponential family their extensions to robust glmms and their comparative advantages in modelling are described some possible modifications of the robust glmm estimation methods are given to provide further flexibility for applying the method

semiparametric bayesian analysis of survival data abstract this review article investigates the potential of bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function the nonparametric part of every model is assumed to be a realization of a stochastic process the parametric part which may include a regression parameter or a parameter quantifying the heterogeneity of a population is assumed to have a prior distribution with possibly unknown hyperparameters careful applications of some recently popular computational tools including sampling based algorithms are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures the methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies here we focus on univariate survival data in the presence of fixed and time dependent covariates multiple event time data for repeated nonfatal events

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

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

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

global dynamics of a mathematical model of competition in the chemostat general response functions and differential death rates a model of exploitative competition of n species in a chemostat for a single essential nonreproducing growth limiting resource is considered s b hsu siam j appl math 34 1978 pp 760 763 applies lasalle s extension theorem of lyapunov stability theory to study the asymptotic behavior of solutions in the special case that the response functions are modeled by michaelis menten dynamics g j butler and g s k wolkowicz siam j appl math 45 1985 pp 138 151 on the other hand allow more general response functions including monotone and nonmonotone functions but their analysis requires the assumption that the death rates of all the species are negligible in comparison with the washout rate and hence can be ignored by means of lyapunov stability theory the global dynamics of the model for a large class of response functions are studied including both monotone and nonmonotone functions though it is not as general as the class studied by butler and wolkowicz and the results in

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

geometric integrators and nonholonomic mechanics a geometric derivation of nonholonomic integrators is developed it is based in the classical technique of generating functions adapted to the special features of nonholonomic systems the theoretical methodology and the integrators obtained are different from those obtained in cortes and martinez nonholonomic integrators nonlinearity 14 1365 1392 2001 in the case of mechanical systems with linear constraints a family of geometric integrators preserving the nonholonomic constraints is given

hamiltonian dynamics and constrained variational calculus continuous and discrete settings the aim of this paper is to study the relationship between hamiltonian dynamics and constrained variational calculus we describe both using the notion of lagrangian submanifolds of convenient symplectic manifolds and using the so called tulczyjew triples the results are also extended to the case of discrete dynamics and nonholonomic mechanics interesting applications to the geometrical integration of hamiltonian systems are obtained

functional inference in frailty measurement error models for clustered survival data using the simex approach we consider frailty models for clustered survival data in the presence of measurement errors in covariates we first show that when the measurement error is accounted for in a full likelihood analysis but the distribution of the unobserved covariate is misspecified the maximum likelihood estimators are asymptotically biased especially for the variance component whose bias can be substantial we then discuss making inference using functional estimation via the simex method where no distribution of the unobserved error prone covariate is assumed the simex method is easy to implement by repeatedly fitting standard frailty models we study the asymptotic properties of the simex estimates and show that they are consistent and asymptotically normal in simulation studies we compare the simex method and the likelihood method in terms of efficiency and robustness we also propose a simex score test for the variance component to test for the within cluster correlation and evaluate its performance through simu

investigating trial and treatment heterogeneity in an individual patient data meta analysis of survival data by means of the penalized maximum likelihood approach in a meta analysis combining survival data from different clinical trials an important issue is the possible heterogeneity between trials such intertrial variation can not only be explained by heterogeneity of treatment effects across trials but also by heterogeneity of their baseline risk in addition one might examine the relationship between magnitude of the treatment effect and the underlying risk of the patients in the different trials such a scenario can be accounted for by using additive random effects in the cox model with a random trial effect and a random treatment by trial interaction we propose to use this kind of model with a general correlation structure for the random effects and to estimate parameters and hazard function using a semi parametric penalized marginal likelihood method maximum penalized likelihood estimators this approach gives smoothed estimates of the hazard function which represents incidence in epidemiology the idea for the approach in this paper comes from the study of heterogeneity in a large meta analysis of randomized trials in patients with head and neck cancers meta analysis of chemotherapy in head and neck cancers and the effect of adding chemotherapy to locoregional treatment the simulation study and the application demonstrate that the proposed approach yields satisfactory results and they illustrate the need to use a flexible variance covariance structure for the random effects

hierarchical likelihood approach for frailty models systematic likelihood inference for frailty models is possible using lee nelder s 1996 hierarchical likelihood we develop an inferential method for frailty models via hierarchical likelihood which gives a simple unified framework and a numerically efficient algorithm simulations and practical examples are presented to illustrate the new method

modeling spatial survival data using semiparametric frailty models we propose a new class of semiparametric frailty models for spatially correlated survival data specifically we extend the ordinary frailty models by allowing random effects accommodating spatial correlations to enter into the baseline hazard function multiplicatively we prove identifiability of the models and give sufficient regularity conditions we propose drawing inference based on a marginal rank likelihood no parametric forms of the baseline hazard need to be assumed in this semiparametric approach monte carlo simulations and the laplace approach are used to tackle the intractable integral in the likelihood function different spatial covariance structures are explored in simulations and the proposed methods are applied to the east boston asthma study to detect prognostic factors leading to childhood asthma

consistent estimators in generalized linear mixed models abstract a simple method based on simulated moments is proposed for estimating the fixed effects and variance components in a generalized linear mixed model glmm it is shown that the method is not only computationally attractive but also leads to consistent estimators on the other hand simulation shows that the method can be quite inefficient

minimum hellinger distance estimation for k component poisson mixture with random effects the k component poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations however the residual maximum likelihood estimation reml of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination in the literature the minimum hellinger distance mhd estimation has been investigated to obtain robust estimation for finite poisson mixtures this article aims to develop a robust mhd estimation approach for k component poisson mixtures with normally distributed random effects by applying the gaussian quadrature technique to approximate the integrals involved in the marginal distribution the marginal probability function of the k component poisson mixture with random effects can be approximated by the summation of a set of finite poisson mixtures simulation study shows that the mhd estimates perform satisfactorily for data without outlying observation s and outperform the reml estimates when data are contaminated application to a data set of recurrent urinary tract infections uti with random institution effects demonstrates the practical use of the robust mhd estimation method

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

comments on the presymplectic formalism and the theory of regular lagrangians with constraints the lagrangian formalism for systems with constraints is developed using a singular lagrangian defined in the extended tangent bundle t q r the dynamics defined by the new extended lagrangian that incorporates the constraints is studied using the formalism of the presymplectic geometry a comparative study with other geometric approaches is presented

fitting conditional survival models to meta analytic data by using a transformation toward mixed effects models frailty models are widely used to model clustered survival data classical ways to fit frailty models are likelihood based we propose an alternative approach in which the original problem of fitting a frailty model is reformulated into the problem of fitting a linear mixed model using model transformation we show that the transformation idea also works for multivariate proportional odds models and for multivariate additive risks models it therefore bridges segregated methodologies as it provides a general way to fit conditional models for multivariate survival data by using mixed models methodology to study the specific features of the proposed method we focus on frailty models based on a simulation study we show that the proposed method provides a good and simple alternative for fitting frailty models for data sets with a sufficiently large number of clusters and moderate to large sample sizes within covariate level subgroups in the clusters the proposed method is applied to data from 27 randomized trials in advanced colorectal cancer which are available through the meta analysis group in cancer

case control survival analysis with a general semiparametric shared frailty model a pseudo full likelihood approach in this work we deal with correlated failure time age at onset data arising from population based case control studies where case and control probands are selected by population based sampling and an array of risk factor measures is collected for both cases and controls and their relatives parameters of interest are effects of risk factors on the failure time hazard function and within family dependencies among failure times after adjusting for the risk factors due to the retrospective sampling scheme large sample theory for existing methods has not been established we develop a novel technique for estimating the parameters of interest under a general semiparametric shared frailty model we also present a simple easily computed and non iterative nonparametric estimator for the cumulative baseline hazard function we provide rigorous large sample theory for the proposed method we also present simulation results and a real data example for illustrating the utility of the proposed method

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

multilevel models for survival analysis with random effects a method for modeling survival data with multilevel clustering is described the cox partial likelihood is incorporated into the generalized linear mixed model glmm methodology parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction blup at the initial step of estimation and is extended to obtain residual maximum likelihood reml estimators of the variance component estimating equations for a three level hierarchical survival model are developed in detail and such a model is applied to analyze a set of chronic granulomatous disease cgd data on recurrent infections as an illustration with both hospital and patient effects being considered as random only the latter gives a significant contribution a simulation study is carried out to evaluate the performance of the reml estimators further extension of the estimation procedure to models with an arbitrary number of levels is also discussed

global stability of a model for competing predators an extension of the ardito ricciardi lyapunov function global stability of a model for competing predators an extension of the ardito ricciardi lyapunov function

higher order discrete variational problems with constraints an interesting family of geometric integrators for lagrangian systems can be defined using discretizations of the hamilton s principle of critical action this family of geometric integrators is called variational integrators in this paper we derive new variational integrators for higher order lagrangian mechanical system subjected to higher order constraints from the discretization of the variational principles we show that our methods are automatically symplectic and in consequence with a very good energy behavior additionally the symmetries of the discrete lagrangian imply that momentum is conserved by the integrator moreover we extend our construction to variational integrators where the lagrangian is explicitly time dependent finally some motivating applications of higher order problems are considered in particular optimal control problems for explicitly time dependent underactuated systems and an interpolation problem on riemannian manifolds

penalized partial likelihood for frailties and smoothing splines in time to first insemination models for dairy cows in many epidemiological studies time to event data are clustered and the physiological relationship between time dependent covariates and the log hazard is often not linear as assumed in the cox model introducing frailties in the cox model can account for the clustering of the data and smoothing splines can be used to describe nonlinear relations these two extensions of the cox model are introduced jointly and it is shown how penalized partial likelihood techniques can be used to fit the extended model we demonstrate the need for such a model to study the relation between the physiological covariates milk ureum and protein concentration and the log hazard of first insemination in dairy cows with the farms as clusters

permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study when analysing multicentre data it may be of interest to test whether the distribution of the endpoint varies among centres in a mixed effect model testing for such a centre effect consists in testing to zero a random centre effect variance component it has been shown that the usual asymptotic 2 distribution of the likelihood ratio and score statistics under the null does not necessarily hold in the case of censored data mixed effects cox models have been used to account for random effects but few works have concentrated on testing to zero the variance component of the random effects we propose a permutation test using random permutation of the cluster indices to test for a centre effect in multilevel censored data results from a simulation study indicate that the permutation tests have correct type i error rates contrary to standard likelihood ratio tests and are more powerful the proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients copyright 2014 john wiley sons ltd

robust estimation of variance components outliers may occur with respect to any of the random components in the mixed linear model a procedure for limiting the influence of these outliers on the estimates of the model parameters is described given the variances or estimates of them the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects as appropriate and winsorized the robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of huber s proposal 2 a numerical example illustrates the use of the methodology both as a diagnostic and as an estimation tool

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

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

penalized likelihood in cox regression in a cox regression model instability of the estimated regression coefficients can be reduced by maximizing a penalized partial log likelihood where a penalty function of the regression coefficients is substracted from the partial log likelihood in this paper we choose the optimal weight of the penalty function by maximizing the predictive value of the model as measured by the crossvalidated partial log likelihood our methods are illustrated by a study of ovarian cancer survival and by a study of centre effects in kidney graft survival

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

prospective survival analysis with a general semiparametric shared frailty model a pseudo full likelihood approach summary we provide a simple estimation procedure for a general frailty model for the analysis of prospective correlated failure times the large sample properties of the proposed estimators of both the regression coefficient vector and the dependence parameter are described and consistent variance estimators are given a brief outline of the proofs is given in a simulation study under the widely used gamma frailty model our proposed approach was found to have essentially the same efficiency as the em based maximum likelihood approach considered by other authors with negligible difference between the standard errors of the two estimators however the proposed approach provides a framework capable of handling general frailty distributions with finite moments and yields an explicit consistent variance estimator

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

group sequential analysis incorporating covariate information abstract in this article we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is fitted to accumulating data and provide a unified theory that explains the independent increments structure commonly seen in group sequential test statistics our theory covers normal linear models including the case of correlated observations and asymptotic results extend to generalized linear models and the proportional hazards regression model for survival data the asymptotic results are derived using standard methods for the nonsequential case and they hold as long as these nonsequential techniques are applicable at each individual analysis in all cases the joint distribution of the sequence of parameter estimates has the same form exactly or asymptotically as that of the sequence of means of an increasing number of independent identically distributed normal variables thus our results provide the formal basis for extending the scope of s

mechanical integrators derived from a discrete variational principle many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion in this paper we present a procedure to construct time stepping algorithms that approximate the flow of continuous odes for mechanical systems by discretizing hamilton s principle rather than the equations of motion the discrete equations share similarities to the continuous equations by preserving invariants including the symplectic form and the momentum map we first present a formulation of discrete mechanics along with a discrete variational principle we then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of noether s theorem we then use the discrete mechanics formulation to develop a procedure for constructing symplectic momentum mechanical integrators for lagrangian systems with holonomic constraints we apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators

the geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems the vakonomic bracket a vakonomic mechanical system can be alternatively described by an extended lagrangian using the lagrange multipliers as new variables since this extended lagrangian is singular the constraint algorithm can be applied and a dirac bracket giving the evolution of the observables can be constructed

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

mixture cure model with random effects for clustered interval censored survival data the mixture cure model is an effective tool for analysis of survival data with a cure fraction this approach integrates the logistic regression model for the proportion of cured subjects and the survival model either the cox proportional hazards or accelerated failure time model for uncured subjects methods based on the mixture cure model have been extensively investigated in the literature for data with exact failure censoring times in this paper we propose a mixture cure modeling procedure for analyzing clustered and interval censored survival time data by incorporating random effects in both the logistic regression and ph regression components under the generalized linear mixed model framework we develop the reml estimation for the parameters as well as an iterative algorithm for estimation of the survival function for interval censored data the estimation procedure is implemented via an em algorithm a simulation study is conducted to evaluate the performance of the proposed method in various practical situations to demonstrate its usefulness we apply the proposed method to analyze the interval censored relapse time data from a smoking cessation study whose subjects were recruited from 51 zip code regions in the southeastern corner of minnesota