models for longitudinal data with random effects and ar 1 errors abstract for longitudinal data on several individuals linear models that contain both random effects across individuals and autocorrelation in the within individual errors are studied a score test for autocorrelation in the within individual errors for the conditional independence random effects model is first developed an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and autoregressive ar 1 errors is then derived empirical bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with ar 1 errors model are also considered a numerical example is presented to illustrate these methods

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

exponential synchronizationlike criterion for state dependent impulsive dynamical networks this paper focuses on the problem of the exponential synchronizationlike criteria for state dependent impulsive dynamical networks sidns two types of sufficient conditions which are applied to ensure every solution intersecting each impulsive surface exactly once are derived for each type of collision conditions combining with comparison principle and inequality techniques some sufficient conditions are obtained to ensure local exponential synchronizationlike for sidn moreover a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed finally an example is given to demonstrate the effectiveness of our results

the effect of network topology on the stability of discrete state models of genetic control boolean networks have been proposed as potentially useful models for genetic control an important aspect of these networks is the stability of their dynamics in response to small perturbations previous approaches to stability have assumed uncorrelated random network structure real gene networks typically have nontrivial topology significantly different from the random network paradigm to address such situations we present a general method for determining the stability of large boolean networks of any specified network topology and predicting their steady state behavior in response to small perturbations additionally we generalize to the case where individual genes have a distribution of expression biases and we consider a nonsynchronous update as well as extension of our method to non boolean models in which there are more than two possible gene states we find that stability is governed by the maximum eigenvalue of a modified adjacency matrix and we test this result by comparison with numerical simulations we also discuss the possible application of our work to experimentally inferred gene networks

mixed effects nonlinear regression for unbalanced repeated measures repeated measures data such as clinical pharmacokinetic data growth data and dose response data are often inherently nonlinear with respect to a given response function and are frequently incomplete and or unbalanced nonlinear random effects models together with a variety of estimation procedures have been proposed for the analysis of such data this paper is concerned with a straightforward procedure for estimating and comparing the parameters of a generalized mixed effects nonlinear regression model the asymptotic properties of the proposed estimators are given and large sample tests of hypothesis provided the results are applied to in vitro data on the water transport kinetics of hemodialyzers used in the treatment of patients with chronic renal failure

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

non linear models for the analysis of longitudinal data given the importance of longitudinal studies in biomedical research it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data a great deal of attention has also been given to non linear models for repeated measurements particularly in the field of pharmacokinetics in this article a brief overview of non linear models for the analysis of repeated measures is given particular emphasis is placed on mixed effects non linear models and on various estimation procedures proposed for such models several of these estimation procedures are compared via a simulation study in addition simulation is used to investigate the effects of model misspecification particularly with respect to one s choice of random effects a relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

laplace s approximation for nonlinear mixed models summary an approximation to laplace s method for integrals is applied to marginal distributions of data arising from models in which both fixed and random effects enter nonlinearly the approach provides alternative derivations of some recent algorithms for fitting such models and it has direct ties with gaussian restricted maximum likelihood and the accompanying mixed model equations

bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters i a use of bootstrap standard error in population pharmacokinetic studies one of the main objectives is to estimate population pharmacokinetic parameters specifying the population distributions of pharmacokinetic parameters confidence intervals for population pharmacokinetic parameters are generally estimated by assuming the asymptotic normality which is a large sample property that is a property which holds for the cases where sample sizes are large enough in actual clinical trials however sample sizes are limited and not so large in general likelihood functions in population pharmacokinetic modelling include a multiple integral and are quite complicated we hence suspect that the sample sizes of actual trials are often not large enough for assuming the asymptotic normality and that the asymptotic confidence intervals underestimate the uncertainties of the estimates of population pharmacokinetic parameters as an alternative to the asymptotic normality approach we can employ a bootstrap approach this paper proposes a bootstrap standard error approach for constructing confidence intervals for population pharmacokinetic parameters comparisons between the asymptotic and bootstrap confidence intervals are made through applications to a simulated data set and an actual phase i trial

estimation in covariance components models abstract estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes the estimation of fixed and random effects when the variances and covariances are known is presented in bayesian terms point estimates of the unknown variances and covariances are computed using the em algorithm for maximum likelihood estimation from incomplete data the techniques are illustrated with data on law schools field mice and professional football teams

shape invariant modeling of circadian rhythms with random effects and smoothing spline anova decompositions medical studies often collect physiological and or psychological measurements over time from multiple subjects to study dynamics such as circadian rhythms under the assumption that the expected response functions of all subjects are the same after shift and scale transformations shape invariant models have been applied to analyze this kind of data the shift and scale parameters provide efficient and interpretable data summaries while the common shape function is usually modeled nonparametrically to provide flexibility however due to the deterministic nature of the shift and scale parameters potential correlations within a subject are ignored furthermore the shape of the common function may depend on other factors such as disease in this article we propose shape invariant mixed effects models a second stage model with fixed and random effects is used to model individual shift and scale parameters a second stage smoothing spline anova model is used to study potential covariate effects on the common shape function we apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol a hormone that is affected by stress we find that patients with cushing s syndrome lost circadian rhythms and their 24 hour means were elevated to very high levels patients with major depression had the same circadian shape and phases as normal subjects however their 24 hour mean levels were elevated and amplitudes were dampened for some patients

determinants torsion and strings we apply the results of bf1 bf2 on determinants of dirac operators to string theory for the bosonic string we recover the holomorphic factorization of belavin and knizhik witten s global anomaly formula is used to give sufficient conditions for anomaly cancellation in the heterotic string for arbitrary background spacetimes to prove the latter result we develop certain torsion invariants related to characteristic classes of vector bundles and to index theory

a note on the use of laplace s approximation for nonlinear mixed effects models the asymptotic properties of estimates obtained using laplace s approximation for nonlinear mixed effects models are investigated unlike the restricted maximum likelihood approach e g wolfinger 1993 here the laplace approximation is applied only to the random effects of the integrated likelihood this results in approximate maximum likelihood estimation the resulting estimates are shown to be consistent with the rate of convergence depending on both the number of individuals and the number of observations per individual conditions under which the leading term laplace approximation should be avoided are discussed

synchronization of dynamical hypernetworks dimensionality reduction through simultaneous block diagonalization of matrices we present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems we are able to reduce the dimensionality of the problem by using simultaneous block diagonalization of matrices we obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower dimensional problems and test the predictions of our low dimensional analysis through numerical simulations under certain conditions this technique may yield a substantial reduction of the dimensionality of the problem for example for a class of dynamical hypernetworks analyzed in the paper we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2 we apply our reduction technique to a number of different examples including the class of undirected unweighted hypermotifs with 3 nodes

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

small area inference for binary variables in the national health interview survey abstract the national health interview survey is designed to produce precise estimates of finite population parameters for the entire united states but not for small geographical areas or subpopulations our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months to include all sources of variation in the model we carry out a bayesian hierarchical analysis for the desired finite population quantities first for each cluster county a separate logistic regression relates the individual s probability of a doctor visit to his or her characteristics second a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level we describe the numerical methods needed to obtain the desired posterior moments then we compare estimates produced using the exact numerical method with approximations finally we compare the hierarchical bayes estimates to empirical bayes estimates and to stand

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

a general approach for two stage analysis of multilevel clustered non gaussian data in this article we propose a two stage approach to modeling multilevel clustered non gaussian data with sufficiently large numbers of continuous measures per cluster such data are common in biological and medical studies utilizing monitoring or image processing equipment we consider a general class of hierarchical models that generalizes the model in the global two stage gts method for nonlinear mixed effects models by using any square root n consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model and by extending the stage 2 model to accommodate random effects from multiple levels of clustering the second stage model is a standard linear mixed effects model with normal random effects but the cluster specific distributions conditional on random effects can be non gaussian this methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest for estimation of the population parameters we propose a conditional restricted maximum likelihood creml approach and establish the asymptotic properties of the creml estimators the proposed general approach is illustrated using quartiles as cluster specific parameters estimated in the first stage and applied to the data example from a collagen fibril development study we demonstrate using simulations that in samples with small numbers of independent clusters the creml estimators may perform better than conditional maximum likelihood estimators which are a direct extension of the estimators from the gts method

nonlinear regression with variance components abstract the nonlinear model with variance components which combines a nonlinear model for the mean with additive random effects is applicable to split plot and nested experiments we propose two methods of estimation for the parameters of the nonlinear model for the mean 1 estimated generalized least squares egls and 2 maximum likelihood mle by the method of scoring using a generalization of klimko and nelson s theorem on strong consistency of least squares estimators it is possible to show that both the mle and the egls estimators are strongly consistent asymptotically normal and asymptotically efficient

a case study in exploratory functional data analysis geometrical features of the internal carotid artery this pilot study is a product of the aneurisk project a scientific program that aims at evaluating the role of vascular geometry and hemodynamics in the pathogenesis of cerebral aneurysms by means of functional data analyses we explore the aneurisk dataset to highlight the relations between the geometric features of the internal carotid artery expressed by its radius profile and centerline curvature and the aneurysm location after introducing a new similarity index for functional data we eliminate ancillary variability of vessel radius and curvature profiles through an iterative registration procedure we then reduce data dimension by means of functional principal components analysis last a quadratic discriminant analysis of functional principal components scores allows us to discriminate patients with aneurysms in different districts

hyperparameter estimation using stochastic approximation with application to population pharmacokinetics a stochastic approximation algorithm is proposed for recursive estimation of the hyperparameters characterizing in a population the probability density function of the parameters of a statistical model for a given population model defined by a parametric model of a biological process an error model and a class of densities on the set of the individual parameters this algorithm provides a sequence of estimates from a sequence of individuals observation vectors convergence conditions are verified for a class of population models including usual pharmacokinetic applications this method is implemented for estimation of pharmacokinetic population parameters from drug multiple dosing data its estimation capabilities are evaluated and compared to a classical method in population pharmacokinetics the first order method nonmem on simulated data

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

some simple methods for estimating intraindividual variability in nonlinear mixed effects models methods are proposed to improve both population and individual inference within the nonlinear random coefficient regression framework by incorporating possible heterogeneity in the intraindividual variance structure these methods extend existing variance function estimation techniques by pooling information across individuals the methods are appropriate when it is reasonable to assume that there exists a common intraindividual variance structure

the nonlinear mixed effects model with a smooth random effects density summary the fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood the density of the random effects is assumed to be smooth but is otherwise unrestricted the method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood standard algorithms are used for optimization empirical bayes estimates of random coefficients are obtained by computing posterior modes the method is applied to data from pharmacokinetics and properties of the method are investigated by application to simulated data

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

nonlinear component of variance models summary general aspects of nonlinearity in the context of component of variance models are discussed and two special topics are examined in detail firstly simple procedures both formal and informal are proposed for describing departures from normal theory linear models transformation models are shown to be a special case of a more general formulation and data on blood pressure are analyzed in illustration secondly an approximate likelihood is proposed and its accurate performance is examined numerically using examples of exponential regression and the analysis of several related 2 x 2 tables in the latter example the approximate score test has improved power over the mantelhaenszel test

fieller s theorem scheffe simultaneous confidence intervals and ratios of parameters of linear and nonlinear mixed effects models the issue of joint confidence region and simultaneous confidence interval estimation for ratios of the parameters of a nonlinear mixed effects model is addressed using a fieller s theorem approach the method presented is similarly applicable to linear mixed effects models in addition previous work on linear fixed effects models is demonstrated to be a special case of the present method the methodology is applied to the ratios of slopes in a study of gestational maturation of placental glucose transfer capacity in sheep

identification and accommodation of outliers in general hierarchical models summary by their nature hierarchical models involve a considerable number of structural and distributional assumptions for example normality and linearity are common assumptions considerations of robustness therefore suggest that some form of model elaboration is necessary however it is not clear how to achieve this in the already complex setting of hierarchical models whilst maintaining reasonable tractability in the analysis we provide a comprehensive account of the way in which methods based on the contaminated normal niodel can be applied to the general hierarchical model and investigate the influence of data on estimates of posterior distributions

accelerated degradation tests modeling and analysis high reliability systems generally require individual system components having extremely high reliability over long periods of time short product development times require reliability tests to be conducted with severe time constraints frequently few or no failures occur during such tests even with acceleration thus it is difficult to assess reliability with traditional life tests that record only failure times for some components degradation measures can be taken over time a relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure time distribution this article describes degradation reliability models that correspond to physical failure mechanisms we explain the connection between degradation reliability models and failure time reliability models acceleration is modeled by having an acceleration model that describes the effect that temperature or another accelerating variable has on

bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters ii a bootstrap modification of standard two stage sts method for phase i trial for population pharmacokinetics in phase i trials the standard two stage sts method is quite appealing especially to non statisticians because the method is theoretically and computationally simple the method however does not take into account the uncertainty in estimating individual specific parameters and gives biased estimates for population variances of pharmacokinetic parameters this is one of the main reasons why the sts method is not generally recommended this paper proposes a simple bootstrap modification of the sts method for estimating confidence intervals of population means and standard deviations of pharmacokinetic parameters in phase i trials the proposed approach adopts a bootstrap bias correction in estimating population variances of pharmacokinetic parameters applications are given to a simulated data set and an actual phase i trial to show how the proposed approach works in practice

autoregressive growth curves and kalman filtering the first part of this paper describes how a kalman filter can be used to construct maximum likelihood ml estimates of autoregressive ar and polynomial parameters in polynomial growth curves with ar 1 errors and irregularly spaced data the second part introduces a disturbed highest derivative polynomial dhdp as a model for growth curves this model does not depend on regression coefficients variances of the highest derivative disturbance and the observation error are estimated by ml using a kalman filter the estimated dhdp growth curve is obtained by optimally smoothing the output of the filter equally spaced data is not required the dhdp model and analysis are developed for an individual and extended to a population growth curve using data from many individuals with covariates

a deconvolution approach to source localization due to its low resolution the conventional beamformer cbf has generally been neglected in the recent literature on array processing and considerable attention devoted to the high resolution hr techniques applying a deconvolution approach to the output of the cbf the authors obtain a source localization procedure whose performances are comparable to those of the most efficient hr techniques the scheme moreover also furnishes estimates of the source powers and comprises a test that detects the number of sources present it can indeed be seen as a means to obtain maximum likelihood estimates mle when the cbf output is taken as the observed data

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

cluster and group synchronization in delay coupled networks we investigate the stability of synchronized states in delay coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics using a master stability approach we find that the master stability function shows a discrete rotational symmetry depending on the number of groups the coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum which helps to simplify the evaluation of the master stability function our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times multiple coupling functions but also with multiple kinds of local dynamics in the networks nodes we illustrate our results by calculating stability in the example of delay coupled semiconductor lasers and in a model for neuronal spiking dynamics

some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models nonlinear mixed effects models allow investigating individual differences in drug concentration profiles pharmacokinetics and responses pharmacogenetics focuses on the genetic component of this variability two tests often used to detect a gene effect on a pharmacokinetic parameter are 1 the wald test assessing whether estimates for the gene effect are significantly different from 0 and 2 the likelihood ratio test comparing models with and without the genetic effect because those asymptotic tests show inflated type i error on small sample size and or with unevenly distributed genotypes we develop two alternatives and evaluate them by means of a simulation study first we assess the performance of the permutation test using the wald and the likelihood ratio statistics second for the wald test we propose the use of the f distribution with four different values for the denominator degrees of freedom we also explore the influence of the estimation algorithm using both the first order conditional estimation with interaction linearization based algorithm and the stochastic approximation expectation maximization algorithm we apply these methods to the analysis of the pharmacogenetics of indinavir in hiv patients recruited in the cophar2 anrs 111 trial results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden one of the four f distribution based approaches provides a correct type i error estimate for the wald test and should be further investigated

evaluation by simulation of tests based on non linear mixed effects models in pharmacokinetic interaction and bioequivalence cross over trials we propose tests based on non linear mixed effects models nlmem in pharmacokinetic interaction and bioequivalence cross over trials comparing two treatments or two formulations to compare the logarithm of the area under the curve auc using these models two approaches are studied in the first one concentration data are analysed globally with and without the estimation of a treatment effect and in the second one they are analysed separately in each treatment group with the estimation of the individual parameters four tests for comparison of the logarithm auc between two treatment arms are studied a likelihood ratio test lrt a wald test and two tests parametric and non parametric comparing the individual empirical bayes eb estimates these tests are adapted to the case of equivalence except the lrt which does not have any simple extension we evaluate by simulation of the type i error and the power for both comparison and equivalence tests they are compared to the standard tests recommended by the fda and the emea based on non compartmental nc auc trials for a usual pk model are simulated under h0 and several h1 using s plus software and analysed with the nlme function different configurations of the number of subjects n 12 24 and 40 and of the number of samples per subject j 10 5 and 3 are studied the type i error of lrt and wald comparison test in the 5000 replications of interaction cross over trials is found to be 20 9 per cent and 21 7 per cent respectively in the original design n 12 j 10 which is far superior to 5 per cent and decreases when n increases when n is fixed is found to increase with j power is satisfactory for both tests after correction of the significance threshold results of eb and nc tests are similar with satisfactory powers and a type i error close to 5 per cent except when j 3 for eb tests similar results are obtained for equivalence tests except for eb and nc student tests which are not of a great interest nc tests keep their place when the number of samples per subject j is large but nlmem seem useful for cross over studies performed in special populations where j limited the evaluation by monte carlo simulations of empirical threshold seems however necessary because of the inflation of the type i error copyright 2005 john wiley sons ltd

the evaluation map in field theory sigma models and strings ii in this paper we examine specifically the role of the evaluation map in sigma models and strings we discuss the difference between sigma models and field theory as far as anomaly cancellation is concerned the introduction of the wess zumino terms in different sigma models is considered anomalies in string theory are discussed with special attention to the conformal anomalies and to the sigma model anomalies for the imbedded or immersed world sheet of the string conformal anomalies in two dimensions are connected to holomorphic and gravitational anomalies in order to have the cancellation of the sigma model anomalies of the string certain topological conditions must be satisfied by the ambient manifold the role of the evaluation map in the calculations of global anomalies is also discussed both for field theories and for sigma models in particular global anomalies are connected with the differential characters of cheeger and simons we show that the absence of global anomalies in sigma models is guaranteed by the absence of torsion in suitable homology groups of the target space

network synchronization of groups in this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups both continuous time and discrete time systems are considered we initially focus on the case where two groups are present and the network has bipartite topology i e links exist between nodes in different groups but not between nodes in the same group we also show that group synchronous motions are compatible with more general network topologies where there are also connections within the groups

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

a bayesian approach to nonlinear random effects models nonlinear random effects models are considered from the bayesian point of view the method of analysis follows closely that of lindley and smith 1972 journal of the royal statistical society series b 34 1 42 the numerical method is related to the em algorithm

bayesian approach for a nonlinear growth model nonlinear least squares methods are currently used for fitting a well known growth model namely the jenss model to the length measurements of a child followed throughout the first six years of life an empirical bayes approach is developed for fitting the model and the prior distribution of the growth model parameters is estimated from a large sample of least squares parameters an expression which is proportional to the posterior distribution is derived so that the posterior mode can be estimated given the observations on a child this posterior mode provides bayes estimates of the jenss curve parameters for the child

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

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

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a relative off set orthogonality convergence criterion for nonlinear least squares an orthogonality convergence criterion using relative offset is proposed this criterion is compared to currently used criteria and its advantages are discussed