on the asymptotic convergence of b spline wavelets to gabor functions a family of nonorthogonal polynomial spline wavelet transforms is considered these transforms are fully reversible and can be implemented efficiently the corresponding wavelet functions have a compact support it is proven that these b spline wavelets converge to gabor functions modulated gaussian pointwise and in all l sub p norms with 1

new dual type decomposition algorithm for nonconvex separable optimization problems abstract the aim of the paper is to present a new dual type decomposition algorithm for large scale nonconvex optimization problems of general separable structure after reformulation of the augmented lagrange function and introduction of auxiliary variables called approximation points separable local optimization problems are created the lower level of the method consists of a few optimization runs of these problems for subsequently improved approximation points whereas standard updating of lagrange multipliers constitutes the highest level simple rules for adjusting the approximation points and the lagrange multipliers are given and thoroughly analysed applicability conditions and example numerical results indicate that the presented algorithm eliminates to a great extent drawbacks of the previous approaches

assessing normality in random effects models when one uses the unbalanced mixed linear model mathbf y i mathbf x i mathbf alpha mathbf z i mathbf beta i varepsilon i i 1 cdots n to analyze data from longitudinal experiments with continuous outcomes it is customary to assume varepsilon i sim operatorname ind mathscr n mathbf 0 sigma 2 mathbf i i independent of mathbf beta i sim operatorname iid mathscr n mathbf 0 delta where sigma 2 and the elements of an arbitrary mathbf delta are unknown variance and covariance components in this paper we describe a method for checking model adequacy and in particular the distributional assumption on the random effects mathbf beta i we generalize the weighted normal plot to accommodate dependent nonidentically distributed observations subject to multiple random effects for each individual unit under study one can detect various departures from the normality assumption by comparing the expected and empirical cumulative distribution functions of standardized linear combinations of estimated residuals for each of the individual units through application of distributional results for a certain class of estimators to our context we adjust the estimated covariance of the empirical cumulative distribution function to account for estimation of unknown parameters several examples of our method demonstrate its usefulness in the analysis of longitudinal data

baseline risk as predictor of treatment benefit three clinical meta re analyses a relationship between baseline risk and treatment effect is increasingly investigated as a possible explanation of between study heterogeneity in clinical trial meta analysis an approach that is still often applied in the medical literature is to plot the estimated treatment effects against the estimated measures of risk in the control groups as a measure of baseline risk and to compute the ordinary weighted least squares regression line however it has been pointed out by several authors that this approach can be seriously flawed the main problem is that the observed treatment effect and baseline risk measures should be viewed as estimates rather than the true values in recent years several methods have been proposed in the statistical literature to potentially deal with the measurement errors in the estimates in this article we propose a vague priors bayesian solution to the problem which can be carried out using the bayesian inference using gibbs sampling bugs implementation of markov chain monte carlo numerical integration techniques different from other proposed methods it uses the exact rather than an approximate likelihood while it can handle many different treatment effect measures and baseline risk measures the method differs from a recently proposed bayesian method in that it explicitly models the distribution of the underlying baseline risks we apply the method to three meta analyses published in the medical literature and compare the results with the outcomes of the other recently proposed methods in particular we compare our approach to mcintosh s method for which we show how it can be carried out using standard statistical software we conclude that our proposed method offers a very general and flexible solution to the problem which can be carried out relatively easily with existing bayesian analysis software a confidence band for the underlying relationship between true effect measure and baseline risk and a confidence interval for the value of the baseline risk measure for which there is no treatment effect are easily obtained by products of our approach

estimating local and global measures of association for bivariate interval censored data with a smooth estimate of the density measures of association for bivariate interval censored data have not yet been studied extensively betensky and finkelstein statist med 1999 18 3101 3109 proposed to calculate kendall s coefficient of concordance using a multiple imputation technique but their method becomes computer intensive for moderate to large data sets we suggest a different approach consisting of two steps firstly a bivariate smooth estimate of the density of log event times is determined the smoothing technique is based on a mixture of gaussian densities fixed on a grid with weights determined by a penalized likelihood approach secondly given the smooth approximation several local and global measures of association can be estimated readily the performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from the signal tandmobiel study

efficient estimation for patient specific rates of disease progression using nonnormal linear mixed models this article presents a new class of nonnormal linear mixed models that provide an efficient estimation of subject specific disease progression in the analysis of longitudinal data from the modification of diet in renal disease mdrd trial this new analysis addresses the previously reported finding that the distribution of the random effect characterizing disease progression is negatively skewed we assume a log gamma distribution for the random effects and provide the maximum likelihood inference for the proposed nonnormal linear mixed model we derive the predictive distribution of patient specific disease progression rates which demonstrates rather different individual progression profiles from those obtained from the normal linear mixed model analysis to validate the adequacy of the log gamma assumption versus the usual normality assumption for the random effects we propose a lack of fit test that clearly indicates a better fit for the log gamma modeling in the analysis of the mdrd data the full maximum likelihood inference is also advantageous in dealing with the missing at random mar type of dropouts encountered in the mdrd data

linear mixed models for skew normal independent bivariate responses with an application to periodontal disease bivariate clustered correlated data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model framework with underlying normality assumptions of the random effects and within subject errors however such normality assumptions might be questionable if the data set particularly exhibit skewness and heavy tails using a bayesian paradigm we use the skew normal independent sni distribution as a tool for modeling clustered data with bivariate non normal responses in a linear mixed model framework the sni distribution is an attractive class of asymmetric thick tailed parametric structure which includes the skew normal distribution as a special case we assume that the random effects follows multivariate skew normal independent distributions and the random errors follow symmetric normal independent distributions which provides substantial robustness over the symmetric normal process in a linear mixed model framework specific distributions obtained as special cases viz the skew t the skew slash and the skew contaminated normal distributions are compared along with the default skew normal density the methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth ppd and clinical attachment level cal

on ternary quotients of cubic hecke algebras we prove that the quotient of the group algebra of the braid group introduced by funar commun math phys 173 513 558 1995 collapses in characteristic distinct from 2 in characteristic 2 we define several quotients of it which are connected to the classical hecke and birman wenzl murakami quotients but which admit in addition a symmetry of order 3 we also establish conditions on the possible markov traces factorizing through it

group sequential methods for an ordinal logistic random effects model under misspecification interim analyses in clinical trials are planned for ethical as well as economic reasons general results have been published in the literature that allow the use of standard group sequential methodology if one uses an efficient test statistic e g when wald type statistics are used in random effects models for ordinal longitudinal data these models often assume that the random effects are normally distributed however this is not always the case we will show that when the random effects distribution is misspecified in ordinal regression models the joint distribution of the test statistics over the different interim analyses is still a multivariate normal distribution but a sandwich type correction to the covariance matrix is needed in order to obtain the correct covariance matrix the independent increment structure is also investigated a bias in estimation will occur due to the misspecification however we will also show that the treatment effect estimate will be unbiased under the null hypothesis thus maintaining the type i error extensive simulations based on a toenail dermatophyte onychomycosis trial are used to illustrate our results

complex reflection groups braid groups hecke algebras presentations a la coxeter are given for all irreducible nite com plex re ection groups they provide presentations for the corresponding generalized braid groups for all but six cases which allow us to generalize some of the known properties of nite coxeter groups and their associated braid groups such as the computation of the center of the braid group and the construction of deformations of the nite group algebra hecke algebras we introduce monodromy representations of the braid groups which factorize through the hecke algebras extending results of cherednik opdam kohno and others summary introduction complex re ection groups and their presentations a background from complex re ection groups b presentations braid groups and their diagrams a generalities about hyperplane complements b generalities about the braid groups c the braid diagrams proofs of the main theorems for the braid groups b de e r a notation and prerequisites b computation of b de e r and of its center for d c computation of b e e r and of its center hecke algebras a background from di erential equations and monodromy b a family of monodromy representations of the braid group c hecke algebras diagrams and tables appendix generators of the monodromy around a divisor appendix tables to mathematics subject classi cation primary g we thank jean michel peter orlik pierre vogel for useful conversations and the isaac newton institute for its hospitality while the last version of this manuscript was written up the second named author gratefully acknowledges nancial support by the fondation alexander von humboldt for his stays in paris michel brou e gunter malle raphael rouquier

a maximal cubic quotient of the braid algebra i abstract we study a quotient of the group algebra of the braid group in which the artin generators satisfy a cubic relation this quotient is maximal among the ones satisfying such a cubic relation we also investigate the proper quotients of it that appear in the realm of quantum groups and describe another maximal quotient related to the usual hecke algebras finally we describe the connection between this algebra and a quotient of the algebra of horizontal chord diagrams introduced by vogel we prove that these two are isomorphic for n 5

a comparison of three random effects approaches to analyze repeated bounded outcome scores with an application in a stroke revalidation study discrete bounded outcome scores bos i e discrete measurements that are restricted on a finite interval often occur in practice examples are compliance measures quality of life measures etc in this paper we examine three related random effects approaches to analyze longitudinal studies with a bos as response 1 a linear mixed effects lm model applied to a logistic transformed modified bos 2 a model assuming that the discrete bos is a coarsened version of a latent random variable which after a logistic normal transformation satisfies an lm model and 3 a random effects probit model we consider also the extension whereby the variability of the bos is allowed to depend on covariates the methods are contrasted using a simulation study and on a longitudinal project which documents stroke rehabilitation in four european countries using measures of motor and functional recovery

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

lattice extensions of hecke algebras abstract we investigate the extensions of the hecke algebras of finite complex reflection groups by lattices of reflection subgroups that we introduced for some of them in our previous work on the yokonuma hecke algebras and their connections with artin groups when the hecke algebra is attached to the symmetric group and the lattice contains all reflection subgroups then these algebras are the diagram algebras of braids and ties of aicardi and juyumaya we prove a structure theorem for these algebras generalizing a result of espinoza and ryom hansen from the case of the symmetric group to the general case we prove that these algebras are symmetric algebras at least when w is a coxeter group and in general under the trace conjecture of broue malle and michel

bayesian semiparametric variable selection with applications to periodontal data a normality assumption is typically adopted for the random effects in a clustered or longitudinal data analysis using a linear mixed model however such an assumption is not always realistic and it may lead to potential biases of the estimates especially when variable selection is taken into account furthermore flexibility of nonparametric assumptions e g dirichlet process on these random effects may potentially cause centering problems leading to difficulty of interpretation of fixed effects and variable selection motivated by these problems we proposed a bayesian method for fixed and random effects selection in nonparametric random effects models we modeled the regression coefficients via centered latent variables which are distributed as probit stick breaking scale mixtures by using the mixture priors for centered latent variables along with covariance decomposition we could avoid the aforementioned problems and allow efficient selection of fixed and random effects from the model we demonstrated the advantages of our proposed approach over other competing alternatives through a simulated example and also via an illustrative application to a data set from a periodontal disease study copyright 2017 john wiley sons ltd

an estimation method for the semiparametric mixed effects model summary a semiparametric mixed effects regression model is proposed for the analysis of clustered or longitudinal data with continuous ordinal or binary outcome the common assumption of gaussian random effects is relaxed by using a predictive recursion method newton and zhang 1999 to provide a nonparametric smooth density estimate a new strategy is introduced to accelerate the algorithm parameter estimates are obtained by maximizing the marginal profile likelihood by powell s conjugate direction search method monte carlo results are presented to show that the method can improve the mean squared error of the fixed effects estimators when the random effects distribution is not gaussian the usefulness of visualizing the random effects density itself is illustrated in the analysis of data from the wisconsin sleep survey the proposed estimation procedure is computationally feasible for quite large data sets

random effects models with non parametric priors we discuss the performance of non parametric maximum likelihood npml estimators for the distribution of a univariate random effect in the analysis of longitudinal data for continuous data we analyse generated and real data sets and compare the npml method to those that assume a gaussian random effects distribution and to ordinary least squares for binary outcomes we use generated data to study the moderate and large sample performance of the npml compared with a method based on a gaussian random effect distribution in logistic regression we find that estimated fixed effects are compatible for all approaches but that appropriate standard errors for the npml require adjusting the likelihood based standard errors we conclude that the non parametric approach provides an attractive alternative to gaussian based methods though additional evaluations are necessary before it can be recommended for general use

complete decomposition algorithm for nonconvex separable optimization problems and applications abstract in this paper we present a complete decomposition algorithm for nonconvex separable optimization problems applied in the optimal control problems this complete decomposition algorithm combines recursive quadratic programming with the dual method when our algorithm is applied to discretized optimal control problems a simple and parallel computation and a simple and regular data flow pattern between consecutive computational steps results this paper also suggests an approach for developing a hardware implementation of our algorithm and gives an estimation of the execution time needed to solve a practical example

new lagrangian function for nonconvex primal dual decomposition abstract in this paper a new lagrangian function is reported which is particularly suited for large scale nonconvex optimization problems with separable structure our modification convexifies the standard lagrangian function without destroying its separable structure so that the primal dual decomposition technique can be applied even to nonconvex optimization problems furthermore the proposed lagrangian results in two levels of iterative optimization as compared with the three levels needed for techniques recently proposed for nonconvex primal dual decomposition

bayesian inference in semiparametric mixed models for longitudinal data we consider bayesian inference in semiparametric mixed models spmms for longitudinal data spmms are a class of models that use a nonparametric function to model a time effect a parametric function to model other covariate effects and parametric or nonparametric random effects to account for the within subject correlation we model the nonparametric function using a bayesian formulation of a cubic smoothing spline and the random effect distribution using a normal distribution and alternatively a nonparametric dirichlet process dp prior when the random effect distribution is assumed to be normal we propose a uniform shrinkage prior usp for the variance components and the smoothing parameter when the random effect distribution is modeled nonparametrically we use a dp prior with a normal base measure and propose a usp for the hyperparameters of the dp base measure we argue that the commonly assumed dp prior implies a nonzero mean of the random effect distribution even when a base measure with mean zero is specified this implies weak identifiability for the fixed effects and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function we propose an adjustment using a postprocessing technique we show that under mild conditions the posterior is proper under the proposed usp a flat prior for the fixed effect parameters and an improper prior for the residual variance we illustrate the proposed approach using a longitudinal hormone dataset and carry out extensive simulation studies to compare its finite sample performance with existing methods

estimation and prediction in linear mixed models with skew normal random effects for longitudinal data this paper extends the classical linear mixed model by considering a multivariate skew normal assumption for the distribution of random effects we present an efficient hybrid ecme nr algorithm for the computation of maximum likelihood estimates of parameters a score test statistic for testing the existence of skewness preference among random effects is developed the technique for the prediction of future responses under this model is also investigated the methodology is illustrated through an application to framingham cholesterol data and a simulation study

discriminant analysis using a multivariate linear mixed model with a normal mixture in the random effects distribution we have developed a method to longitudinally classify subjects into two or more prognostic groups using longitudinally observed values of markers related to the prognosis we assume the availability of a training data set where the subjects allocation into the prognostic group is known the proposed method proceeds in two steps as described earlier in the literature first multivariate linear mixed models are fitted in each prognostic group from the training data set to model the dependence of markers on time and on possibly other covariates second fitted mixed models are used to develop a discrimination rule for future subjects our method improves upon existing approaches by relaxing the normality assumption of random effects in the underlying mixed models namely we assume a heteroscedastic multivariate normal mixture for random effects inference is performed in the bayesian framework using the markov chain monte carlo methodology software has been written for the proposed method and it is freely available the methodology is applied to data from the dutch primary biliary cirrhosis study

non parametric inference for clustered binary and count data when only summary information is available summary data in the form of pairs x y where the response y is a count arise in many applications including problems involving stratified or two stage sampling such data are often analysed by using random effects models where the distribution of y conditional on x and on an unobserved random parameter is taken to be either binomial or poisson and the distribution of is connected through a link function to a random effect the latter is sometimes supposed to be normally distributed but that assumption can lead to serious biases if it is not satisfied this difficulty has motivated an extensive literature on non parametric techniques for cases where the random effect distribution is unknown but that methodology requires detailed cluster level data no non parametric techniques are available for instances where only summary data are accessible we show that the random effect distribution is actually non parametrically identifiable from crude summary data and we suggest a sieve method for inference in this case non parametric approaches to both parameter estimation and prediction are introduced and empirical techniques are developed for choosing tuning parameters these methods are shown to outperform their parametric counterparts when the model is misspecified and to perform almost as well as parametric methods when the model is correct

goodness of fit tests for mixed model diagnostics a simple goodness of fit test is proposed for checking distributional assumptions involved in a mixed linear model an estimated critical value of the test statistic is derived and is shown to be asymptotically correct under mild conditions as a special case the test may be applied to linear regression models to formally check distribution of the errors finite sample performance of the proposed test is examined and compared with that of a previously proposed test by simulations

optimality tests for partitioning and sectional search algorithms this paper revives a familiar idea for use in solving optimization problems particularly unstructured nonlinear programs with many variables the idea involves partitioning variables into groups and successively performing a sectional search with respect to one group at a time the paper addresses various difficulties normally associated with this type of procedure and proposes ways to solve them these include testing optimality of the point at termination and developing ways to restart the process upon finding that the terminating point is not optimal the paper also briefly discusses some useful implications of the results on how to group variables in unstructured nonlinear programs so as to improve convergence

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

a linear mixed effects model with heterogeneity in the random effects population abstract this article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed effects model it shows that if the distribution of random effects is a finite mixture of normal distributions then the random effects may be badly estimated if normality is assumed and the current methods for inspecting the appropriateness of the model assumptions are not sound further it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then compare the fitted model with the gaussian model all of this is illustrated on two practical examples

a diagnostic test for the mixing distribution in a generalised linear mixed model summary we introduce a diagnostic test for the mixing distribution in a generalised linear mixed model the test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model we derive the asymptotic variance of this difference and propose a test statistic that has a limiting chi squared distribution under the null hypothesis that the mixing distribution is correctly specified this strategy uses an idea presented by hausman 1978 who considered analogous tests for the linear mixed model an important advantage of the methods outlined here is that the resulting diagnostic test is easily implemented in commercial software we illustrate the method by applying it to data from a clinical trial investigating the effect of hormonal contraceptives in women

a latent class mixture model for incomplete longitudinal gaussian data in the analyses of incomplete longitudinal clinical trial data there has been a shift away from simple methods that are valid only if the data are missing completely at random to more principled ignorable analyses which are valid under the less restrictive missing at random assumption the availability of the necessary standard statistical software nowadays allows for such analyses in practice while the possibility of data missing not at random mnar cannot be ruled out it is argued that analyses valid under mnar are not well suited for the primary analysis in clinical trials rather than either forgetting about or blindly shifting to an mnar framework the optimal place for mnar analyses is within a sensitivity analysis context one such route for sensitivity analysis is to consider next to selection models pattern mixture models or shared parameter models the latter can also be extended to a latent class mixture model the approach taken in this article the performance of the so obtained flexible model is assessed through simulations and the model is applied to data from a depression trial

mixed coordination method for long horizon optimal control problems we present a new approach to solving long horizon discrete time optimal control problems using the mixed coordination method the idea is to decompose a long horizon problem into subproblems along the time axis the requirement that the initial state of a subproblem equal the terminal state of the preceding subproblem is relaxed by using lagrange multipliers the lagrange multipliers and initial state of each subproblem are then selected as high level variables the equivalence of the two level formulation and the original problem is proved for both convex and non convex cases the low level subproblems are solved in parallel using extended differential dynamic programming ddp an efficient way to find the gradient and hessian of a low level objective function with respect to high level variables is developed the high level problem is solved using the modified newton method an effective procedure is developed to select initial values of multipliers based on the initial trajectory the method can conv

deconvolution methods for non parametric inference in two level mixed models summary we develop a general non parametric approach to the analysis of clustered data via random effects assuming only that the link function is known the regression functions and the distributions of both cluster means and observation errors are treated non parametrically our argument proceeds by viewing the observation error at the cluster mean level as though it were a measurement error in an errors in variables problem and using a deconvolution argument to access the distribution of the cluster mean a fourier deconvolution approach could be used if the distribution of the error in variables were known in practice it is unknown of course but it can be estimated from repeated measurements and in this way deconvolution can be achieved in an approximate sense this argument might be interpreted as implying that large numbers of replicates are necessary for each cluster mean distribution but that is not so we avoid this requirement by incorporating statistical smoothing over values of nearby explanatory variables empirical rules are developed for the choice of smoothing parameter numerical simulations and an application to real data demonstrate small sample performance for this package of methodology we also develop theory establishing statistical consistency

bayesian bent cable growth mixture tobit models for longitudinal data with skewness and detection limit application to aids studies this paper presents a new bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in hiv aids studies or other related fields estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change we assess this clinically important feature of the longitudinal hiv aids data using the bent cable framework within a growth mixture tobit model to account for heterogeneity of drug resistance among subjects the parameters of the bent cable growth mixture tobit model are also allowed to differ by subgroups subpopulations of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left censoring the proposed methods are illustrated using real data from an aids clinical study copyright 2016 john wiley sons ltd

a functional based distribution diagnostic for a linear model with correlated outcomes in this paper we present an easy to implement graphical distribution diagnostic for linear models with correlated errors houseman et al 2004 constructed quantile quantile plots for the marginal residuals of such models suitably transformed we extend the pointwise asymptotic theory to address the global stochastic behaviour of the corresponding empirical cumulative distribution function and describe a simulation technique that serves as a computationally efficient parametric bootstrap for generating representatives of its stochastic limit thus continuous functionals of the empirical cumulative distribution function may be used to form global tests of normality through the use of projection matrices we generalised our methods to include tests that are directed at assessing the normality of particular components of the error thus tests proposed by lange ryan 1989 follow as a special case our method works well both for models having independent units of sampling and for those in which all observations are correlated

measurement error instrumental variables and corrections for attenuation with applications to meta analyses macmahon et al present a meta analysis of the effect of blood pressure on coronary heart disease as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor the correction for attenuation used by these authors is compared to others already existing in the literature as well as to a new instrumental variable method the assumptions justifying the various methods are examined and their efficiencies are studied via simulation compared to the methods we discuss the method of macmahon et al may have bias in some circumstances because it does not take into account i possible correlations among the predictors within a study ii possible bias in the second measurement or iii possibly differing marginal distributions of the predictors or measurement errors across studies a unifying asymptotic theory using estimating equations is also presented

random effects logistic regression analysis with auxiliary covariates summary we study a semiparametric estimation method for the random effects logistic regression when there is auxiliary covariate information about the main exposure variable we extend the semiparametric estimator of pepe and fleming 1991 journal of the american statistical association86 108 113 to the random effects model using the best linear unbiased prediction approach of henderson 1975 biometrics31 423 448 the method can be used to handle the missing covariate or mismeasured covariate data problems in a variety of real applications simulation study results show that the proposed method outperforms the existing methods we analyzed a data set from the collaborative perinatal project using the proposed method and found that the use of ddt increases the risk of preterm births among us children

fractional brownian motion and multivariate t models for longitudinal biomedical data with application to cd4 counts in hiv positive patients longitudinal data are widely analysed using linear mixed models with random slopes models particularly common however when modelling for example longitudinal pre treatment cd4 cell counts in hiv positive patients the incorporation of non stationary stochastic processes such as brownian motion has been shown to lead to a more biologically plausible model and a substantial improvement in model fit in this article we propose two further extensions firstly we propose the addition of a fractional brownian motion component and secondly we generalise the model to follow a multivariate t distribution these extensions are biologically plausible and each demonstrated substantially improved fit on application to example data from the concerted action on seroconversion to aids and death in europe study we also propose novel procedures for residual diagnostic plots that allow such models to be assessed cohorts of patients were simulated from the previously reported and newly developed models in order to evaluate differences in predictions made for the timing of treatment initiation under different clinical management strategies a further simulation study was performed to demonstrate the substantial biases in parameter estimates of the mean slope of cd4 decline with time that can occur when random slopes models are applied in the presence of censoring because of treatment initiation with the degree of bias found to depend strongly on the treatment initiation rule applied our findings indicate that researchers should consider more complex and flexible models for the analysis of longitudinal biomarker data particularly when there are substantial missing data and that the parameter estimates from random slopes models must be interpreted with caution

a new technique for nonconvex primal dual decomposition of a large scale separable optimization problem the primal dual approach is quite effective in decomposing a convex separable optimization problem into several subproblems of smaller sizes in this paper we present a new technique which extends the primal dual approach to nonconvex problems since a straightforward application of the multiplier method destroys separability a new lagrangian function is proposed which preserves separability based on this new function we develop a new iterative method for finding an optimal solution to the problem and show that the method is locally convergent to an optimal solution furthermore the effect of certain parameters on the ratio of convergence is investigated and simple examples are given to illustrate the proposed approach

smooth random effects distribution in a linear mixed model a linear mixed model with a smooth random effects density is proposed a similar approach to p spline smoothing of eilers and marx 1996 statistical science 11 89 121 is applied to yield a more flexible estimate of the random effects density our approach differs from theirs in that the b spline basis functions are replaced by approximating gaussian densities fitting the model involves maximizing a penalized marginal likelihood the best penalty parameters minimize akaike s information criterion employing gray s 1992 journal of the american statistical association 87 942 951 results although our method is applicable to any dimensions of the random effects structure in this article the two dimensional case is explored our methodology is conceptually simple and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by zhang and davidian 2001 biometrics 57 795 802 a simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings consistency of the estimates is shown in a particular case

finite mixture modeling with mixture outcomes using the em algorithm summary this paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables the research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome more generally this model can be seen as a combination of latent class modeling and conventional mixture modeling the em algorithm is used for estimation as an illustration a random coefficient growth model for the prediction of alcohol dependence from three latent classes of heavy alcohol use trajectories among young adults is analyzed

independent and identically distributed monte carlo algorithms for semiparametric linear mixed models hybrid versions of independent and identically distributed weighted chinese restaurant wcr algorithms are developed for inference in semiparametric linear mixed models under minimal assumptions for the random effects distributions the wcr method of working with the posterior partition structure leads to rao blackwell estimates for higher order moments of random effects such as skewness and kurtosis and can be used to estimate densities for random effects a key feature of our approach is the manner in which we incorporate external estimates into our algorithms the use of such information leads to simplified computational procedures reduces the amount of user input required for specifying models and results in numerical stability and accuracy the resulting procedures are automated and can be readily used in standard statistical software our methods are tested by simulation and illustrated by application to a longitudinal study involving chronic renal disease

two level primal dual proximal decomposition technique to solve large scale optimization problems we describe a primal dual application of the proximal point algorithm to nonconvex minimization problems motivated by the work of spingarn and more recently by the work of hamdi et al about the primal resource directive decomposition scheme to solve nonlinear separable problems this paper discusses some local results of a primal dual regularization approach that leads to a decomposition algorithm

bayesian semiparametric nonlinear mixed effects joint models for data with skewness missing responses and measurement errors in covariates it is a common practice to analyze complex longitudinal data using semiparametric nonlinear mixed effects snlme models with a normal distribution normality assumption of model errors may unrealistically obscure important features of subject variations to partially explain between and within subject variations covariates are usually introduced in such models but some covariates may often be measured with substantial errors moreover the responses may be missing and the missingness may be nonignorable inferential procedures can be complicated dramatically when data with skewness missing values and measurement error are observed in the literature there has been considerable interest in accommodating either skewness incompleteness or covariate measurement error in such models but there has been relatively little study concerning all three features simultaneously in this article our objective is to address the simultaneous impact of skewness missingness and covariate measurement error by jointly modeling the response and covariate processes based on a flexible bayesian snlme model the method is illustrated using a real aids data set to compare potential models with various scenarios and different distribution specifications

a finite mixture of nonlinear random coefficient models for continuous repeated measures data nonlinear random coefficient models nrcms for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development or growth over time in measured variables as an extension of this model this study considers the finite mixture of nrcms that combine features of nrcms with the idea of finite mixture or latent class models the efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations thus allowing the simultaneous investigation of intra individual within person variability inter individual between person variability and subpopulation heterogeneity effectiveness of this model to work under real data analytic conditions was examined by executing a monte carlo simulation study the simulation study was carried out using an r routine specifically developed for the purpose of this study the r routine used maximum likelihood with the expectation maximization algorithm the design of the study mimicked the output obtained from running a two class mixture model on task completion data

mixed coordination method for non linear programming problems with separable structures static optimization with linear equality constraints and separable structures is studied by using the mixed coordination method the idea is to relax equality constraints via lagrange multipliers and create a hierarchy where the lagrange multipliers and part of the decision variables are selected as high level variables the method was proposed about ten years ago with a simple high level updating scheme we show that the solution of the high level problem is a saddle point and the simple updating scheme has a linear convergence rate under appropriate conditions to obtain faster convergence the modified newton method is adopted at the high level there are two difficulties associated with this approach one is how to obtain the hessian matrix in determining the newton direction since second order derivatives of the objective function with respect to all high level variables are needed the second is when to stop in performing a line search along the newton direction as the high level problem is a ma

cluster analysis using multivariate mixed effects models a common situation in the biological and social sciences is to have data on one or more variables measured longitudinally on a sample of individuals a problem of growing interest in these areas is the grouping of individuals into one of two or more clusters according to their longitudinal behavior recently methods have been proposed to deal with cases where individuals are classified into clusters through a linear model of mixed univariate effects deriving from a longitudinally measured variable the method proposed in the current work deals with the case of clustering and then classification based on two or more variables measured longitudinally through the fitting of non linear multivariate mixed effect models and with consideration given to parameter estimation for balanced and unbalanced data using an em algorithm the application of the method is illustrated with an example in which the clusters are identified and the classification into clusters is compared with the true membership of individuals in one of two groups which is known at the end of the follow up period

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

bayesian nonparametric longitudinal data analysis abstractpractical bayesian nonparametric methods have been developed across a wide variety of contexts here we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry cs and autoregressive ar covariance structures ar structure is often specified through the use of a gaussian process gp with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart we allow for ar structure by considering a broader class of models that incorporates a dirichlet process mixture dpm over the covariance parameters of the gp we are able to take advantage of modern bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations we also take advantage of the generality of our model which provides for estimation

discriminant analysis for longitudinal data with multiple continuous responses and possibly missing data multiple outcomes are often used to properly characterize an effect of interest this article discusses model based statistical methods for the classification of units into one of two or more groups where for each unit repeated measurements over time are obtained on each outcome we relate the observed outcomes using multivariate nonlinear mixed effects models to describe evolutions in different groups due to its flexibility the random effects approach for the joint modeling of multiple outcomes can be used to estimate population parameters for a discriminant model that classifies units into distinct predefined groups or populations parameter estimation is done via the expectation maximization algorithm with a linear approximation step we conduct a simulation study that sheds light on the effect that the linear approximation has on classification results we present an example using data from a study in 161 pregnant women in santiago chile where the main interest is to predict normal versus abnormal pregnancy outcomes

regularized finite mixture models for probability trajectories finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time in practice trajectories are usually modeled as polynomials which may fail to capture important features of the longitudinal pattern focusing on dichotomous response measures we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates we show how parameter estimation and inference for whether trajectories are time invariant linear time varying or nonlinear time varying can be carried out for such models to illustrate the method we use simulation studies and data from a long term longitudinal study of children at high risk for substance abuse

minimax multiple shrinkage estimation on presente des nouveaux estimateurs qui incorporent l information partielle a priori en utilisant les donnees comme emulation du comportement et du risque des estimateurs consideres les plus efficaces

a semi parametric bayesian approach to average bioequivalence bioequivalence assessment is an issue of great interest development of statistical methods for assessing bioequivalence is an important area of research for statisticians bioequivalence is usually determined based on the normal distribution we relax this assumption and develop a semi parametric mixed model for bioequivalence data the proposed method is quite flexible and practically meaningful our proposed method is based on a mixture normal distribution and a non parametric bayesian approach using a dirichlet process mixture prior a numerical example illustrates the use of our procedure

a cubic defining algebra for the links gould polynomial abstract we define a finite dimensional cubic quotient of the group algebra of the braid group endowed with a essentially unique markov trace which affords the links gould invariant of knots and links we investigate several of its properties and state several conjectures about its structure

discovering subpopulation structure with latent class mixed models the linear mixed model is a well known method for incorporating heterogeneity for example subject to subject variation into a statistical analysis for continuous responses however heterogeneity cannot always be fully captured by the usual assumptions of normally distributed random effects latent class mixed models offer a way of incorporating additional heterogeneity which can be used to uncover distinct subpopulations to incorporate correlated non normally distributed outcomes and to classify individuals the methodology is motivated with examples in health care studies and a detailed illustration is drawn from the nutritional prevention of cancer trials latent class models are used with longitudinal data on prostate specific antigen psa as well as incidence of prostate cancer the models are extended to accommodate prostate cancer as a survival endpoint this is compared to treating it as a binary endpoint four subpopulations are identified which differ both with regard to their psa trajectories and their incidence rates of prostate cancer

a smooth nonparametric estimate of a mixing distribution using mixtures of gaussians abstract we propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h this approach can lead to estimates of many shapes with smoothness controlled by parameter h we show that the resulting estimate will always be a finite mixture of gaussians each having variance h the nonparametric maximum likelihood estimate can be viewed as a special case with h 0 the method can be extended to estimate multivariate mixing distributions examples and the results of a simulation study are presented

semiparametric estimation in generalized linear mixed models with auxiliary covariates a pairwise likelihood approach auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects this article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data we propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation based inference procedure by treating both the error structure and random effects as nuisance parameters this method is robust against misspecification of either error structure or random effects distribution and allows for dependence between random effects and covariates we show that the resulting estimators are consistent and asymptotically normal extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method we illustrate the method with two real data examples

density estimation in the presence of heteroscedastic measurement error we consider density estimation when the variable of interest is subject to heteroscedastic measurement error the density is assumed to have a smooth but unknown functional form that we model with a penalized mixture of b splines we treat the situation in which multiple mismeasured observations of each variable of interest are observed for at least some of the subjects and the measurement error is assumed to be additive and normal the measurement error variance function is modeled with a second penalized mixture of b splines the article s main contributions are to address the effects of heteroscedastic measurement error effectively explain the biases caused by ignoring heteroscedasticity and present an equivalent kernel for a spline based density estimator derivation of the equivalent kernel may be of independent interest we use small sigma asymptotics to approximate the biases incurred by assuming that the measurement error is homoscedastic when it actually is heteroscedastic the biases incurred

score test for conditional independence between longitudinal outcome and time to event given the classes in the joint latent class model latent class models have been recently developed for the joint analysis of a longitudinal quantitative outcome and a time to event these models assume that the population is divided in g latent classes characterized by different risk functions for the event and different profiles of evolution for the markers that are described by a mixed model for each class however the key assumption of conditional independence between the marker and the event given the latent classes is difficult to evaluate because the latent classes are not observed using a joint model with latent classes and shared random effects we propose a score test for the null hypothesis of independence between the marker and the outcome given the latent classes versus the alternative hypothesis that the risk of event depends on one or several random effects from the mixed model in addition to the latent classes a simulation study was performed to compare the behavior of the score test to other previously proposed tests including situations where the alternative hypothesis or the baseline risk function are misspecified in all the investigated situations the score test was the most powerful the methodology was applied to develop a prognostic model for recurrence of prostate cancer given the evolution of prostate specific antigen in a cohort of patients treated by radiation therapy

prediction of random effects in linear and generalized linear models under model misspecification statistical models that include random effects are commonly used to analyze longitudinal and correlated data often with the assumption that the random effects follow a gaussian distribution via theoretical and numerical calculations and simulation we investigate the impact of misspecification of this distribution on both how well the predicted values recover the true underlying distribution and the accuracy of prediction of the realized values of the random effects we show that although the predicted values can vary with the assumed distribution the prediction accuracy as measured by mean square error is little affected for mild to moderate violations of the assumptions thus standard approaches readily available in statistical software will often suffice the results are illustrated using data from the heart and estrogen progestin replacement study using models to predict future blood pressure values

improving likelihood based inference in control rate regression control rate regression is a diffuse approach to account for heterogeneity among studies in meta analysis by including information about the outcome risk of patients in the control condition correcting for the presence of measurement error affecting risk information in the treated and in the control group has been recognized as a necessary step to derive reliable inferential conclusions within this framework the paper considers the problem of small sample size as an additional source of misleading inference about the slope of the control rate regression likelihood procedures relying on first order approximations are shown to be substantially inaccurate especially when dealing with increasing heterogeneity and correlated measurement errors we suggest to address the problem by relying on higher order asymptotics in particular we derive skovgaard s statistic as an instrument to improve the accuracy of the approximation of the signed profile log likelihood ratio statistic to the standard normal distribution the proposal is shown to provide much more accurate results than standard likelihood solutions with no appreciable computational effort the advantages of skovgaard s statistic in control rate regression are shown in a series of simulation experiments and illustrated in a real data example r code for applying first and second order statistic for inference on the slope on the control rate regression is provided

a likelihood reformulation method in non normal random effects models in this paper we propose a practical computational method to obtain the maximum likelihood estimates mle for mixed models with non normal random effects by simply multiplying and dividing a standard normal density we reformulate the likelihood conditional on the non normal random effects to that conditional on the normal random effects gaussian quadrature technique conveniently implemented in sas proc nlmixed can then be used to carry out the estimation process our method substantially reduces computational time while yielding similar estimates to the probability integral transformation method j comput graphical stat 2006 15 39 57 furthermore our method can be applied to more general situations e g finite mixture random effects or correlated random effects from clayton copula simulations and applications are presented to illustrate our method

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

growth mixture modeling with non normal distributions a limiting feature of previous work on growth mixture modeling is the assumption of normally distributed variables within each latent class with strongly non normal outcomes this means that several latent classes are required to capture the observed variable distributions being able to relax the assumption of within class normality has the advantage that a non normal observed distribution does not necessitate using more than one class to fit the distribution it is valuable to add parameters representing the skewness and the thickness of the tails a new growth mixture model of this kind is proposed drawing on recent work in a series of papers using the skew t distribution the new method is illustrated using the longitudinal development of body mass index in two data sets the first data set is from the national longitudinal survey of youth covering ages 12 23 years here the development is related to an antecedent measuring socioeconomic background the second data set is from the framingham heart study covering ages 25 65 years here the development is related to the concurrent event of treatment for hypertension using a joint growth mixture survival model

semi parametric modelling of the distribution of the baseline risk in meta analysis in meta analysis of clinical trials often meta regression analyses are performed to explain the heterogeneity in treatment effects that usually exist between trials a popular explanatory variable is the risk observed in the control group the baseline risk the relationship between the treatment effect and the baseline risk is investigated by fitting a linear model that allows randomness on the true baseline risk by assuming a normal distribution with unknown mean and variance however the normality assumption could be too strong to adequately describe the underlying distribution therefore we developed a new semi parametric method that relaxes the normality assumption to a more flexible and general distribution we applied a penalized gaussian mixture distribution to represent the baseline risk distribution furthermore a bivariate hierarchical model is formulated in order to take into account the correlation between the baseline and treatment effect to fit the proposed model a penalized likelihood function is maximized by an expectation maximization em algorithm we illustrate our method on a number of simulated data sets and on a published meta analysis data set

bayesian accelerated failure time model with multivariate doubly interval censored data and flexible distributional assumptions in this article we consider the relationship of covariates to the time to caries of permanent first molars this involves an analysis of multivariate doubly interval censored data to describe this relationship we suggest an accelerated failure time model with random effects taking into account that the observations are clustered indeed up to four permanent molars per child enter into the analysis implying up to four caries times for each child each distributional part of the model is specified in a flexible way as a penalized gaussian mixture with an overspecified number of mixture components a bayesian approach with the markov chain monte carlo methodology is used to estimate the model parameters and a software package in the r language has been written that implements it

on the quotients of cubic hecke algebras between the rank 3 quotients of cubic hecke algebras there is essentially one of maximal dimension we prove it has a unique markov trace having values in a torsion module therefore the description of a markov trace on the cubic hecke algebra corresponding tox 3 1 and having the parameters 1 1 is derived thus we obtain a numerical link invariant of finite degree and define a whole sequence of 3rd order vassiliev invariants

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

empirical bayes estimation of individual growth curve parameters and their relationship to covariates summary the analysis of growth curves has long been important in biostatistics work has focused on two problems the estimation of individual curves based on many data points and the estimation of the mean growth curve for a group of individuals this paper extends a recent approach that seeks to combine data from a group of individuals in order to improve the estimates of individual growth parameters growth is modeled as polynomial in time and the group model is also linear incorporating growth related covariates into the model the estimation used is empirical bayes the estimation formulas are illustrated with a set of data on rat growth originally presented by box 1950 biometrics 6 362 389