a two step approach to measurement error in time dependent covariates in nonlinear mixed effects models with application to igf i pharmacokinetics abstract the usual approach to the analysis of population pharmacokinetic studies is to represent the concentration time data by a nonlinear mixed effects model primary objectives are to characterize the pattern of drug disposition in the population and to identify individual specific covariates associated with pharmacokinetic behavior we consider data from a study of insulin like growth factor i igf i administered by intravenous infusion to patients with severe head trauma failure to maintain steady state levels of igf i was thought to be related to the temporal pattern of several covariates measured in the study and an analysis investigating this issue was of interest observations on these potentially relevant covariates for each subject were made at time points different from those at which igf i concentrations were determined moreover the covariates themselves were likely subject to measurement error the usual approach to time dependent covariates in population analysis is to invoke a simple

linear and nonlinear mixed effects models for censored hiv viral loads using normal independent distributions summary hiv rna viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays hence the responses are either left or right censored linear and nonlinear mixed effects models with modifications to accommodate censoring are routinely used to analyze this type of data and are based on normality assumptions for the random terms however those analyses might not provide robust inference when the normality assumptions are questionable in this article we develop a bayesian framework for censored linear and nonlinear models replacing the gaussian assumptions for the random terms with normal independent ni distributions the ni is an attractive class of symmetric heavy tailed densities that includes the normal student s t slash and the contaminated normal distributions as special cases the marginal likelihood is tractable using approximations for nonlinear models and can be used to develop bayesian case deletion influence diagnostics based on the kullback leibler divergence the newly developed procedures are illustrated with two hiv aids studies on viral loads that were initially analyzed using normal censored mixed effects models as well as simulations

pseudo maximum likelihood approach for the analysis of multivariate left censored longitudinal data the linear mixed effects model based on a full likelihood is one of the few methods available to model longitudinal data subject to left censoring however a full likelihood approach is complicated algebraically because of the large dimension of the numeric computations and maximum likelihood estimation can be computationally prohibitive when the data are heavily censored moreover for mixed models the complexity of the computation increases as the dimension of the random effects in the model increases we propose a method based on pseudo likelihood that simplifies the computational complexities allows a wide class of multivariate models and that can be used for many different data structures including settings where the level of censoring is high the motivation for this work comes from the need for a joint model to assess the joint effect of pro inflammatory and anti inflammatory biomarker data on 30 day mortality status while simultaneously accounting for longitudinal left censoring and correlation between markers in the analysis of genetic and inflammatory markers for sepsis study conducted at the university of pittsburgh two markers interleukin 6 and interleukin 10 which naturally are correlated because of a shared similar biological pathways and are left censored because of the limited sensitivity of the assays are considered to determine if higher levels of these markers is associated with an increased risk of death after accounting for the left censoring and their assumed correlation copyright 2016 john wiley sons ltd

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

simultaneous inference for semiparametric nonlinear mixed effects models with covariate measurement errors and missing responses semiparametric nonlinear mixed effects nlme models are flexible for modeling complex longitudinal data covariates are usually introduced in the models to partially explain interindividual variations some covariates however may be measured with substantial errors moreover the responses may be missing and the missingness may be nonignorable we propose two approximate likelihood methods for semiparametric nlme models with covariate measurement errors and nonignorable missing responses the methods are illustrated in a real data example simulation results show that both methods perform well and are much better than the commonly used naive method

multivariate student t regression models pitfalls and inference we consider likelihood based inference from multivariate regression models with independent student t errors some very intruiging pitfalls of both bayesian and classical methods on the basis of point observations are uncovered bayesian inference may be precluded as a consequence of the coarse nature of the data global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space a bayesian analysis on the basis of set observations is proposed and illustrated by several examples

estimating variance parameters from multivariate normal variables subject to limits of detection mle reml or bayesian approaches likelihood based approaches which naturally incorporate left censoring due to limit of detection are commonly utilized to analyze censored multivariate normal data however the maximum likelihood estimator mle typically underestimates variance parameters the restricted maximum likelihood estimator reml which corrects the underestimation of variance parameters cannot be easily extended to analyze censored multivariate normal data in the light of the connection between the reml and a bayesian approach discovered in 1974 by dr harville this paper describes a bayesian approach to censored multivariate normal data this bayesian approach is justified through its link to the reml via laplace s approximation and its performance is evaluated through a simulation study we consider the bayesian approach as a valuable alternative because it yields less biased variance parameter estimates than the mle and because a solid reml is technically difficult when data are left censored copyright 2009 john wiley sons ltd

cocharacter closure and the rational hilbert mumford theorem for a field k let g be a reductive k group and v an affine k variety on which g acts using the notion of cocharacter closed g k orbits in v we prove a rational version of the celebrated hilbert mumford theorem from geometric invariant theory we initiate a study of applications stemming from this rationality tool a number of examples are discussed to illustrate the concept of cocharacter closure and to highlight how it differs from the usual zariski closure

powering up with space time wind forecasting the technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality high quality short term forecasts of wind speed are vital to making this a more reliable energy source gneiting et al 2006 have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information the forecasts produced by this model are accurate and subject to accuracy the predictive distribution is sharp that is highly concentrated around its center however this model is split into nonunique regimes based on the wind direction at an offsite location this paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model it is robust in many experiments such as predicting wind at other locations we compare this with the more common approach of modeling wind speeds and directions in the cartesian space and use a skew t distribution for the errors the quality of t

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

robust tests for heteroskedasticity in the one way error components model this paper constructs tests for heteroskedasticity in one way error components models in line with baltagi et al baltagi b h bresson g pirotte a 2006 joint lm test for homoskedasticity in a one way error component model journal of econometrics 134 401 417 our tests have two additional robustness properties first standard tests for heteroskedasticity in the individual component are shown to be negatively affected by heteroskedasticity in the remainder component we derive modified tests that are insensitive to heteroskedasticity in the component not being checked and hence help identify the source of heteroskedasticity second gaussian based lm tests are shown to reject too often in the presence of heavy tailed e g t student distributions by using a conditional moment framework we derive distribution free tests that are robust to non normalities our tests are computationally convenient since they are based on simple artificial regressions after pooled ols estimation

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

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

estimating overall exposure effects for the clustered and censored outcome using random effect tobit regression models the random effect tobit model is a regression model that accommodates both left and or right censoring and within cluster dependence of the outcome variable regression coefficients of random effect tobit models have conditional interpretations on a constructed latent dependent variable and do not provide inference of overall exposure effects on the original outcome scale marginalized random effects model mrem permits likelihood based estimation of marginal mean parameters for the clustered data for random effect tobit models we extend the mrem to marginalize over both the random effects and the normal space and boundary components of the censored response to estimate overall exposure effects at population level we also extend the average predicted value method to estimate the model predicted marginal means for each person under different exposure status in a designated reference group by integrating over the random effects and then use the calculated difference to assess the overall exposure effect the maximum likelihood estimation is proposed utilizing a quasi newton optimization algorithm with gauss hermite quadrature to approximate the integration of the random effects we use these methods to carefully analyze two real datasets copyright 2016 john wiley sons ltd

pseudo gaussian and rank based optimal tests for random individual effects in large n small t panels we consider the problem of detecting unobserved heterogeneity that is the problem of testing the absence of random individual effects in an n t panel we establish a local asymptotic normality property with respect to intercept regression coefficient the scale parameter of the error and the scale parameter u of individual effects which is the parameter of interest for given scaled density f 1 of the error terms when n tends to infinity and t is fixed this result allows via the hk representation theorem for developing asymptotically optimal rank based tests for the null hypothesis u 0 absence of individual effects these tests are locally asymptotically optimal at correctly specified innovation densities f 1 but remain valid irrespective of the actual underlying density the limiting distribution of our test statistics is obtained both under the null and under sequences of contiguous alternatives a local asymptotic linearity property is established in order to control for the effect of substituting estimators for nuisance parameters the asymptotic relative efficiencies of the proposed procedures with respect to the corresponding pseudo gaussian parametric tests are derived in particular the van der waerden version of our rank based tests uniformly dominates from the point of view of pitman efficiency the classical honda test small sample performances are investigated via a monte carlo study and confirm theoretical findings

censored observations repeated measures and mixed effects models an approach using the em algorithm and normal errors summary maximum likelihood estimation of a vector regression parameter and variance com ponents is considered for the mixed effects model when observations are right censored a general scheme of estimation is given using the em algorithm and detailed results found for the model with between and within block variation this model is applied to the logarithms of survival times from a repeated measures design in this paper we consider the estimation of the parameters when some of the observa tions are right censored this can occur with repeated measurements on subjects where the response is a waiting time and the variability in log times is modelled by a normal distribution alternative models for this situation are given by clayton cuzick 1985 and their methods involve partially parametric techniques using ranks and are based on models involving extreme value log gamma and logistic distributions we are concerned with use of the em algorithm dempster laird rubin 1977 to estimate the parameters of the mixed model for uncensored data hartley rao 1967 have considered this solution the analysis leads to a method which is straightforward to implement for the repeated measures model dempster et al 1984 give an account of the method with uncensored observations in 2 we consider a general implementation of the em algorithm for the pure random effects model with censored data and then in 3 we give explicit results for the simple random effects model section 4 uses these results for the analysis of repeated measures and 5 discusses some miscellaneous points arising finally in 6 we give an example involving skin graft data where there has been extensive analysis using matched pairs techniques

mixed effects models with censored data with application to hiv rna levels summary mixed effects models are often used for estimating fixed effects and variance components in longitudinal studies of continuous data when the outcome being modelled is a laboratory measurement however it may be subject to lower and upper detection limits i e censoring in this paper the usual em estimation procedure for mixed effects models is modified to account for left and or right censoring

examples of tensor categories let g be a tensor category over a field k of characteristic 0 in his paper i w 7 delinge had established rather general conditions for g to be the category of representations of an algebraic group he has shown that if any object nec satisfies the condition a n 0 for a sufficiently large n then 0 is equivalent to the category rep g of representations of a proalgebraic group scheme g over k for tensor categories over fields of positive characteristic this result is no longer true in the first part of this paper we present a construction of a class of tensor categories over fields of positive characteristic for which an analogue of deligne s theorem does not hold to describe these categories denote by gz an algebraic chevalley group over z and by g the corresponding group over fp for a sufficiently large p our category c will be a certain subquotient of the category r g of finite dimensional representations of g more precisely let s be the full subcategory of r g whose objects called small representations are direct sums of the irreducible representations of g with highest weights inside the fundamental alcove let also sl 2 c g be the principal slz subgroup in g and slz im c sl2 be the infinitesimal neighbourhood of the cartan subgroup h in sl2 denote by o the full subcategory of r g consisting of representations m of g called quasiprojective representations such that the restriction of m to sl2 m is projective the category 0 is a quotient of the subcategory s pcr g in the last section of the paper we show that the same approach can be applied to representations of quantum groups let u be the quantum group at a root of prime order p of 1 which is a hopf algebra over the ring of integers in a cyclotomic field see 2 3 starting from the category of representations of u we construct a semisimple braided category g p with the finite number of simple objects on the other hand in wess zumino witten conformal field theory one encounters the category o g m of integrable representations of the correspond

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

semiparametric bayesian latent variable regression for skewed multivariate data for many real life studies with skewed multivariate responses the level of skewness and association structure assumptions are essential for evaluating the covariate effects on the response and its predictive distribution we present a novel semiparametric multivariate model and associated bayesian analysis for multivariate skewed responses similar to multivariate gaussian densities this multivariate model is closed under marginalization allows a wide class of multivariate associations and has meaningful physical interpretations of skewness levels and covariate effects on the marginal density other desirable properties of our model include the markov chain monte carlo computation through available statistical software and the assurance of consistent bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions we illustrate the practical advantages of our methods over existing alternatives via simulation studies and the analysis of a clinical study on periodontal disease

generalized linear mixed model for binary outcomes when covariates are subject to measurement errors and detection limits longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease however biomarkers are subject to measurement error and some are also subject to left censoring due to a lower limit of detection statistical methods to address these issues are few we herein propose a generalized linear mixed model and estimate the model parameters using the monte carlo newton raphson mcnr method inferences regarding the parameters are made by applying louis s method and the delta method simulation studies were conducted to compare the proposed mcnr method with existing methods including the maximum likelihood ml method and the ad hoc approach of replacing the left censored values with half of the detection limit hdl the results showed that the performance of the mcnr method is superior to ml and hdl with respect to the empirical standard error as well as the coverage probability for the 95 confidence interval the hdl method uses an incorrect imputation method and the computation is constrained by the number of quadrature points while the ml method also suffers from the constrain for the number of quadrature points the mcnr method does not have this limitation and approximates the likelihood function better than the other methods the improvement of the mcnr method is further illustrated with real world data from a longitudinal study of local cervicovaginal hiv viral load and its effects on oncogenic hpv detection in hiv positive women

nilpotent commuting varieties of reductive lie algebras let g be a connected reductive algebraic group over an algebraically closed field k of characteristic p 0 and lie g in positive characteristic suppose in addition that p is good for g and the derived subgroup of g is simply connected let denote the nilpotent variety of and nil x y x y 0 the nilpotent commuting variety of our main goal in this paper is to show that the variety nil is equidimensional in characteristic 0 this confirms a conjecture of vladimir baranovsky see 2 when applied to gl n our result in conjunction with an observation in 2 shows that the punctual local hilbert scheme n hilb n 2 is irreducible over any algebraically closed field

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

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

semiparametric efficient and robust estimation of an unknown symmetric population under arbitrary sample selection bias we propose semiparametric methods to estimate the center and shape of a symmetric population when a representative sample of the population is unavailable due to selection bias we allow an arbitrary sample selection mechanism determined by the data collection procedure and we do not impose any parametric form on the population distribution under this general framework we construct a family of consistent estimators of the center that is robust to population model misspecification and we identify the efficient member that reaches the minimum possible estimation variance the asymptotic properties and finite sample performance of the estimation and inference procedures are illustrated through theoretical analysis and simulations a data example is also provided to illustrate the usefulness of the methods in practice

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

flexible longitudinal linear mixed models for multiple censored responses data in biomedical studies and clinical trials repeated measures are often subject to some upper and or lower limits of detection hence the responses are either left or right censored a complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution the multivariate censored linear mixed effect mlmec model is a frequently used tool for a joint analysis of more than one series of longitudinal data in this context we develop a robust generalization of the mlmec based on the scale mixtures of normal distributions to take into account the autocorrelation existing among irregularly observed measures a damped exponential correlation structure is considered for this complex longitudinal structure we propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed effects and variance components using a stochastic approximation of the em algorithm this approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects the predictions of unobservable values of the responses and the log likelihood function as a byproduct the proposed method is applied to analyze a set of aids data and is examined via a simulation study

pooling designs for outcomes under a gaussian random effects model due to the rising cost of laboratory assays it has become increasingly common in epidemiological studies to pool biospecimens this is particularly true in longitudinal studies where the cost of performing multiple assays over time can be prohibitive in this article we consider the problem of estimating the parameters of a gaussian random effects model when the repeated outcome is subject to pooling we consider different pooling designs for the efficient maximum likelihood estimation of variance components with particular attention to estimating the intraclass correlation coefficient we evaluate the efficiencies of different pooling design strategies using analytic and simulation study results we examine the robustness of the designs to skewed distributions and consider unbalanced designs the design methodology is illustrated with a longitudinal study of premenopausal women focusing on assessing the reproducibility of f2 isoprostane a biomarker of oxidative stress over the menstrual cycle

correlation coefficient estimation involving a left censored laboratory assay variable when assessing a correlation between two exposure or biological marker variables one sometimes encounters the problem of indeterminate values for one of the variables due to an assay detection limit in this event investigators often report correlation coefficients computed after removing the pairs involving non detectable values or after substituting some small constant for those values these ad hoc practices can lead to bias in both point and confidence interval estimates of the true correlation coefficient to address this issue we consider two parametric techniques for estimating the correlation in the presence of left censoring for one of the variables the first is a maximum likelihood approach and the second is an adaptation of multiple imputation motivated primarily by potential benefits in confidence interval coverage both of the estimators studied reduce to the standard pearson s correlation coefficient in the event of no censoring and hence are valid in cases where this measure would be appropriate for the complete data we assess these approaches empirically and contrast them with ad hoc methods for estimating the correlation between cervicovaginal human immunodeficiency virus hiv viral load measurements and cd4 lymphocyte counts from hiv positive women enrolled in a clinical trial conducted in bangkok thailand

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

isoparametric hypersurfaces in complex hyperbolic spaces we review some results of an ongoing research on isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in the complex hyperbolic space in order to motivate this topic we recall first the main steps of its long history

asymptotic form of the kullback leibler divergence for multivariate asymmetric heavy tailed distributions abstract an asymptotic expression for the kullback leibler kl divergence measure of multivariate skew t distributions mst is derived this novel class of flexible family distributions incorporates a shape and degree of freedom parameters in order to manipulate the skewness and heavy tail presence of the data respectively the quadratic form expressions of mst models are used to provide asymptotic measures additional inequalities for mst entropy and simulation studies are reported finally the expected values of the kl divergence of a sample correlation matrix obtained by pearson s correlation coefficient are discussed

an analogue of the jacobson morozov theorem for lie algebras of reductive groups of good characteristics let g be the lie algebra of a connected reductive group g over an algebraically closed field of characteristic p 0 suppose that g 1 is simply connected and p is good for the root system of g given a one dimensional torus a c g let g a i denote the weight component of ad i corresponding to weight i e x i z it is proved in the paper that for any nonzero nilpotent element e e g there is a one dimentional torus ae c g such that e e g ae 2 and kerade c fi og ae i

irreducible representations of lie algebras of reductive groups and the kac weisfeiler conjecture letg be the lie algebra of a connected reductive groupg over an algebraically closed field of characteristicp 0 suppose thatg 1 is simply connected andp is good for the root system ofg ifp 2 suppose in addition thatg admits a nondegenerateg invariant trace form letv be an irreducible and faithfulg module withp character g it is proved in the paper that dimv is divisible byp1 2dim where stands for the orbit of under the coadjoint action ofg

block representation type of reduced enveloping algebras let k be an algebraically closed field of characteristic p g a connected reductive k group g lie g x e g and u x g the reduced enveloping algebra of g associated with x assume that g 1 is simply connected p is good for g and g has a non degenerate g invariant bilinear form all blocks of u x g having finite and tame representation type are determined

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

correlating two viral load assays with known detection limits summary a timely objective common to many hiv studies involves assessing the correlation between two different measures of viral load obtained from each of a sample of patients this correlation has scientific utility in a number of contexts including those aimed at a comparison of competing assays for quantifying virus and those aimed at determining the level of association between viral loads in two different reservoirs using the same assay a complication for the analyst seeking valid point and interval estimates of such a correlation is the fact that both variables may be subject to left censoring due to values below assay detection limits we address this problem using a bivariate normal likelihood that accounts for left censoring of two variables that may have different detection limits we provide simulation results to evaluate sampling properties of the resulting correlation estimator and compare it with ad hoc estimators in the presence of nondetects in an effort to obtain improved confidence interval properties relative to the wald approach we evaluate and compare profile likelihood based intervals we apply the methods to hiv viral load data on women and infants from a trial in bangkok thailand and we discuss an extension of the original model to accommodate interval censoring arising due to the study design

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

special transverse slices and their enveloping algebras let g be a simple simply connected algebraic group over image image lie g image image the nilpotent cone of image and e h f an imageimage2 triple in image let s e ker ad f the special transverse slice to the adjoint orbit of e and s0 s image image the coordinate ring image s0 is naturally graded see slodowy simple singularities and simple algebraic groups lecture notes in mathematics vol 815 springer verlag berlin heidelberg new york 1980 let z image be the centre of the enveloping algebra u image and z image image an algebra homomorphism identify image with image via a killing isomorphism and let denote the linear function on image corresponding to e following kawanaka generalized gelfand graev representations and ennola duality in algebraic groups and related topics advanced studies in pure mathematics vol 6 pp 175 206 north holland amsterdam new york oxford 1985 moeglin c r acad sci paris ser i 303 no 17 1986 845 848 and premet invent math 121 1995 79 117 we attach to a nilpotent subalgebra image subset ofimage of dimension dim 2 and a 1 dimensional image module image let imageh height 14 width 14 denote the algebra opposite to endimage u image multiply sign in circleu image image and imageh height 14 width 14 imageh height 14 width 14 multiply sign in circlez image image it is proved in the paper that the algebra imageh height 14 width 14 has a natural filtration such that gr imageh height 14 width 14 the associated graded algebra is isomorphic to image s0 this construction yields natural noncommutative deformations of all singularities associated with the adjoint quotient map of image

bayesian semiparametric mixture tobit models with left censoring skewness and covariate measurement errors common problems to many longitudinal hiv aids cancer vaccine and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time varying covariates with measurement errors there has been relatively little work published simultaneously dealing with these features of longitudinal data in particular left censored data falling below a limit of detection lod may sometimes have a proportion larger than expected under a usually assumed log normal distribution in such cases alternative models which can account for a high proportion of censored data should be considered in this article we present an extension of the tobit model that incorporates a mixture of true undetectable observations and those values from a skew normal distribution for an outcome with possible left censoring and skewness and covariates with substantial measurement error to quantify the covariate process we offer a flexible nonparametric mixed effects model within the tobit framework a bayesian modeling approach is used to assess the simultaneous impact of left censoring skewness and measurement error in covariates on inference the proposed methods are illustrated using real data from an aids clinical study

a two part model for reference curve estimation subject to a limit of detection reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation estimation of reference curves can be complicated by a technical limit of detection lod that censors the measurement from the left as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty we discuss issues with common approaches to the lod problem in the context of our pubertal hormone study and propose a two part model that addresses those issues one part of the proposed model specifies the probability of a measurement exceeding the lod as a function of age the other part of the model specifies the conditional distribution of a measurement given that it exceeds the lod again as a function of age information from the two parts can be combined to estimate the identifiable portion i e above the lod of a reference curve and to calculate the relative standing of a given measurement above the lod unlike some common approaches to lod problems the two part model is free of untestable assumptions involving unobservable quantities flexible for modeling the observable data and easy to implement with existing software the method is illustrated with hormone data from the third national health and nutrition examination survey

nilpotent orbits in good characteristic and the kempf rousseau theory let g be a connected reductive algebraic group over an algebraically closed field k of characteristic p 0 image and suppose that p is a good prime for the root system of g in this paper we give a fairly short conceptual proof of pommerening s theorem pommerening j algebra 49 1977 525 536 j algebra 65 1980 373 398 which states that any nilpotent element in image is richardson in a distinguished parabolic subalgebra of the lie algebra of a levi subgroup of g as a by product we obtain a short noncomputational proof of the existence theorem for good transverse slices to the nilpotent g orbits in image for earlier proofs of this theorem see kawanaka invent math 84 1986 575 616 premet trans amer math soc 347 1995 2961 2988 spaltenstein j fac sci univ tokyo sect ia math 31 1984 283 286 we extend recent results of sommers internal math res notices 11 1998 539 562 to reductive lie algebras of good characteristic thus providing a satisfactory approach to computing the component groups of the centralisers of nilpotent elements in image and unipotent elements in g earlier computations of these groups in positive characteristics relied mostly on work of mizuno j fac sci univ tokyo sect ia math 24 1977 525 563 tokyo j math 3 1980 391 459 our approach is based on the theory of optimal parabolic subgroups for g unstable vectors also known as the kempf rousseau theory which provides a good substitute for the image theory prominent in the characteristic zero case

interim treatment selection using the normal approximation approach in clinical trials we consider a study starting with two treatment groups and a control group with a planned interim analysis the inferior treatment group will be dropped after the interim analysis and only the winning treatment and the control will continue to the end of the study this two stage winner design is based on the concepts of multiple comparison adaptive design and winner selection in a study with such a design there is less multiplicity but more adaptability if the interim selection is performed at an early stage if the interim selection is performed close to the end of the study the situation becomes the conventional multiple comparison where dunnett s method may be applied the unconditional distribution of the final test statistic from the winner treatment is no longer normal the exact distribution of which is provided in this paper but numerical integration is needed for its calculation to avoid complex computations we propose a normal approximation approach to calculate the type i error the power the point estimate and the confidence intervals due to the well understood and attractive properties of the normal distribution the winner design can be easily planned and adequately executed which is demonstrated by an example we also provide detailed discussion on how the proposed design should be practically implemented by optimizing the timing of the interim look and the probability of winner selection

estimation and inference on correlations between biomarkers with repeated measures and left censoring due to minimum detection levels statistical approaches for estimating and drawing inference on the correlation between two biomarkers that are repeatedly assessed over time and subject to left censoring because minimum detection levels are lacking we propose a linear mixed effects model and estimate the parameters with the monte carlo expectation maximization mcem method inferences regarding the model parameters and the correlation between the biomarkers are performed by applying louis s method and the delta method simulation studies were conducted to compare the proposed mcem method with existing methods including the maximum likelihood estimation method the multiple imputation method and two widely used ad hoc approaches replacing the censored values with the detection limit or with half of the detection limit the results show that the performance of the mcem with respect to relative bias and coverage probability for the 95 confidence interval is superior to the detection limit and half of the detection limit approaches and exceeds that of the multiple imputation method at medium to high levels of censoring and the standard error estimates from the mcem method are close to ideal the maximum likelihood estimation method can estimate the parameters accurately however a nonpositive definite information matrix can occur so that the variances are not estimable these five methods are illustrated with data from a longitudinal human immunodeficiency virus study to estimate and draw inference on the correlation between human immunodeficiency virus rna levels measured in plasma and in cervical secretions at multiple time points copyright 2012 john wiley sons ltd

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

maximum likelihood estimation for longitudinal data with truncated observations we obtain maximum likelihood estimates of the parameters when the observations on the response variable in a repeated measures design are truncated above a cutpoint the maximum likelihood equations are solved iteratively using an em like procedure it is observed that these estimates have smaller mean squared error than recently proposed iterative weighted least squares estimates the results are applied to data arising from a study of dioxin elimination in air force veterans published in 2000 by john wiley sons ltd