a discrete time event history approach to informative drop out in mixed latent markov models with covariates summary mixed latent markov mlm models represent an important tool of analysis of longitudinal data when response variables are affected by time fixed and time varying unobserved heterogeneity in which the latter is accounted for by a hidden markov chain in order to avoid bias when using a model of this type in the presence of informative drop out we propose an event history eh extension of the latent markov approach that may be used with multivariate longitudinal data in which one or more outcomes of a different nature are observed at each time occasion the eh component of the resulting model is referred to the interval censored drop out and bias in mlm modeling is avoided by correlated random effects included in the different model components which follow common latent distributions in order to perform maximum likelihood estimation of the proposed model by the expectation maximization algorithm we extend the usual forward backward recursions of baum and welch the algorithm has the same complexity as the one adopted in cases of non informative drop out we illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest one continuous and the other binary

joint modelling of accelerated failure time and longitudinal data summary the accelerated failure time model is an attractive alternative to the cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates several complications arise when the covariates are measured intermittently at different time points for different subjects possibly with measurement errors or measurements are not available after the failure time joint modelling of the failure time and longitudinal data offers a solution to such complications we explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors the procedure is based on maximising the joint likelihood function with random effects treated as missing data a monte carlo em algorithm is used to estimate all the unknown parameters including the unknown baseline hazard function the performance of the proposed procedure is checked in simulation studies a case study of reproductive egg laying data for female mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

shared parameter models under random effects misspecification summary a common objective in longitudinal studies is the investigation of the association structure between a longitudinal response process and the time to an event of interest an attractive paradigm for the joint modelling of longitudinal and survival processes is the shared parameter framework where a set of random effects is assumed to induce their interdependence in this work we propose an alternative parameterization for shared parameter models and investigate the effect of misspecifying the random effects distribution in the parameter estimates and their standard errors

an approximate generalized linear model with random effects for informative missing data this paper develops a class of models to deal with missing data from longitudinal studies we assume that separate models for the primary response and missingness e g number of missed visits are linked by a common random parameter such models have been developed in the econometrics heckman 1979 econometrica 47 153 161 and biostatistics wu and carroll 1988 biometrics 44 175 188 literature for a gaussian primary response we allow the primary response conditional on the random parameter to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness the resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects an example is given to illustrate the approximate approach and simulations are performed to critique the adequacy of the approximation for repeated binary data

a bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time to event motivated by a real data example on renal graft failure we propose a new semiparametric multivariate joint model that relates multiple longitudinal outcomes to a time to event to allow for greater flexibility key components of the model are modelled nonparametrically in particular for the subject specific longitudinal evolutions we use a spline based approach the baseline risk function is assumed piecewise constant and the distribution of the latent terms is modelled using a dirichlet process prior formulation additionally we discuss the choice of a suitable parameterization from a practitioner s point of view to relate the longitudinal process to the survival outcome specifically we present three main families of parameterizations discuss their features and present tools to choose between them

a two part joint model for the analysis of survival and longitudinal binary data with excess zeros many longitudinal studies generate both the time to some event of interest and repeated measures data this article is motivated by a study on patients with a renal allograft in which interest lies in the association between longitudinal proteinuria a dichotomous variable measurements and the time to renal graft failure an interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria 1g day during follow up which introduces a degenerate part in the random effects density for the longitudinal process in this article we propose a two part shared parameter model framework that effectively takes this feature into account and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure

a uniform scheme for the singularly perturbed riccati equation we consider the singularly perturbed riccati equation varepsilon u x a x u 2 x b x u x c x 0 u 0 a and present a new finite difference scheme which is exact when the coeffcientsa b andc are constant we show that under certain restrictions the solution u i h of this difference scheme converges uniformly in e tou xi the solution of the differential equation on the uniform meshxi ih numerical results are presented

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

exponentially derived switching schemes for inviscid flow abstract a class of exponential schemes used for singular perturbation problems is taken and finite difference schemes for inviscid flow with shocks is derived from them in particular exponential schemes are formulated for steady viscous flow in a variable area duct using both a one equation model with the physical viscous terms and the euler equations with artificial viscosity upon taking the limit as the viscosity coefficient goes to zero exponentially derived switching eds schemes are obtained which switch the direction of finite differencing based upon characteristic directions of the reduced problem for the euler equations some of the eds schemes can be identified as flux vector splitting the split coefficient matrix method and a scheme of huang some aspects of uniqueness of finite difference solutions are discussed

variable selection for joint models of multivariate longitudinal measurements and event time data joint modeling of longitudinal and survival data has attracted a great deal of attention some research has been undertaken to extend the joint model to incorporate multivariate longitudinal measurements recently however there is a lack of variable selection methods in the joint modeling of multivariate longitudinal measurements and survival time in this article we develop penalized likelihood methods for the selection of longitudinal features in the survival submodel a multivariate linear mixed effect model is used to model multiple longitudinal processes where random intercepts and slopes serve as essential features of the trajectories we introduce l1 penalty functions to select both random effects in the survival submodel and off diagonal elements in the covariance matrix of random effects an estimation procedure is developed based on laplace approximation our simulations demonstrate excellent selection properties of the proposed procedure we apply our methods to explore the relationship between mortality and multiple longitudinal processes for end stage renal disease patients on hemodialysis we find that lower levels of albumin higher levels of neutrophil to lymphocyte ratio and higher levels of interdialytic weight gain at the beginning of the follow up time as well as decrease in predialysis systolic blood pressure and increase of neutrophil to lymphocyte ratio over time are associated with higher mortality hazard rates

a comparison of optimization based approaches for a model computational aerodynamics design problem abstract the objective of this paper is to compare three optimization based methods for solving aerodynamic design problems we use the euler equations for one dimensional duct flow as a model problem the optimization methods are i the black box method with finite difference gradients ii a modification where gradients are found by an algorithm based on the implicit function theorem and iii an all atonce method where the flow and design variables are simultaneously altered the three methods are applied to the model problem and compared for efficiency robustness and implementation difficulty we also show that the black box implicit gradient method is equivalent to applying the variational or optimal control approach to design optimization directly to the discretized analysis problem rather than to the continuous problem as is usually done the black box method with implicit gradients seems to provide a good compromise of features and can be retrofitted to most existing analysis codes to turn them into design codes although the all at once method was found to be less robust than the black box methods when it succeeded it was considerably more efficient

a semi parametric shared parameter model to handle nonmonotone nonignorable missingness longitudinal studies often generate incomplete response patterns according to a missing not at random mechanism shared parameter models provide an appealing framework for the joint modelling of the measurement and missingness processes especially in the nonmonotone missingness case and assume a set of random effects to induce the interdependence parametric assumptions are typically made for the random effects distribution violation of which leads to model misspecification with a potential effect on the parameter estimates and standard errors in this article we avoid any parametric assumption for the random effects distribution and leave it completely unspecified the estimation of the model is then made using a semi parametric maximum likelihood method our proposal is illustrated on a randomized longitudinal study on patients with rheumatoid arthritis exhibiting nonmonotone missingness

on the invariance of colin de verdiere s graph parameter under clique sums for any undirected graph g let p g be the graph invariant introduced by cohn de verdi e in this paper we study the behavior of p g under clique sums of

convergence of upwind schemes for a stationary shock a nonlinear first order boundary value problem with discontinuous solutions is considered it arises in the study of gasflow through a duct and allows in general for multiple solutions new convergence results for three difference schemes are presented and the sharpness of numerical layers is established for the eo scheme stability of a physically correct solution with respect to time evolution is shown

finite difference schemes for quasilinear singular perturbation problems finite difference schemes for singularly perturbed quasilinear boundary value problems are considered the schemes have fitting factors which guarantee their uniform stability with respect to the perturbation parameter besides the usual stability in the discrete l1 norm we consider the maximum norm stability as well various schemes are compared numerically

existence and uniqueness for an exponentially derived switching scheme an existence and uniqueness result for a certain finite difference scheme applied to an equation governing steady one dimensional inviscid shocked flow in a variable area duct is presented

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

analysis of difference schemes for a stationary shock problem we consider the limit function u of the solutions u varepsilon of a singularly perturbed boundary value problem in general u will be discontinuous two difference approximations of the boundary value problem are studied and the discrete values for varepsilon 0 h to 0 are compared with u error estimates of order o h and o h 2 are proved and the sharpness of numerical layers is established

nonlinear singular perturbation problems and one sided difference schemes we consider the boundary value problem varepsilon y a y y b x y f x 1 leqq x leqq 1 for y 1 and y 1 given and b x 0 equiv 0 b y x y geqq 0 we construct a simple difference scheme approximating varepsilon u xx a u u x b x u f x u t for t geqq 0 1 leqq x leqq 1 with the same boundary conditions and an arbitrary initial guess as the numerical artificial time approaches infinity we prove convergence to a unique steady state solution as the mesh size delta x and the parameter varepsilon approach zero in any order we prove convergence to the solution of the corresponding o d e we use one sided differences to approximate the transport term the method applies equally well to multidimensional analogues we present numerical results verifying the theory

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

a reduction procedure for the colin de verdiere number of a graph abstract we find the colin de verdiere number for all complete multipartite graphs and show that for any graph g there exists a reduction process that results in a complete multipartite graph h with g h we give examples of the upper bounds that can be obtained via this process

steady shock tracking and newton s method applied to one dimensional duct flow abstract a new computational approach combining shock tracking and newton s method is applied to steady one dimensional flow through a variable area duct on a transformed computational grid where the shock is fixed the physical shock location appears explicitly as an unknown in a set of finite difference equations and is coupled to the other unknowns the space time characteristics for the associated time dependent problem are used in formulating the boundary conditions the resulting system is solved by newton s method the computed results agree very well with an exact solution and the newton iterates converge rapidly in comparison to some explicit shock capturing time asymptotic methods

the evaluation of multiple surrogate endpoints surrogate endpoints are desirable because they typically result in smaller faster efficacy studies compared with the ones using the clinical endpoints research on surrogate endpoints has received substantial attention lately but most investigations have focused on the validity of using a single biomarker as a surrogate our paper studies whether the use of multiple markers can improve inferences about a treatment s effects on a clinical endpoint we propose a joint model for a time to clinical event and for repeated measures over time on multiple biomarkers that are potential surrogates this model extends the formulation of xu and zeger 2001 in press and fawcett and thomas 1996 statistics in medicine 15 1663 1685 we propose two complementary measures of the relative benefit of multiple surrogates as opposed to a single one markov chain monte carlo is implemented to estimate model parameters the methodology is illustrated with an analysis of data from a schizophrenia clinical trial

on the colin de verdiere number of graphs abstract let g and g be the colin de verdiere and clique numbers of a graph g respectively it is well known that g g 1 for all graphs our main results include g g for all chordal graphs g tw g 1 for all graphs where tw is the tree width and a characterization of those split chordal graphs for which g g the bound g tw g 1 improves a result of colin de verdiere by a factor of 2

joint models for multivariate longitudinal and multivariate survival data joint modeling of longitudinal and survival data is becoming increasingly essential in most cancer and aids clinical trials we propose a likelihood approach to extend both longitudinal and survival components to be multidimensional a multivariate mixed effects model is presented to explicitly capture two different sources of dependence among longitudinal measures over time as well as dependence between different variables for the survival component of the joint model we introduce a shared frailty which is assumed to have a positive stable distribution to induce correlation between failure times the proposed marginal univariate survival model which accommodates both zero and nonzero cure fractions for the time to event is then applied to each marginal survival function the proposed multivariate survival model has a proportional hazards structure for the population hazard conditionally as well as marginally when the baseline covariates are specified through a specific mechanism in addition the model is capable of dealing with survival functions with different cure rate structures the methodology is specifically applied to the international breast cancer study group ibcsg trial to investigate the relationship between quality of life disease free survival and overall survival

semiparametric analysis of two level bivariate binary data in medical studies paired binary responses are often observed for each study subject over timepoints or clusters a primary interest is to investigate how the bivariate association and marginal univariate risks are affected by repeated measurements on each subject to achieve this we propose a very general class of semiparametric bivariate binary models the subject specific effects involved in the bivariate log odds ratio and the univariate logit components are assumed to follow a nonparametric dirichlet process dp we propose a hybrid method to draw model based inferences in the framework of the proposed hybrid method estimation of parameters is done by implementing the monte carlo expectation maximization algorithm the proposed methodology is illustrated through a study on the effectiveness of tibolone for reducing menopausal problems experienced by indian women a simulation study is also conducted to evaluate the efficiency of the new methodology